
Citation 
 Permanent Link:
 http://ufdc.ufl.edu/AA00000383/00184
Material Information
 Title:
 Chemical engineering education
 Alternate Title:
 CEE
 Abbreviated Title:
 Chem. eng. educ.
 Creator:
 American Society for Engineering Education  Chemical Engineering Division
 Place of Publication:
 Storrs, Conn
 Publisher:
 Chemical Engineering Division, American Society for Engineering Education
 Publication Date:
 December 1963
 Frequency:
 Quarterly[1962]
Annual[ FORMER 19601961] quarterly regular
 Language:
 English
 Physical Description:
 v. : ill. ; 2228 cm.
Subjects
 Subjects / Keywords:
 Chemical engineering  Study and teaching  Periodicals ( lcsh )
 Genre:
 serial ( sobekcm )
periodical ( marcgt )
Notes
 Citation/Reference:
 Chemical abstracts
 Additional Physical Form:
 Also issued online.
 Dates or Sequential Designation:
 1960June 1964 ; v. 1, no. 1 (Oct. 1965)
 Numbering Peculiarities:
 Publication suspended briefly: issue designated v. 1, no. 4 (June 1966) published Nov. 1967.
 General Note:
 Title from cover.
 General Note:
 Place of publication varies: Rochester, N.Y., 19651967; Gainesville, Fla., 1968
Record Information
 Source Institution:
 University of Florida
 Rights Management:
 All applicable rights reserved by the source institution and holding location.
 Resource Identifier:
 01151209 ( OCLC )
70013732 ( LCCN ) 00092479 ( ISSN )
 Classification:
 TP165 .C18 ( lcc )
660/.2/071 ( ddc )

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THE
CHEMIC/
JOURNAL
OF
ENGINEERING
EDUCATION
L/_ _^
Volume
Number 2
December 1963
~5&di~aC
THE JOURNAL OF CHEMICAL ENGINEERING EDUCATION
Volume 2, Number 2, December 1963
Editor: Robert Lemlich
Associate Editor: Daniel Hershey
Editorial 2
Interpretation of Viscous Stress in
a Newtonian Fluid R. E. Rosensweig 3
Conversion Factors William Squire 10
Radiant Heat Exchange to Tubes in Enclosed
Muffle Furnaces Charles E. Dryden 16
Shorter Communication: The Role of Computer
Training in Undergraduate Engineering
Curricula R. S. Ramalho 2
Shorter Communication: Thereare no "Small"
Mathematical Errors in Engineering Work
 L. S. Kowalczyk 28
Miscellany:
Try This One (Problem) 36
Information for Contributors and 26
Subscribers
Index of Titles with Translation 33
The Journal of Chemical Engineering Education is published
at irregular intervals at the University of Cincinnati, Cincinnati
21, Ohio, U.S.A. Opinions expressed by contributors are their
own and do not necessarily reflect those of the editor or the
University. Annual subscription: In the U.S.A. and Canada, $2.00;
elsewhere, $3.00. Prepayment is requested. Further information
may be found on page 24.
PROGRESS
We are now completing the second year of publication.
Time does indeed seem to fly.
To date, five issues have appeared containing twentytwo
articles plus a number of smaller items. We acknowledge with
appreciation the help recieved from many people,
Economy of operation, combined with the indirect support
of the University of Cincinnati, has enabled the Journal to
give all 1962 subscribers an automatic extension through
1963 at no additional cost. With continued favorable experience,
we hope to repeat this twoforone bonus for 1964 subscribers.
Subscription fees for 1964 are due now. They are still
two dollars in the U.S.A. and Canada, and three dollars
elsewhere. Remittance should accompany the order since our
low cost of operation makes billing awkward.
Checks should be made payable to the University of
Cincinnati (which acts as repository for the funds) and
mailed with the subscription order directly to the Journal.
Prompt raittal will be appreciated and will help greatly
in our bookkeeping.
R.L.
INTERPRETATION OF VISCOUS STRESS IN A NEWTONIAN FLUID
Dr. R. E. Rosensweig
Avco Research and Development Division
Wilmington, Massachusetts
Presented here is an alternative view of
some important considerations in fluid mechanics. Editor
This writer has found it possible to picture the
viscous stress of an incompressible Newtonian fluid in terms
of a rather simple physical model. This is in contrast to a
standard approach* which begins in a formal manner assuming
eighty one constants to linearly relate the nine components
of stress to the nine rateofstrain components. The eighty
one constants are reduced to two which are independent by
elaborate arguments entailing invariancy conditions applicable
to any isotropic fluid.
As an alternative to this abstract approach the following
presents what is thought to be a more physically apparent
derivation; the procedure is to make a single, plausible
physical statement, then to translate this statement to its
mathematical equivalent in a straight forward manner. As a
preliminary the kinematics of fluid motion will be reviewed
before presenting the rather short derivation.
Review of Kinematics
t
The vector velocity of fluid at a point P is nrwhile
the vector velocity at a nearby point P' is denoted .? The
vector directed from P to P' is denoted A, When the points
are close ?is related tof/,by a general expression which
results from a Taylor expansion arranged in physically
meaningful terms.
fltr = I V x X + \ 4 (I)
I  ll
TRIAWSLAT,0Wo. ROrft ^ v
;See for example Reference 1. This text is recommended
as a fluidmechanically motivated primer of elementary tensor
analysis and contains more details concerning kinematics
reviewed herein.
aLX8x) is identical to rigid body rotation about an axis
through P with angular velocity specified by JE; i.e. the axis
of rotation is along the direction ofi and the angular velocity
is ~iJt. All the fluid in the neighborhood of the points share
in this rotation motion. 2 the rotation, is equal to half
the vorticity.
S X7 rV (2)
This relationship identifies Jl with spatial derivatives of
the velocity components. No relative separation of the points
is caused by the rotational motion as may be confirmed by
considering the projection of ] x. ^ along AX which is
proportional to (J{g ). ~ and hence is zero.
The last term in equation 1 being what is left over
and hence representing strain motion contains a tensor operator
( ;. ~e7 is a second order tensor and consists of nine
elements which may be displayed as. its array.
ie e^ e*4
L ~ '
According to the definition of the tensor operator the
operational meaning of is
< 4?,Q
I^el r\' xz 3) 2
Thus the operation of the tensor al on the vector
yields another vector. The general component of EQJ is
expressed in terms of velocity component derivatives as
given by the following.
I e e e t
In the next section the actual physical modelling is presented,
Physical Modelling
It was shown above that the relative motion tending to
separate two fluid points whose instantaneous separation is
described by the vector 6r< is given by the expression ex
It follows that the vector velocity of this strain motion per
unit length is e Now & may be considered as a normal
vector to a fluid plane of small area. Thus Zi
is the unit normal to the plane and the normalized strain
motion may be written simple2 aslevi Consider that there
will exist a vector force dF on the fluid plane of area dA
whose normal is q this force being the result of strain
motion of the fluid. Accordingly a vector stress is defined
as rYd~cF/A Up to this point no physical assumptions
have been made; now it is desired to relate to the motion
of the fluid and so e fluid property. The crux of this argument
is to assume that 0* is proportional to ij] i.e. that the
vector stress is proportional to the vector rateofstrain both
in magnitude and velocity. Figure 1 illustrates this statement.
The constant of proportionality is set equal to 2 A where t&
is the viscosity of the fluid,
S3)
It is to be emphasized that G is a relative motion with
direction and magnitude and that is proportional in the
vector sense. Equation 3 contains all the information
pertaining to the viscous stresses both tangential stresses
and normal stresses. It is rather compact and so, below, it
is unfolded in order that its implications may be examined.
Cartesian Form of the Viscous Stress
Equation 3 is the final result of this note. The purpose
of the following is simply to demonstrate the correctness of
this result.
>
The viscous stress has a component along the .
direction of the normal Y given by the scalar product V
This represents a stress perpendicular to the small fluid plane.
+ ('i, 3
2f Ce2
4'
S d1 {Y34 E'3rj34 e 3 4
C 4, i? IyZ e $ Ly' 'z 3 l 3 )i '1 3 v1
a. Imagine an arbitrary fluid plane through a point P
b. Imagine the unit normal to the plane
c. Imagine the fluid in the vicinity of the tip of the normal vector.
This fluid is in strain motion fr relative to fluid at point P.
In the text s
d. The viscous stress vector A is aligned with Ar
^
i is the vector force per unit area acting on the fluid plane
through P,
FIGURE 1. ILLUSTRATION OF THE PHYSICAL ORIGIN OF VISCOUS STRESS.
This latter expression is rather complex due to the generality
inherent to it. To obtain a more recognizeable result choose
a particular direction. First suppose r, :, or that
,=t 1, l = o The above expression then reduces to the
following.
(jA ii) ,)
Similar expressions follow for the normal stresses in the
other two directions. Thus the viscous, normal stress
components are
s,, ) i ell ./k
AA
These expressions are in agreement with the standard results.
Next examine the tangential stresses. The foregoing determined
the stress component parallel to the normal ~ by use of the
scalar product. For finding the perpendicular component to
1 and hence the parallel component to the fluid plane we
may use the vector cross product which is suitable for the job.
The force is s so that 7x' is a vector with the proper
magnitude and is in the proper plane though it is ninety
degrees rotated from the proper direction in the plane.
Another cross product with rotates it to the correct
direction. Thus
Hence
A cross product may be expanded according to the following
vector identity.
/ \ C f 5 ,
Applied to the expression for s this gives
J shear
~(\HTy 113 7
The first term in the brackets gives the original force .
It is easily recognized that the second term is the vector
normal force 'nrmalfound previously. The difference between
these must then represent the shear component as found. This
result could have been written immediately.
Previously (following equation 4) we made a definition
for (
Thus 
G 3(O A, [k
And also
[Og? )t= II Yi ,l +
4 243 413ivli3 y 3)
Consider the component S representing the shear in the X2
direction on a plane perpendicular to the XL direction. Thus
(i l : = or l,=' ~123 =o and it is the
coefficient of A2 in the foregoing expression which applies.
This reduces as follows.
( a ^~1 n, ^ ^ O  3+
but
z(e,. , +i a
thus
This too is the generally accepted result for tangential hear.
Detailed verification of S13, S23, S31, and S21 is left
to the reader. The general result is expressed as follows.
This applies to both the normal and tangential stresses
originating from the mechanism of viscosity.
When Newton's law (f=ma) is applied to a small mass of
fluid taking account of pressure forces, the above given
viscous forces, and any body forces which act, the result
is the NavierStokes equations.
Literature Cited;
1. Long, R. R., "Mechanics of Solids and Fluids", Prentice
Hall (1961).
CONVERSION FACTORS
William Squire
Professor, AeroSpace Engineering
West Virginia University
Morgantown, West Virginia
Abstract: A convenient notation for conversion factors
is developed and some properties of conversion factors are
discussed. The use of arrays of conversion factors is
emphasized.
Introduction
It is often necessary, in scientific or engineering work,
to convert data given in one set of units to some other set
of units. There is no practical possibility of eliminating
this in the immediate future. Even if international agreement
could be reached on a standard set of units with a strictly
enforced ban on nonconforming publications, it would be a
generation before the existing body of literature was replaced
or became obsolete. In spite of the simplicity of the under
lying principle involved in changing units, almost everyone
makes an occasional error in converting. It is hoped that
the rather abstract presentation in this paper will appeal
to some students and fix the principles in their minds in
such a way as to minimize errors.
Conversion Factors
The treatment is based on a notation in which the
value of a physical quantity in a certain unit is designated
by a lower case letter with the unit (or an abbreviation)
written as a superscript, For example,yFt means a length
measured in feet. The numerical value of the measurement is
inserted in parentheses, so that 2Ft (3) means a length of
3 feet. Conversion factors are written as capital letters
with the unit converted from as a subscript, and the unit
converted to as a superscript. Again, the numerical value
is written in parentheses. Thus, LFt (3) means that the
ys
conversion factorfrom yards to feet is 3.
The basic equation for using a conversion factor is
S= L' (1)
A numerical example is
{Ft (9) = LFt (3) d (3) (2a)
yd
or
9 ft = 3 (3 yards). (2b)
There are exceptional cases such as pH, decibel scales,
and stellar magnitudes which are defined by a logarithmic
relation, i.e.,
pH = log0 (conc. of H ions in moles/liter).
(3)
Such quantities do not come within the scope of this
treatment.
The numerical value of a conversion factor is found by
converting a relation
a (unit i) = b (unit j) (4)
into a ratio
L = b/a (5a)
or
L = a/b (5b)
Normally, a relation in which either a or b is unity is used,
but this is not essential. The relation
1/12 ft = 1/36 yd (6a)
based on their relation to the inch is obviously equivalent to
3 ft = i yd. (6b)
Strictly speaking, some modification of the equality sign
to designate "physically equivalent" instead of "numerically
equal" should be used in equations 4 and 6, but the usage of
the equality sign in both cases is well established.
Equation 1 can be interpreted as a cancellation of the
subscript in the conversion factor, and the superscript in
the measurement to be converted. Following this approach,
uwo ([or moro) conversion factors for thl inm ajp, 01
iriasurement can be multiplied together, provided that tht.
subscripts and superscripts are the same, to define another
conversion factor, as
L Lk = L Lk L (7a)
L? L. L = L (7b)
i J k i
1 iiLote that order is unimportant, though in equation 7b
if the sequence is changed to L L" Lk, the last two factors
A kJ i
just be multiple first as Lk Li is meaningless.
It can be taken as a basic principle that all expressions
for a conversion factor as a product of other conversion factors
must give the same value. From this, two important results
can be obtained:
I) Ci is always unity
i j
LI) C. and C. are always reciprocals.
The first result follows from the fact that any number
of multiplications of C0 gives C., therefore, it must be 1,
I 1
the only common root of unity. If only two multiplications
were considered, we would have C' =\FT which is satisfied by
+ 1, but three multiplications give C1 = \3 which is
satisfied by + 1 and two complex numbers. Similarly,
for n multiplications + 1 is always a root, making it the
only common root.
The second result follows from
Cj Ci = () (8)
1 3 1
It would be preferable if the sequence of proof could be
reversed and the more complex principle derived from the simple
results which are obvious from the definitions of the conversion
factor in equation 5.
Arrays
We now transfer our attention from the individual
conversion factor to arrays of conversion factors such as are
found in handbooks. A simplified example of such an array
is
Table I
cm in fft meter
cm in ft met
cm () L (.394) L (.0328 Lme (001)
cm cm cm cm
inch Lom (2.54) Lin (1) Lf (1/12) met(.0254)
in in in in
ft Lcm (30.48) Lin (12) Lf (1) Lmet(.3048)
ft ft ft ft
meter t (100) (39.4) L ft (3.28) Let (I)
Lmet (00) Let met met
Of course, in a handbook table only the numerical value is
given. The table gives the factor for converting from the
unit shown in the column in the left to the unit shown in the
row on top. It is not necessary to test the units in the same
sequence in the row and column, but doing this introduces
symmetry into the array. The diagonal elements become unity
and elements symmetric with respect to the diagonal are
reciprocals. A matrix having these properties is obtained
by taking the antilog of each term in an antisymmetric
matrix, but the conversion factor array is not a matrix as
it does not obey the matrix rules for addition or multiplication.
The array for m units has m2 terms, of which m are always
unity. The remaining m (ml) entries are determined by (m1)
independent quantities. A set of (m1) independent conversion
factors is a set in which no member can be defined by
multiplication of the other members. There are a large
number of independent sets. For example, a set consisting
of the conversion factors for any one unit to all the other
units is obviously an independent set from which the rest of
the array can be calculated by equation 7.
Compound Conversion Factors
In.a sense, the material presented above is a complete
treatment of the problem of changing units. For any physical
quantity, a conversion factor array can be set up which enables
the necessary conversions to be made. There is, however, the
important practical problem of calculating what can be called
a compound conversion factor from simple conversion factors.
For example, if conversion factors for length and time are
considered simple; velocity, area, and volume would be
compound. Actually, there is no rigorous rule for distinguishing
between simple and compound quantities; to a large extent, the
difference is conventional and depends on the current modes
of measurement,
The previous notation for measurements and conversion
factors is modified by dividing the superscripts and subscripts
into parts by commas, as qP'.s and Q, As examples, an'area
ljj
in square feet would be written asc ft and Amet met (.0929)
ft, ft
would be the conversion factor from square feet to square meters.
When multiplying conversion factors together to form a
compound conversion factor, there is no cancellation but
rather a merger of subscripts and superscripts. In principle,
units can be switched from the top to the bottom and inverted
simultaneously.
Thus, we have
Vmile, hr1 (.682) = L miles hrl
(.682) = L) F 1 (3600)
ft, sec 5280 sec
and this could be rewritten as
vmiles,hr m= iles,sec Lmiles Tsec (3
ft,sec ft,hr ft 25o hr )
However, this is not recommended as it is likely to introduce
errors.
It would appear that arrays for compound quantities
could be obtained by multiplication of corresponding terms in
the arrays for simpler quantities, i.e., obtain an array for
area conversion by squaring each term in the length conversion
array. There are two difficulties. First, many compound
quantities have units (such as acre for area), which are not
defined directly from the units in the simpler array. Second,
every permutation of products of simple units defines a
possible compound unit, and some of these hybrids are
encountered in practice. For example, irrigation engineers
use acreft as a unit of volume.
However, there is a tendency to employ systems of
units, such as c. g. s, (centimeter, gram, second,) m. k.
s. (meter, kilogram, seconds), or English units (ft, Ib, sec)
in which compound units are directly related to the simple
units. If we limit ourselves to such consistent systems,
simple arrays can be multiplied to form arrays for compound
quantities by multiplication of corresponding elements. In
practice, it is difficult to remain within such consistent
systems; for example, in countries employing the metric
system, speedometers do not read in cm/sec or meters/sec
but in kilometers/hr.
Recommendations
While the use of the notation developed in this paper
is suitable for calculating individual conversion factors,
the concept of an array greatly simplifies practical work.
It is suggested that students and young engineers
prepare a collection of arrays for those conversions which
they encounter in their work. Then, when a new unit is
encountered for a particular quantity, a row and column can
be added to that array. It will be found that such a
collection is a valuable time saver, and will more than
repay the original effort and the work required to keep it
current.
The most complete collection of such arrays that the
present writer knows of is Reference 1, which contains 34
arrays, and can, therefore, be a useful starting point.
Even this contains some surprising omissions. For example,
the Specific Energy array (Table 16) does not contain the
units ft /sec2 or meters /sec2 which would be essential
for gas dynamical calculations. Fortunately,
cft2sec2
ft lb Slug
and
2 2
Meters sec (103)
joules gm
so that it is very easy to add these to the array.
Literature Cited:
1. Kinslow and Majors, "Systems of Units and Conversion
Tables", AEDCTDR 626, (Feb. 1962)
RADIANT HEAT EXCHANGE TO TUBES IN ENCLOSED
MUFFLE FURNACES
Charles E. Dryden*
Department of Chemical Engineering
The Ohio State University
Columbus, Ohio
Abstract:
A method is presented for direct calculation of heat
interchange between banks of tubes or rods adjacent to a
refractory roof and a radiating planar source or sink
at the bottom of a refracborywalled muffle furnace.
Use of a derived geometric factor P for the configuration
eliminates the fictitious plane approach in solving problems
of finite geometry furnaces.
In muffle furnaces containing tube banks, radiant heat
transfer was calculated by Hottel. (5) assuming a fictitious
plane just below the tubes. The fictitious emissivity of this
grey plane was then computed, taking into account a refractory
backed wall and the area and emissivity of the tube surface.
A shape factor, was then calculated which included this
grey plane emissivity, the emissivity of the radiating muffle
plane, and geometric view factors.
A more realistic approach in terms of avoiding the
fictitious plane concept and dealing only with the exchange
between the tube bank and muffle plane was presented by
Foust et al.(2) but their method, as presented, is limited
to infinite geometry.
Both of these methods leave something to be desired in
teaching students to visualize real systems. The aim of the
approach used in this paper is to base the calculations on
interchange between the grey tube surfaces and a grey muffle
plane, using only the easily conceived sinksource system.
On loan to the Indian Institute of Technology,
Kanpur, India, 19631965.
Derivation of the Method:
The standard method is used for handling heat exchange
in an enclosure in which all of the tube surface can be
considered as a single greybody source. The receiving
plane of finite size at a finite distance below and parallel
to the tube plane is considered the greybody sink. The
source and sink designations can be reversed depending on
the nature of the heat exchange. The wellknown formula
for the geometric exchange factor is
12 = A81
1 + 1 ) + 1 1 (1)
Pl2 1) / [2 2
where: Subscript 1 refers to muffle surface
Subscript 2 refers to tube surface
F = geometric view factor for the sinksource
1 with refractory surfaces
e = emissivity
A = areas involved in the exchange process
The net heat exchange in Btu/hr is then computed as:
q12= A1 12 r (T14 T24) (2)
where: G = 0.173 x 108
T = Temperature of surface, OR
The geometric view factor F12 between the plane and tubes
can be obtained by a combination of analytical methods described
by Hottel(3,4), but the calculation for tubes plus a plane
surface of finite size with multiple emitting refractory
surfaces becomes excessively difficult. For the purposes of
the present computation of F12, it is adequate to use a
fictitious plane below the tubes coupled with exchange to
the real plane, all surfaces being considered black. The
values of F12 are then plotted versus C/d with S/D as a
parameter. Here C is the center center distance between
tubes in the row, d is the outside diameter of the tube,
S is the side of the square plane geometry, and D is the
distance between the tube plane and the muffle plane. These
design curves are given in Figures 1 and 2. The procedure
for computing F12 was based on the formula:
2 1 (3)
1 +( 
Fp
where: F = geometric view factor between identical
P parallel black planes.
o( = effective emissivity of the plane just below
the tube bank.
Equation 3 is derived by application of equation 1 first
to the black tubes and a fictitious plane just below the
surface. F for this case is the geometric view factor
derived by Hottel (3) as the effective area for exchange.
Reference 2, Fig. 15.33, p. 263 is a source of these data.
It is seen that the resultant 'r is simply an effective
emissivity 4 for the plane just below the tubes which then
exchanges with the black muffle plane. Equation 1 is applied
a second time with obtained first by Hottel and Keller (4)
and plotted as Fig. 15.32, p. 262 of reference 2. F12 is the
net result, rather than "6,2 since our system is composed of
a black sinksource.
A sample calculation follows:
C/d =2, 2 = 0.88
S/D =, = 0.53
F12 = 1 = 0.49
12 1_ + 1 1
0.53 0.B
Use of Method:
The working curves of Figures 1 and 2 yield F12 for
a series of finite geometries with single and double rows
of tube banks respectively in square planar array. Other
design curves can be computed by use of Equation 3, but
in many cases an average F12 can be obtained by geometric
mean of the values of F12 for square planes of the shorter
and the longer size.
Sample Problem (See Reference 1, p.80. Illustration 6):
A muffle type furnace in which the carborundum muffle
forms a continuous floor of dimensions 15 by 20 ft. has its
ultimate heatreceiving surface in the form of a single row
of 4in, tubes on 9in. centers above and parallel to the muffle
and backed by a well insulated refractory roof; the distance
between muffle top and the row of tubes is 10 ft. The tubes
fill the furnace top, of area equal to that of the carborundum
floor. The average mufflesurface temperature is 2100OF; the
tubes are at 6000F. The side walls are assumed to reradiate
as much heat as they receive. The tubes of oxidized steel
have an emissivity of 0.8, the carborundum has an emissivity
of 0.7.
Find the radiantheat transmission between the carborundum
floor and the tubes above, taking into account reradiation
from the side walls.
Use Figure 1 with C/d = 2.25.
For 15ft. squares separated by 10 ft.,
S/D = 1.5 and F12 = 0.550
For 20ft. squares separated by 10 ft.,
S/D = 2.0 and F12 = 0.605
The average Fl2 = V0.550 x 0.605 = 0.582
Using Equation 1,
12 = 1 = 0.431
1 +/ 1 1) + 9 / 1 
0.5b2 C 0.7 / 1 (.75 )
The fictitious plane method used by Hottel gives 12 = 0.433
which shows excellent agreement between the two procedures.
This result is given as Case 1 in Table 1.
Discussion:
Use of Figures 1 and 2 to obtain directly P12 view
factors for finite geometry, tubemuffle combinations enables
single step computation of the geometric factor by means of
the wellknown Equation 1. This procedure was tested for a
number of cases, a few of which are reported in Table 1.
The agreement between the Hottel fictitious plane method
and the direct view factor procedure of this paper is well
within the error of graphical readout and slide rule
accuracy. Although the derived curves are useful for nearly
all designs of such furnaces, derivation of other F12 curves
may be necessary. For instance, the curves used to obtain c
1.0
0.9
0.8
0.7
0.6
0.4
0.3
iLu 0.2
0.1
O cT O
C/d CentertoCenter Distance of Tubes in Row
Outside Diameter of Tubes
FIGURE1. View Factors for One Row of Tubes to a Plane Within
a Refractory Muffle Furnace
"0.6N
01.0
F 0.4
11
ILL
0.3
0.2
04
I I I I I I I
1 2 3 4 5 6 7 8
C/ = CentertoCenter Distance of Tubes in Rows
'd Outside Diameter of Tubes
FIGURE. 2. View Factors for Two Rows of Tubes to a Plane Within
a Refractory Muffle Furnace
in Equation 3 were based on placing the tubes a distance
of greater than d/2 away from the wall. If tubes are placed
at a closer distance, then the graph recently reported by
Chao (1) can be used to obtain a better value of o( ,
The maximum reduction in ,4 is about 10% when the tubes
just touch the refractory wall. Most designers, however,
prefer to place the tubes away from the wall at least one
diameter to obtain better convection transfer from the
tube area (6).
Literature Cited:
1. Chao, K.C., Amer. Inst. Chem. Engrs. Jour., 9:555 (1963).
2. Foust, A.S., Wentzel, L.A,, Clump, C.W., Maus, L. and
Anderson, L.B., "Principles of Unit Operations,"
p.263, Wiley (1960).
3. Hottel, H.C., Trans. Amer. Soc. Mech. Engrs. 5:267 (1931).
4. Hottel, H.C., and Keller, J.D., Trans. Amer. Soc. Mech.
Engrs., Iron and Steel, 55:39 (1933).
5. Hottel, H.C. in McAdams "Heat Transmission," 3rd
edition, pp.8081, McGrawHill (1954).
6. Mathis, H.M., Schweppe, J.L., and Wimpress, R.N.,
Pet. Ref. 39:No.4,177 (1960).
Table 1. Comparison of the Fictitious Plane Method with the
View Factor Method of this Paper
Fixed Conditions:
Muffle size = 15 ft. x 20 ft.
Size of tubes in a single row, d = 4.0 inches diameter
61 for muffle = 0.7
C2 for tubes = 0.8
( = fictitious plane emissivity (calculated)
3
Temperature of muffle = 25600R
Temperature of tubes = 10600R
Variables:
D = Distance between flour and
tubes, ft.
C = Tube center distance, inches
C/d
Fictitious Plane Method:
0( ordinatee of Figure 1 @ S/D=to)
A / A2 = A / A2
63
F12 = \F (15 ft) x F (20 ft)
ordinatee of Figure 1 @
C/d = l,S/D)
13
6
13 X 10
View Factor Method:
F (15') from Fig. 1, this paper
F (20') from Fig. 1, this paper
12 =VF (15 ft.) x F (20 ft.) =
n12
6
q12 x 10
q12 q13 x 100, %
q13
1
10
9
2.25
0.845
0.714
0.730
Case No.
2
10
5
1.25.
0.975
0.399
0.890
3
0
27
6.75.
o.4oo
2.148
0.328
4
20
9
2.25
0.845
0.714
0.730
0.660 0.660 0,660 0.481
0.433 0.483 0.252 0.349
9.38 10i57
0.550
0.605
0.582
0.431
9.37
0.614
0.678
0.645
0.480
10.50
5.46 7.61
0.322
0.340
0.331
0.478
0.401
0.438
0.251 0.347
5.47 7.57
0.1% 0.07% +0.1% o.5%
Shorter Communication
THE ROLE OF COMPUTER TRAINING IN
UNDERGRADUATE ENGINEERING CURRICULA
R. S. Ramalho
Associate Professor of Chemical Engineering
University of Rochester
Rochester, N. Y.
In this paper the author's object is to attempt
answering three questions for engineering educators, namely:
I. Why should computer training constitute a required
discipline of undergraduate engineering curricula?
II. How should computer techniques be taught?
III. When should such training be offered during the under
graduate engineering program?
I. Why?
The widespread use of computers in this country leads
educators into considering provision for some sort of computer
training at the undergraduate level.
One might argue, however, that many of the graduating
engineers do not have to do a great deal of computer pro
gramming themselves, but rather they will be directing tech
nicians who will do the actual programming for them. Conse
quently, those who think in this manner, do not feel that
formal computer training is necessary in the undergraduate
engineering curriculum.
The author does not believe that this argument is valid,
but rather, that a reasonably intimate knowledge of computers
is of importance for the graduating engineer. At least two
reasons may be given to support the latter point of view:
1. Many times in an engineering office the technicians
are too busy to translate the engineer's problem into a com
puter program. Also, it is not so easy to explain a complex
engineering problem to one who really does not know much
engineering and, in fact, has no direct interest in the problem
himself. This communication problem does exist and although
a technician can be helpful at times, there are certain
occasions when it would be time saving for the engineer
to write his own program or at least to prepare a detailed
flow chart for the problem.
2. A fairly intimate knowledge of the computer gives
the engineer a better appreciation of its capabilities. In
many cases the best approach to the solution of a problem when
one has in mind its solution by means of a computer is dif
ferent from the conventional approach employed by the user
of paperpencilslide rule. Knowledge of the computer enables
the engineer to select this best approach. Usually the tech*
nician will not be able to help the engineer in making these
preliminary "high level decisions" on the approach to the
problem solution.
II. How?
This is a controversial question. Many educators seem
to favor the socalled "black box approach," and recommend
teaching only compiler language as exemplified by FORTRAN.
The author favors teaching first, machine language and
symbolic program systems. Three reasons can be presented
to justify this opinion:
1. Once machine language is understood the student can
pick up relatively easily the use of a compiler,
but the reverse is not true.
2. If a compiler source program does not work at first,
the knowledge of machine language may become very
helpful in "debugging" the program.
3. A third factor which might be labelled as the
"psychological factor" may be mentioned. One
derives a certain amount of satisfaction in under
standing what is going on "inside the black box."
Learning only a compiler is a comparable experience
to that of one who learns how to use a slide rule
without knowing what a logarithm is: true, it can
be done, but this approach might not be too appeal
ing to the sophisticated mind.
III. When?
It is not a new idea in engineering curriculum to utilize
a few summer weeks for required Engineering courses. Chemical
Engineering students at the University of Rochester, for
example, take an intensive 3week summer course in "Chemical
Engineering Unit Operations" between the junior and the
senior year.
It is believed that the introduction of a 4week summer
course in computer programming between the freshman and
sophomore year would be most beneficial. The course could
include machine language, symbolic program systems and com
pilers. The mornings would be devoted to lectures and black
board exercises. Afternoons could be used to a large extent
in actual machine experience.
During the sophomore year in most schools, engineering
students take the first professional courses within their
chosen fields. In view of freshly acquired acquaintance
with computational techniques, these courses could be ef
fectively assisted by computers. Computerassisted courses
should also become a common occurrence during the junior and
senior year.
Literature
1. O'Connell, F.P., Chem. Eng. Education 1, 8 (1962).
2. Pehlice, R.D., Sinott, M.J., Journal of Engineering
Education 52, 573 (1962).
(continued on next page)
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Appendix
This is an outline for the course "Chemical Engineering
Computer Calculations" as taught this year in the Department
of Chemical Engineering of the University of Rochester.
Texts used:
1. Germain, C. B. "Programming the IBM 1620" 
PrenticeHall, Inc. (1962)
2. IBM 1620 FORTRAN Reference Manual IBM Publication
C2656190 (1962)
I. Computing Fundamentals
a. Evolution of computers
b. Digital and analog computers
c. The stored program concept
d. The fundamental units of a digital computer
e. Numerical analysis and digital computers
f. Flow diagrams
II. The IBM 1620 and its Component Parts
III. 1620 Instructions
IV. Operation of the 1620
V. The
a,
b.
c.
d.
e.
Symbolic Program System
Pseudo instruction
Declarative operations
Address arithmetic
Unique Mnemonics
Operation of the SPS processor
VI. Program Planning and Debugging
VII. Subroutines and Floating Point Arithmetic
VIII. FORTRAN
a. Compilers
b. Writing the 1620 FORTRAN program.
c, Operating principles
d. Analysis of the FORTRAN program.
e. The FORTRAN precompiler
IX. Project Write a computer program for solution of
a fairly complex chemical engineering problem. An
individual assignment is made to each student,
Shorter Communication
THERE ARE NO "SMALL" MATHEMATICAL ERRORS IN ENGINEERING WORK
Professor L. S. Kowalczyk
Chairman, Department of Chemical Engineering
University of Detroit
Detroit 21, Michigan
A mathematical error in the solution to a problem is just
an error and it will effect only the student's grade for the
course. In engineering work, however, the consequences of an
error are more serious and may lead to a loss of money and
prestige by the design organization and, certainly, to the loss
of a job by the unfortunate designer.
Many engineering students are not aware of the serious
ness of the problem. When penalized for errors in a calcula
tion problem, they try to involve the instructor in lengthy
discussions pointing out the correctness of the procedure used,
smallness of the error, etc. To avoid wasting time on this
sort of discussion, I present my point of view on this matter
to the students in the very first engineering course. In
these comments, emphasis is placed on the following points:
1. The procedure, leading to the solution of a given
problem, is usually evident from class discussions and text or
reference books. It is a result of understanding the statement
of the problem but it cannot be substituted for a numerical
answer.
2. Using the selected procedure and other tools available
(mathematical tables, handbooks, slide rule, computer), the
engineer and engineering student must obtain the true numerical
answer.
3. Any error in calculations may cause a deviation from
the correct answer. Accordingly, there is no room for any
mathematical error in engineering calculations.
4. Errors in engineering work must be discouraged by
all possible means.
To stress more strongly the undesirability of errors in
engineering and to illustrate the serious consequences of
error, I usually discuss the following examples.
1. Error in sign.
This is quite a common error but may cause a great
deal of confusion. For instance,
a cooler is installed instead of a reboiler in the
distillation column,
a missile, instead of heading to the moon, goes to the
center of the earth,
a promising chemical reaction does not yield any pro
duct (error insign in free energy calculations),
multiplication, let's say, by 10' instead of by 10,
as in the rate of chemical reaction, results in a 1010 error,
change of sign in the work term of the mechanical energy
balance will result in suction instead of pressure and may re
verse the direction of fluid flow in pipes.
2. Division insteadof multiplication.
Here the error is of a2 order where a is the number
in question.
3. Error indecimal_point.
Let's suppose that a 10plate column is needed for
the requested separation. The error in decimal point makes
it either a singleplate or 100plate column. Or a 10 story
house is reduced to a ranchstyle house or enlarged to a 100
story sky scraper,
4. Omission of a term in an equation.
This case can readily be illustrated by an omission
of reboiler or condenser in the distillation column, the first
floor or roof in a house, a span in a bridge, a power house in
a plant, etc.
5. Distortion of a term in anequation.
Distortion of a term will be followed by replacement
of the required piece of equipment or material by a different
item, such as a condenser on the column by a vacuum pump, a
jaw crasher by a pulverizer, water by gasolene, etc.
6. Using log instead ofIn.
The error is evident from the relationship
In a = 2.303 log a
7. Use of indefinite integral.
The use of the indefinite integral in calculations,
i.e., neglecting the integration constant, introduces the error
equivalent to this constant. No error though if C = 0.
8. Reversing the limits of integration.
This error results in the change of sign.
9. Dimension checking in the course of calculations is
a highly recommendable practice. It may lead to early discovery
of errors.
These illustrations, although drastic, are not exaggerated.
They may be useful in explaining to the students the signifi
cance of the most common mathematical errors.
Try This One
If on Earth an astronaut of the future weighs 200 lb
with his space suit and small emergency rocket belt, from
approximately how large an isolated asteroid (minor planet)
of the same density as Earth could he escape with his belt
fueled to provide 100 lb of thrust for 10 seconds?
(Solution on following page.)
(Solution on following page.)
Solution to Problem on Preceding Page
Applying Newton's Law of Gravity to the center of the
masses involved, the gravitational acceleration gR at the surface
of an asteroid of mass M, radius R, and same density as Earth, is
gR = 32.2 (M RE\2 = 32.2 R E 2 = 32.2 R =32.2R=0.00812R (1)
ME 3963
where ME is the Earth's mass and RE is the Earth's radius which
is 3963 miles. The gravitational acceleration at a point above
the asteroid's surface, ( miles from its center, is
S= R = 0.00812 R3 (2)
x R ) 0x00
Since the rocket belt is small, the change in its mass
occasioned by fuel consumption must be even smaller. Therefore,
we can take the total mass of 200 lb. as substantially
invariant.
The net force in poundals exerted on the 200 lb. of mass
during thrust is
F = 100 x 32.2 200 g (3)
However, the thrust will be completed near the surface so we
can substitute gR for gx in equation 3, especially since the
term will turn out to be only of small influence on the final
result. Also, F = ma = mdv/dT so that FdT = mdv. Substituting
in the latter and integrating,
(3220 200gR) Odr = 200 dv (4)
0o 0
from which the escape velocity in ft/sec is
v = 161 lOgR (5)
In order to escape, the kinetic energy imparted must equal
the work required to move the mass in question from the surface
of the asteroid outward against the pull of gravity, theoretically
to infinity. Thus,
2 m = 5280 gx m d (6)
R
Solution to Problemcon't
Cancelling m, substituting equations 1,2, and 5 into 6,
and then integrating, gives
1/2 (1610.0812R) = 5280 0.00812Rs dX =42.9R2
X
Solving equation 7 yields R = 17.2 miles radius. Thus he
could escape from an asteroid of up to approximately 34 miles
in diameter.
Try This One Too
A certain neighborhood grocer weighs his pennies 100 at
a time, rather than counting them. He claims that because his
scale is quite accurate he has "never made an error". If the
average deviation in the weight of single pennies in circulation
is 1%, would the grocer's claim of near infallibility seem
plausible?
R.L.
The solution will appear in the next issue.
INDEX OF TITLES
German Translation by M. Zimmer
Spanish Translation by Saturnino Fanlo
A chronological index for all issues to date is presented
below.
As a courtesy to subscribers in other countries, translations
of the titles into German and Spanish are included. In the future
such translations will be presented at the beginning of each article.
Volume 1, Number 1, March 1962
Page
An Integrated Approach to the Teaching of
Chemical Engineering Thermodynamics.C. M. Thatcher 3
Un enfoque unificado en la ensenanza de
Termodinamica on Ingenieria Quimica.
Eine Zusammenstellung fuer den Unterricht der
Thermodynamik in chemischer Technologie
Teaching Statistical Mechanics to ThirdYear
Students.Myron Tribus 11
Ensenando Mechanica a estudiantes de Tercer
Ano.
Unterricht in statistischer Mechanik fuer Studenten
im 3. Ausbildungsjahr
Chemical Systems Engineering Training Course in
a Petrochemical Company.C. J. Huang, T. Q. Eliot,
and D. R. Longmire 19
Curso de Entrenamiento de Sistemas de Ingenieria
Quimica en una Industria Petroquimica.
Eine Vorlesung fuer chemische Systeme in
Ingenieurwesen in einer petrochemischen Firma
Reaction Selectivity.J. F. Woodham 26
Selectividad de Reaccion.
Selektivitaet von Reaktionen
Shorter Communication: Specialized vs Generalized
Engineering Education, a Narrow Viewpoint
E. Ja Henley 35
Breve Communicacion: Ensenanza de Ingenieria
Especializada vs Ingenieria Generalizada, un estrecho
punto de vista.
Notizen: Spezialisierte oder allgemeine Ausbildung
im Ingenieurwesen, ein engbegrenzter Standpunkt.
Miscellany:
Ragnarok and the Second Law. 10
Congress in Puerto Rico; Session on Education. 38
Miscelanea:
Ragnarok y la Segunda Ley
Congress en Puerto Rico; Sesion sobre Educacion
Verschiedenes:
Ragnarok und das Zweite Gesetz
Congress in Puerto Rico; Setzung ueber
Erziehungsfragen
Volume 1, Number 2, October 1962
The Postgraduate Curriculum An Approach Through
Critical Path Programming.L. A. Wenzel 3
El curriculum de postgraduado Un acercamiento
usando una trayectoria critical programada.
Ein Diplomanden Ausbildungsplan. Eine Ausbildung
durch kritische schrittweise Programmierung
Teaching Professionalism A seminar Method
William Licht 9
Ensenando professionalism El metodo de Seminarios
Das Lehren des Berufsethos. Eine Seminar Methode.
The Unit Operations Laboratory.R. L. Huntington 14
El laboratories de Operaciones Unitarias
Labormethoden im halbtechnischen Massstab
A Nuclear Power Plant Simulator for Educational
Purposes.F. T. Dunckhorst and G. Houghton 20
Un simulador de una plant de fuerza nuclear de
propositop pedagogicos
Ein Kernreaktorsimulator fuer Ausbildungswecke
The Misuse of the Arithmetic Mean Driving Temperature
in a Double Pipe Heat Exchanger.S. Middleman 35
El uso erroneo de la media aritmetica de
diferencia de temperature en un intercambiador de
calor de double tabo
Der Missbrauch des arithmetischen Mittels der
Betriebstemperatur in einem Doppelroehren
Hitzeaustauscher
Shorter Communication: The Mole as a Cardinal
Number of Molecular Species.Niels Madsen
Breve communication: El mol como numero cardinal
de species moleculares
Notizen: Das Mol als eine Kardinalzahl fuer
Mole kuelarten
Volume 2, Number L, June 1963
Chemical Engineering Education in Western
Europe.Allen N. Smith 3
Ensenanza de Ingenieria Quimica en Europa Occidental.
Chemische Technologie Ausbildung in West Europa
Chemical Engineering Education in the U.S.S.R.
Nathan Gilbert 12 .
Ensenanza de Ingenieria Quimica en la Union
Sovietica
Chemische Technologie Ausbildung in USSR
Chemical Engineering: Its Past, Present and
Future.Gerald Houghton 18
Ingenieria Quimica: Pasado, Presente y Futuro
6hemische Technologie, ihre Vergangenheit, Gegenwart
und Zukunft
A SelfInstructed Program to Simplify Computations.
J. S. Ratcliffe 26
Un program autodidacta para simplificar calculos
Ein selbstgelehrtes Programm zur Vereinfachung
von Berechnungen.
Shorter Communioation: The Analogy Between
Chemical and Dimensional Equation.William Squire 33
Breve Comunicacion: Analogia entire Equaciones
quimicas y dimensionales
Notizen: Die Analogie zwischen chemischen und
dimensionalen Gleichungen.
Miscellany:
Brief Note: ProblemSolving Technique. 25
Favorite Classroom Demonstration: Boiling Heat
Transfer Sami Atallah 38
Miscelanea:
Nota: Tecnica de solucionar problems
Mi experiment de catedra favorite: Transferencia
de calor en un liquid en ebullicion
Verschiedenes: Problemloesende Technik
Beliebte Unterrichtsvorfuehrung: HitzeAustausch
in einem kochenden Medium.
Volume 2, Number 2, December 1963
Interpretation of Viscous Stress in a Newtonian
Fluid.Dr. R. E. Rosensweig 3
Interpretacion del esfuerzo de viscosidad en un
flujo Newtoniano
Interpreation von viskosem stress in einer
Newtontschen Fluessigkeit
Conversion Factors,William Squire 10
Factores de Conversion
Umrechnungsfaktoren
Radiant Heat Exchange to Tubes in Enclosed
Muffle Furnaces.Charles E. Dryden 16
Transferencia de calor por radiacion a tubos
encerrados en hornos mufla
Hitzeaustansch durch Strahlung zu Rohren in
gesohlossenen muffelefen.
The Role of Computer Training in Undergraduate
Engineering Curricula.R. S. Ramalho 22
La importancia del entrenamiento en el uso de
"Computers" en los curricula de Ingenieria
Die Rolle der Computer Ausbildung im Technologie
Studium fuer Anfaenger
There are no "Small" Mathematical Errors in
Engineering Work.L. S. Kowalczyk 26
No existen "pequenos" errors matematicos en los
calculos de Ingenieria
Es gibt keine "kleinen" mathematischen Fehler in der
Technologies,
I'
1

Full Text 
PAGE 1
THE JOURNAL OF CHEMICAL ENGINEERING EDUCATION Volume 2 Number 2 December 1963
PAGE 3
i THE JOURNAL OF CHEMICAL ENGINEERING EDUCATION Volume 2, Number 2, December 1963 Editor: Robert Lemlich Associate Editor: Daniel Hershey Editorial 2 Interpretation of Viscous Stress in a Newtonian Fluid R. E. Rosensweig Conversion Factors William Squire Radiant Heat Exchange to Tubes in Enclosed Muffle Furnaces Charles E. Dryden Shorter Communication: The Role of Computer Training in Undergraduate Engineering Curricula R. s. Ramalho Shorter Communication: Therear.e no 11 Small" Mathematical Errors in Engineering Work ~. $. Kowalczyk Miscellany: Try This One (Problem) Information for Contributors and Subscribers Index of Titles with Translation 3 10 16 .30 26 33 The Journal of Chemical Engineering Education is published at irregular intervals at the University of Cincinnati, Cincinnati 21, Ohio, U.S.A. Opinions expressed by contributors are their own and do not necessarily reflect those of the editor or the University. Annual subscription: In the u.s.A. and Canada, $2.00; elsewhere, $3.00. Pvepayment is requested. Further information may be found on page 24. l
PAGE 5
PROGRESS We are now completing the second year of publication. Time does indeed seem to fly. To date, five issues have appeared containing twentytwo articles plus a number of smaller itemso We acknowledge with appreciation the help recieved from many people. Economy of operation, combined with the indirect support of the University of Cincinnati, has enabled the Journal to give all 1962 subscribers an automatic extension through 1963 at no additional cost. With continued favorable experience, we hope to repeat this twoforone bonus for 1964 subscribers. Subscription fees for 1964 are due now. They are still two dollars in the U.S.A. and Canada, and three dollars elsewhere. Remittance should accompany the order since our low cost of operation makes billing awkward. Checks should be made payable to the University of Cincinnati (which acts as repository for the funds) and mailed with the subscription order directly to the Journal. Prompt remitt a(L will be appreciated and will help greatly in our bookkeeping. R.L. 2
PAGE 7
INTERPRETATION OF VISCOUS STRESS IN A NEWTONIAN FLUID Dr. R. E. Rosensweig Avco Research and Development Division Wilmington, Massachusetts Presented here is an alternative view of some important considerations in fluid mechanics.Editor This writer has found it possible to picture the viscous stress of an incompressible Newtonian fluid in terms of a rather simple physical model. This is in contrast to a standard approach~:which begins in a forma 1 manner assuming eighty one constants to linearly relate the nine components of stress to the nine rateofstrain components. The eighty one constants are reduced to two which are independent by elaborate arguments entailing invariancy conditions applicable to any isotropic fluid. As an alternative to this abstract approach the following presents what is thought to be a more physically apparent derivation; the procedure is to make a single, plausible physical statement, then to translate this statement to its mathematical equivalent in a straight forward manner. As a preliminary the kinematics of fluid motion will be reviewed before presenting the rather short derivation. Review of Kinematics The vector velocity of fluid at a point P is~ while the vector velocity at a nearby point pt is denoted.?'. The vector directed from P to pt is denoted~~. When the points are close Mis related to /ii: by a general expression which results from a Taylor expansion arranged in physically meaningful terms. ? (tr f\To + ....DX .6X +\e 1 6x ( 1) iR t\tJSLl'IT,o\J RoTl\i,oN STlilf\w ~:See for example Reference L This text is recommended as a fluidmechanically motivated primer of elementary tensor analysis and contains more details concerning kinematics reviewed herein. 3
PAGE 9
4 7 ~Lxox is identical to rigid body rotation about an axis through P with angular velocity specif,ted by~; i.e. the axis of rotation is along the direction of..K. and the an g ular velocity is \lt.\. All the fluid iq the neighborhood of the points share in this rotation motion.jf, the rotation, is equal to half the vorticity. (2) rhis relationship identifies ..n with spatial derivatives of the velocity components. No relative separation of the points is caused by the rotational mot_ion as may be ~confirmed by considering the projection of Ji..><&;._ along 6.X which is proportional to (_"iix ;5x ) l)X' and hence is zero. The last term in equation l being what is left over and h~nce representing strain motion contains a tensor operator \ _gJ \el is a second order tensor and consists of nine elements which may be displayed as its array. \ e, (2 I?.. Q \ 3 'I i el .::: (? i' 2.. .. I I,.: 2?> ie. L I e ::.1.. @__ s3 According to the definition of the tensor operator the operational meaning of \ej is \(E'Ll~X I I I n. Y1. <22.. 11 3 ') Z 2 \\E' ., /::; Y ;;;1 i e; 26>< \C?3;0X'5) ,(? rhus the operation of the tensor \e \ on the vector ;;:_ yields another vector. The general component of@] is expressed in terms of velocity component derivatives as given Toy the following. e = J /V +J l ) In the next section the a~tual physical modelling is presented. 4
PAGE 11
Physical Modelling It was shown above that the relative motion tending to separate two fluid points whose instantaneous separation is described by the vector 6'x' is given by the expression(~ Ex It follows that the vector velocity of this strain motion per unit length is fel~&1 Now may be considered as a normal vector to a fluid '{:iane of small area. ThusWitXI=~ where 7l is the unit normal to the plane a~ the normalized strain motion may be written simp!:.i as[~h1. Consider that there will exist a vec~,or fo~ce dF on the fluid plane of area dA who se normal is this force being the result of strain motion of the fluid. Accordingly a vector stress is defined as iy:=: df/c\f\. Up to this point no physical assumptions have been made; now it is desired to relate ?y to the motion of the fluid and sggie fluid property. The crux of this argument is to assume that ry is proportional to@]Yl i.e. that the vector stress is proportional to the vector rateofstrain both in magnitude and velocity. Figure l illustrates this statement. The constant of proportionality is set equal to 2 ).l where )A. is the viscosity of the fluid. It is to be emphasized that 0rf is a relative motion with direction and magnitude and that 1 is proportional in the vector sense. Equation 3 contains all the information pertaining to the viscous stresses both tangential stresses and normal stresses It is rather compact and so, below, it is unfolded in order that its implications may be examined. Cartesian Form of the Viscous Stress Equation 3 is the final result of this noteo The purpose of the following is simply to demonstrate the correctness of this result. The viscous stress X has a component along the direction of the normal "l given by the scalar product "Yvi (3) This represents a stress perpendicular to the small fluid plane. A( vt = ( )~ (4) \e I~== (e 11 vt 1 \e1i.v1 ... + e,1Y1) ') A., 7 + Ce2., ~. ,..e2. "~ + E\_3 ~) ") J..1... .\.(e,,~, .+ ~1. + e i Y1 > l e 3 1.J1 1 le 3 ) "l 3 Yl ') 5
PAGE 13
a. Imagine an arbitrary fluid plane through a point P b. Imagine the unit normal to the plane c. Imagine the fluid in the vicinity of the tip of the normal vector. ,l> '>,. /\r. ?' This fluid is in strain motion I\{ relative to fluid at point P. In the text =\g] vf d. The viscous stress vector I is aligned with /\F.s ___ ,>,,;;,,, tv 5 ry is the vector force per unit area acting on the fluid plane through P. FIGURE l. ILLUSTRATION OF THE PHYSICAL ORIGIN OF VISCOUS STRESS. 6
PAGE 15
This latter expression is rather complex due to the generality inherent to it. To obtain a more recognizea~le _J'esult choose a particular direction. First suppose ~:~,~.=~, or that 1 111 0 The above expression then reduces to the Yl,. 'l.. 'I') following. J.( <:.~ u.., <::Ju.., \ .::) u.., \ fe\ ;r ) := '2 1 1 ~' ~11 = Q 'I :::: 2. \. X \ t & X \ ) ==d X i Similar expressions follow for the normal stresses in the other two directions. Thus the viscous, normal stress components are ~+~') s1, 2..))..e 11 _(_l dY of. I S7 2 =2. M 2.:: A ( u~ + ;) ~1.. ) :) X "l :) >( ... ,. 2 1 e ~ 1A ( ) u ) + J u ? ) :::, 3 3 /V'3, .:l 3V3 JxJ cs) These expressions are in agreement with the standard results. Next examine the tangential stresses. The foregoing determined the stress component paralle l to the normal~ by use of the scalar product. For finding the perpendicular component to 1( and hence the parallel component to the fluid plane we may use the vsctor cros~ product which is suitable for the job. The force is ry so that tirx~ is a vector with the proper magnitude and is in the proper plane though it is ninety degrees rotated from the proper direction in the plane. Another cross product with r I'otates it to the correct direction. Thus ? ~, ? ;y51IIJ'I;( >( ~\ ) I( vi ( 6 ) Hence 7~1? I .:._;)_ .,lA__ I l\~j vl < 1_ 'I( V{ s11Q\" L A cross product may be expanded according to the following vector identity. ci~i)xc ~(A c )B(s Z)1 ,> Applied to the expression for /\./I this gives ? shear t4 \11~~ = (1g]yt )~ (rt t\ =(\~vivt ')r( 7
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1 11 1
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or The first term in the brackets gives the original force 'Y It is easily recognized that the second term is the vector norma 1 force 1fn6:rmal l found previously. The difference between these must then represent the shear component as foundo This result could have been written immediately. for Previously (following equation 4) we made a definition l~;:;t == q r + q 7 + Q : rl I t 3 '3 Thus , ; (i~ Y{ ) x ;{ ,t ..J...i... <3 o, a'a3 V\\ I'\ L I\ ) And also [( 1 ) 1 J l( 1 = :. ( Q 3 q 3 C j 1 3 C 1 d 4 L /1 0 z ) ~ i.,_ \ G, n 112 a z. 1. ~, Ci., 1 1 3 + q s \'I ) '> I J + i (a YJ 3 .: .. <\34'?. 1 1 Y12as\'\,1,+ q 3 1'1, ~5) Consider the component s 12 representing the shear in the x 2 d~ectJ;_on a plane perpendicular to the x 1 direction 0 Ths ~, '1_,.t,. = ,e,. ~ ?r "1,~ 1 \1<=r') 3 =o and it is the coefficient of A 2 in the foregoing expression which applies. This reduces as fmllows. (a.,v1 ~ 1 (~\'1,l).1_Q113~~+ Cr ,~~~1) ::: 4'l'/,1C(~ S z. .: 2 M Q l but
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thus This too is th 6 generally accepted result for tangential .sh.e.ar. Detailed verification of s 13 s 23 s 31 and s 21 is left to the reader. Th e g e neral result is expressed as follows. S =( t~ll)) )..J M\ d x.. _; rj XA This applies to both the normal and tangential stresses originating from the mechanism of viscosity. When Newton's law (f=ma) is applied to a small mass of fluid taking account of pressure forces, the above given viscous forces, and any body forces which act, the result is the NavierStokes equations. Literature Cited; 1. Long, R. R., "Mechanics of Solids and Fluids", Pr e ntice Ha 11 ( 1961 ) 9
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CONVERSION FACTORS William Squire Professor, AeroSpace Engineering West Virginia University Morgantown, West Virginia Abstract; A convenient notation for conversion factors is developed and some properties of conversion factors are discussed. The use of arrays of coniersion factors is emphasized. Introduction It is often necessary, in scientific or engineering work, to convert data given in one set of units to some other set of units. There is no practical possibility of eliminating this in the immediate future. Even if international agreement could be reached on a standard set of units with a strictly enforced ban on nonconforming publications, it would be a generation before the existing body of literature was replaced or became obsolete. In spite of the simplicity of the under lying principle involved in changing units, almost everyone makes an occasional error in converting. It is hoped that the rather abstract presentation in this paper will appeal to some students and fix the principles in their minds in such a way as to minimize errors. Conversion Factors The treatment is based on a notation in which the value of a physical quantity in a certain unit is designated by a lower case letter with the unit (or an abbreviation) written as a superscripto For example,_tFt means a length measured in feet. The numerical value of the measurement is inserted in parentheses, so that pFt (3) means a length of 10 3 feet. Conversion factors are written as capital letters with the unit converted from as a subscriptJ and the unit converted to)as a superscript. Again, the numerical value is written in parentheses. Thus, 1Ft (3) m0ans that the yds conversion factor from yards to feet is 3. The basic equation for using a conversion factor is ( l)
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A num0rical exampl e is or A:: Pt ( 9 ) = L Ft ( 3 ) f!.._ yd (3 ) yd 9 ft= 3 (3 yards). (2a) (2b) Th0ra are exceptional cases such as pH, decibel scales, and stellar magnitudes which are defined by a logarithmic relation, i.e., pH = log (cone. of H+ ions in moles/liter). 10 (3) Such quantities do not come within the scope of this treatment. The numerical value of a conversion factor is found by converting a relation a (unit i) = b (unit j) (4) into a ratio (5a) or (5b) Normally, a relation in which either a orb is unity is used, but this is not essential. The relation 1/12 ft= 1/36 yd (6a) based on their relation to the inch is obviously equivalent to 3 ft= l yd. (ob) Strictly speaking, some modification of the equality sign to designate 11 physically equivalent 11 instead of "numerically equal 11 should be used in equations 4 and 6, but the usage of the equality sign in both cases is well established. Equation 1 can be interpreted as a cancellation of the subscript in the conversion factor, and the superscript in the measurement to be converted. Following this approach, 11
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Lwu l 01 mor'") conv ...,rs ion factors for ti.1'., : _..1 n 1.., CJ .f, .., 01 ;fi v asurernent can be multipli0d togeth e r, provid e d that th1.., .3ubscripts and superscripts aro the same, to define anoth~r conversion factor, as L~ L~ k Lk Lj = L = (7a) 1 J i j i Lj L~ Lt= L i ( 7b) 1 J k i I'll;; t~ote that order is unimportant, though in equation 7b if th0 sequence is changed to LR 1J L~, the last two factors f k i J uust be multipled first as Lk 1f is meaningless. It can be taken as a basic principle that all expressions for a conversion factor as a product of other conversion factors must give the same valueo From this, tv."O important results can be obtained: I) LI) c~ is always unity 1 c~ and C~ are always raciprocals. J 1. The first result follows frm the fact that any number of multiplications of C~ gives c., therefore, it must be 1, 1. J. the only com..mon root of unity. Jf only two multiplications were considered, we would have C~ =\fl which is satisfied by 1. ,~11 1, but three multiplications give CI= YJ 1 which is satisfied by+ land two complex numbers. Sir.J.ilarly, for n multiplications+ 1 is always a root, making it the only common rooto The second result follows from C j ci = Ci ( 1) i j i (8) It would be prefe1"able if the sequence of' proof could be reversed and the more complex principle derived from the simple results which are obv i ous from the definitions of the conversion factor in equation 5. i. 2
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Arrays We now transfer our attention from the individual conversion factor to arrays of conversion factors such as are found in handbooks. A simplified example of such an array is cm. inch ft meter cm L cm ( 1) cm Lem (2.54) in Lem (30.48) ft Lem (100) met Table I in Lin cm (. 394) ( l) Lin ( 12) ft T,in (39.4) :met ftft L ( .0328 cm 1ft ( 1/12) in 1ft { 1) ft Lft (3.28) met t meter me L ( .001) cm L~:t (. 0254) Lmet ( .3048) ft 1 met ( 1 ) met Of course, in a handbook table only the numerical value is given. The table gives the factor for converting from the unit shown in the column in the left to the unit shown in the row on top. It is not necessary to test the units in the same sequence in the row and column, but doing this introduces symmetry into the array. The diagonal elements become unity and elements symmetric with respect to the diagonal are reciprocals. A matrix having these properties is obtained by taking the antilog of each term in an antisymmetric matrix, but the conversion factor array is not a matrix as it does not obey the matrix rules for addition or multiplication. The array form units has m 2 terms, of which mare always unity. The remaining m (m1) entries are determined by (m1) independent quantities. A set of (m1) independent conversion factors is a set in which no member can be defined by multiplication of the other members. There are a large number of independent sets. For example, a set consisting of the conversion factors for any one unit to all the other units is obviously an independent set from which the rest of the array can be calculated by equation 7. 13
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Compound Conversion Factors In a sense, the material presented above is a complete treatment of the problem of changing units. For any physical quantity, a conversion factor array can be set up which enables the necessary conversions to be made. There is, however, the important practical problem of calculating what can be called a compound conversion factor from simple conversion factors. For example, if conversion factors for length and time are considered simple; velocity, area, and volume would be compound. Actually, there is no rigorous rule for distinguishing between simple and compound quantities; to a large extent, the difference is conventional and depends on the current modes of measurement. The previous notation for measurements and conversion !actors is modified by divi1iqg the superscripts and subscripts into parts by commas, as qP J and Q~,~ As examples, an area 1,J in square feet would be written asJt, ft and (.0929) would be the conversion factor from square feet to square meters. When multiplying conversion factors together to form a compound conversion factor, there is no cancellation but rather a merger of subscripts and superscripts. In principle, units can be switched from the top to the bottom and inverted simultaneously. Thus, we have vmile, hr1 (.682) = ft., sec1 and this could be rewritten as ymiles., hrl = fb,secl V miles, sec ft,hr = Lmiles ft ( l ) Tsec (3600). 528a hr However, this is not recommended as it is likely to introduce errors. It would appear that arrays for compound quantities could be obtained by multiplication of corresponding terms in the arrays for simpler quantities, i.e ., obtain an array for area conversion by squaring each term in the length conversion a~ray. There are two difficulties. First, many compound quantities have units (such as acre for area)., which are not defined directly from the units in the simpler array. Second, 14
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every permutation of products of simple units defines a possible compound unit, and some of these hybrids are encountered in practice. For example, irrigation engineers use acreft as a unit of volumeo However, there is a tendency to employ systems of units, such as c. g. s. (centimeter, gram, second,) m. ke s. (meter, kilogram, seconds), or English units (ft, lb, sec) in which compound units are directly related to the simple units. If we limit ourselves to such consistent systems, simple arrays can be multiplied to form arrays for compound quantities by multiplication of corresponding elements. In practice, it is difficult to remain within such consistent systems; for example, in countries employing the metric system, speedometers do not read in cm/sec or meters/sec but in kilometers/hr. Recommendations While the use of the notati0n developed in this paper is suitable for calculating individual conversion factors, the concept of an array greatly simplifies practical work. It is suggested that students and young engineers prepare a collection of arrays for those conversions which they encounter in their work. Then, when a new unit is encountered for a particular quantity., a row and column can be added to that array. It will be found that such a collection is a valuable time saver, and will more than repay the original effort and the work required to keep it current. The most complete collection of such arrays that the present writer knows of is Reference l, which contains 34 arrays, and can, therefore, be a uaeful starting point. Even this contains some surprising omissions. For example, the Spec~fic Energy arra! (Table 16) does not contain the units ft /sec 2 or meters /sec 2 which would be essential for gas dynamical calculations. Fortunately, 2 cft sec2 l (l) ft lbFSlug and C meters 2 sec2 1 ( 103 ) joules gm so that it is very easy to add these to the array. Literature Cited: 1. Kinslow and Majors, "Systems of Units and Conversion Tables"., AEDCTDR 626, (Feb. 1962) 15
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RADIANT HEAT EXCHANGE TO TUBES IN ENCLOSED MUFFLE FURNACES Charles E. Dryden* Department of Chemical Engineering The Ohio State University Columbus., Ohio Abstract: A method is presented for direct calculation of heat interchange between banks of tubes or rods adjacent to a refractory roof and a radiating planar source or sink at the bottom of a refracnorywalled muffle furnace. Use of a derived geometric factor F for the configuration eliminates the fictitious plane approach in solving problems of finite geometry furnaces. In muffle furnaces containing tube banks., radiant heat transfer was calculated by Hottel (5) assuming a fictitious plane just below the tubes. The fictitious emissivity of this grey plane was then computed., taking into account a refractory backed wall and the area and emissivity of the tube surface. A shape factor'cfl was then calculated which included this grey plane emissivity, the emissivity of the radiating muffle plane, and geometric view factors. A more realistic approach in terms of avoiding the fictitious plane concept and dealing only with the exchange between the tube bank and muffle plane was presented by Foust et al. (2) but their method, as presented, is limited to infinire geometry. Both of these methods leave something to be desired in teaching students to visualize real systems. The aim of the approach used in this paper is to base the calculations on interchange between the grey tube surfaces and a grey muffle plane, using only the easily conceived sinksource system. On loan to the Indian Institute of Technology, Kanpur, India, 19631965. 16
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Derivation of the Method: The standard method is used for handling heat exchange in an enclosure in which all of the tube surface can be considered as a single greybody source. The receiving plane of finite size at a finite distance below and parallel to the tube plane is considered the greybody sink. The source and sink designations can be reversed depending on the nature of the heat exchange. The wellknown formula for the geometric exchange factor is d\ 12 = 1 1 +Ll__1)+i_(_1_l\ F12 \<=1 A2. E2 } ( 1) where: Subscript l refers to muffle surface Subscript 2 refers to tube surface F = geometric view factor for the 12 with refractory surfaces E. = emissivity A = areas involved in the exchange sinksource process The net heat exchange in Btu/hr T 4) 2 is then computed as: \1 (T 4 1 (2) where: = 0., 173 x 108 T Temperature of surface, 0 R The geometric view factor F12 between the plane and tubes can be obtained by a combination of analytical methods described by Hotte1(3,4), but the calculation for tubes plus a plane surface of finite size with multiple emitting refractory surfaces beco mes ex :i essi ve ly difficult. For the pu rp oses of the present co m putation of F12, it is adequate to use a fictitiou s plane below the tubes coupled with exchange to the real plane, all surfaces being considered black. The values of F12 are then plotted versus C/d with S/D as a parameter. Here C is the center center distance between tubes in the row, dis the outside diameter of the tube, Sis the side of the square plane geometry, and Dis the 17
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II
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distance between the tube plane and the muff le plane. These design curves are given in Fi g ures land 2. The procedure for computing F 12 was based on the formula: 1 ( 3) where: F = geometric view factor between identical P parallel black planes. c,<._ = effective emissivity of the plane just below the tube bank. Equation 3 is derived by application of equation 1 first to the black tubes and a fictitious plane just below the surface. F for this case is the geometric view factor derived by Hottel (3) as the effective area for exchange. Reference 2, Fig. 15.33, p. 263 is a source of these data. It is seen that the resultant 'ch is simply an effective emissivity o,J.... for the plane just below the tubes which then exchanges with the black muffle plane. Equation l is applied a second time with Fp, obtained first by Hottel and_Keller (4} and plotted as Fig. 15.32, p. 262 of reference 2. F 12 is the net result, rather than q 2 since our system is composed of a black sinksource. A sample calculation follows: C/d = 2, o( = 0088 S/D = l, Fp = 0.53 Fl2 = 1 = o.49 l + ( 1 1) c.53 a.BE ITse of Method: The working curves of Figures land 2 yield F 12 for a series of finite geometries with single and double rows of tube banks respectively in square planar array. Other design curves can be computed by use of Equation 3, but in many cases an average F 12 can be obtained by geometric mean of the values of F 12 for square planes of the shorter and the longer size. 18
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Sample Problem {See Reference 1 1 p.80. Illustration 6): A muffle type furnace in which the carborundum muffle forms a continuous floor of dimensions 15 by 20 ft. has its ultimate heat~receiving surface in the form of a single row of 4in. tubes on 9in. centers above and parallel to the muffle and backed by a well insulated refractory roof; the distance between muffle top and the row of tubes is 10 ft. The tubes fill the furnace top, of area equal to that of the carborundum floor. The average mufflesurface temperature is 21000F; the tubes are at 6ooF. The side walls are assumed to reradiate as much heat as they receive. The tubes of oxidized steel have an emissivity of o.8, the carborundum has an emissivity of o. 7. Find the radiantheat transmission between the carborundum floor and the tubes above, taking into account reradiation from the side walls. Use Figure 1 with C/d = 2.25. For 15ft. squares separated by 10 ft., S/D = 1.5 and F 12 = 0.550 For 20ft. squares separated by 10 ft., S/D = 2.0 and F 12 = 0.605 The average F 12 = Using Equation 1, \}~o.55o x 0.605 = o.582 dl 12 = ::::,1,,~l +/ 1 1) + 9 ( 1 1) 0.582 0.7 41t TI:13' The fictitious plane method used by Hottel gives~ 12 = o.433 which shows excellent agreement between the two procedures. This result is given as Case 1 in Table 1. Discussion: Use of Figures 1 and 2 to obtain directly F 12 view factors for finite geometry, tubemuffle combinations enables single step computation of the geometric factor by means of the wellknown Equation l. This procedure was tested for a number of cases, a few of which are reported in Table 1. The agreement between the Hottel fictitious plane method and the direct view factor procedure of this paper is well within the error of graphical readout and slide rule accuracy. Although the derived curves are useful for nearly all designs of such furnaces, derivation of other F 12 curves may be necessary. For instance, the curves used to obtaino( 19
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I'
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1.0 0.9 OB 0.7 0.6 L 0.5 0 +' u cu LL 0.4 u L +' Q.3 II ILL 0.2 0.1 1 2 3 4 5 6 7 8 9c! a CentertoCenter Distance of Tubes in Row Outside Diameter of Tubes J:IGURE1. View Factors for One Row of Tubes to a Plane Withb'l a Refractory Muffle Furnace
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0000 1.0
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in Equation 3 were based on placing the tubes a distance of greater than d/2 away from the wall. If tubes are placed at a closer distance, then the graph recently reported by Chao (1) can be used to obtain a better value of o(. The maximum reduction inc,/... is about 10% when the tubes just touch the refractory wall. Most designers, however, prefer to place the tubes away from the wall at least one diameter to obtain better convection transfer from the tube are a ( 6). Literature Cited: 2~ 1. Chao, K.c., Amer. Inst. Chem. Engrs. Jour., 9:5.55 (1963). 2. Foust, A.S., Wentzel, L.A&, Clump, c.w., Maus, L. and Anderson, L.B., "Principles of Unit Operations," ~~263, w11ey (1960). 3e Hottel, H.C., Trans. Amer. Soc. Mecho Engrs. 2.1:267 (1931). 4. Hottel, H.c., and Keller, J.D., Trans. Amer. Soc. Mech. Engrs., Iron and Steel, 55:39 (1933). 5. Hottel, H.C. in McAdams 11 Heat Transmission," )rd edition, pp.8081, McGrawHill (19.54). 6. Mathis, H.M., Schweppe, J.L., and Wimpress, R.N., Pet. Ref. J.2:No.4,177 (1960).
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Table l. Comparison of the Fictitious Plane Method with the View Factor Method of this Paper Fixed Conditions: Muffle size= 15 ft. x 20 ftc Size of tubes in a single row, d = 4.0 inches diameter 1 for muff le = o. 7 2 for tubes = o.8 3 = fictitious plane emissivity (calculated) Temperature of muffle= 256o 0 R Temperature of tubes= l06o 0 R Variables: D = Distance between floor and tubes, ft. C = Tube center distance, inches C/d Fictitious Plane Method: o/.._ ( ordinate of Figure Al/ A2 = A3 / A2 l @ S /D:;: c:,,o ) E3 F12 = VF (15 ft) X F (20 ft) (ordinate of Figure l@ di C/d = l,S/D) 13 106 ql3 X View Factor Method: F (15') from Fig. 1, this paper F (20 1 ) from Fig. 1, this paper F12 =VF (15 ft.) x F (20 ft.)= 'dri2 106 q12 X ql2 ql3 X 100.,
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\
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Shorter Communication THE ROLE OF COMPUTER TRAINING IN UNDERGRADUATE ENGINEERING CURRICULA R. S. Rame.lho Associate Professor of Chemical Engineering University of Rochester Rochester, N. Y. In this paper the authorJ s object is to attempt answering three questions for engineering educators, namely: I. Why should computer training constitute a required discipline of undergraduate engineering curricula? II. How should computer techniques be taught? III. When should such tr a ining be offered during the under graduate engineering program? I. Why? The widespread use of computers in this country leads educators into considering provision for some sort of computer training at the undergraduate level. One might argue, however, that many of the graduating engineers do not have to do a great deal of computer pro gramming themselves, but rather they will be directing tech nicians who will do the actual programming for them. Conse quently, those who think in this manner, do not feel that formal computer training is necessary in the undergraduate engineering curriculum. The author does not believe that this argument is valid, but rather, that a reasonably intimate knowledge of computers is of importance for the graduating engineer. At least two reasons may be given to support the latter point of view: 1. Many times in an engineering office the technicians are too busy to translate the engineer's problem into a com puter program. Also, it is not so easy to explain a complex engineering problem to one who really does not know ma.ch engineering and, in fact, has no direct interest in the problem himself. This communication problem does exist and although a technician can be helpful at times, there are certain occasions when it would be time saving for the engineer to write his own program or at least to prepare a detailed flow chart for the problem. 24
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2. A fairly intimate knowledge of the computer gives the engineer a better appreciation of its capabilities. In many cases the best approach to the solution of a problem when one has in mind its solution by means of a computer is dif ferent from the conventional approach employed by the user of paperpencilslide rule. Knowledge of the computer enables the engineer to select this best approach. Usually the technician will not be able to help the engineer in making these preliminary st high level decisions 11 on the approach to the problem solution. II. How? This is a controversial question. Many educators seem to favor the socalled 11 black box approach," and recommend teaching only compiler language as exemplified by FORTRAN. The author favors teaching first, machine language and symbolic program systems. Three reasons can be presented to justify this opinion: 1. Once machine language is understood the student can pick up relatively easily the use of a compiler, but the reverse is not true. 2. If a compiler source program does not work at first, the knowledge of machine ls nguage may become very helpful in II de bugging" the progJ:'am. 3. A third factor which might be labelled as the 11 psychological factor" may be m e ntioned. One derives a certain amount of satisfaction in under standing what is going on "inside the black box." Learning only a compiler is a comparable experience to that of one who learns how to use a slide rule without knowing what a logarithm is: true, it can be done, but this approach might not be too appeal ing to the sophisticated mind. III. When? It is not a new idea in engineering curriculum to utilize a few summer weeks for required Engineering courses. Chemical Engineering students at the University of Rochester, for example, take an intensive 3week summer course in 11 Chemical Engineering Unit Operations" between the junior and the senior year. It is believed that the introduction of a 4week summer course in computer programming between the freshman and sophomore year would be most beneficial. The course could include machine language, symbolic program systems and com pilers. The mornings would be devoted to lectures and black board exercises. Afternoons could be used to a large extent in actual machine experience.
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,I
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During the sophomore year in most schools, engineering students take the first professional courses within their chosen fields. In view of freshly acquired acquaintance with computational techniques, these courses could beef fectively assisted by computers. Computerassisted courses should also become a common occurrence during the junior and senior year o Literature 1. 0 1 Connell, F.P., Chem. Eng. Education l, 8 (1962). 2. Pehlice, R.D., Sinott, M.J., Journal .2f. Engineering Education 52, 573 (1962). (continued on next page) INFORMATION FOR CONTRIBUTORS Full length articles, shorter communications, and letters to the editor are solicited. Contributions must be original, of course, and must deal with subject matter of interest in chemical engineering education. Naturally, material that has been published elsewhere, or is being considered for publication elsewhere, is not acceptable. (However, a paper that has been merely presented orally at a meeting will be considered provided the author has obtained an appropriate release from the society or other group that sponsored the meeting). Manuscript typing should be double spaced. Three copies should be mailed directly to the editor. Full length papers should include a brief abstract. Authors of manuscripts accepted for publication receive 20 reprints free of charge. SUBSCRIPTION INFORMATION The subscription rate to The Journal of Chemical Engineering Education is $2.00 per year in the u.s.A. and Canada, and $3.00 per year elsewhere. Payment should accompany the subscription order. Checks should be made payable to the University of Cincinnati which acts as repository for the funds, and mailed together with the subscription order directly to: The Journal of Chemical Engineering Education University of Cincinnati Cincinnati 21, Ohio u.s.A.
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.
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Appendix This is an outline for the course "Chemical Engineering Computer Calculations" as taught this year 1n the Department of Chemical Engineering of the University of Rochester. Te xts used: 1. Germain, c. B. "Programming the IBM 1620" PrenticeHall, Inc. (1962) 2. IBM 1620 FORTRAN Reference Manual IBM Publication C2656190 (1962) I. Computing Fundamentals a. Evolution of computers b. Digital and analog computers c. The stored program concept d. The fundamental units of a digital computer e. Numerical analysis and digital computers f. Flow diagrams II. The IBM 1620 and its Component Parts III. 16~0 Instructions IV. Operation of the 1620 V. The Symbolic Program System a$ Pseudo instruction b. Declarative operations c. Address arithmetic d Unique Mnemonics e. Operation of the SPS processor VI. Program Planning and Debugging VII. Subroutines and Floating Point Arithmetic VIII. FORTRAN a. Compilers bo Writing the 1620 FORTRAN program. Ce Operating principles d. Analysis of the FORTRAN program. e. The FORTRAN precompiler IX. Project Write a computer program for solution of a fairly complex chemical engineering problem. An individual assignment is made to each student. 27
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Shorter Communication THERE ARE NO "SMALL" MATHEMATICAL ERRORS IN ENGINEERING WORK Professor L. s. Kowalczyk Chairman, Department of Chemical Engineering University of Detroit Detroit 21, Michigan A mathematical error in the solution to a problem is just an error and it will effect only the student's grade for the course. In engineering work, however, the consequences of an error are more serious and may lead to a loss of money and prestige by the design organization and, certainly, to the loss of a job by the unfortunate designer. Many engineering students are not aware of the serious ness of the problem. When penalized for errors in a calcula~ tion problem, they try to involve the instructor in lengthy discussions pointing out the correctness of the procedure used, smallness of the error, etc. To avoid wasting time on this sort of discussion, I present my point of view on this matter to the students in the very first engineering course. In these comments, emphasis is placed on the following points: 1. The procedure, l e ading to the solution of a given problem, is usually evident from class discussions and text or reference books. It is a result of understanding the statement of the problem but it cannot be substituted for a numerical answer. 2. Using the selected procedure and other tools available (mathematical tables, handbooks, slide rule, computer), the engineer and engineering student must obtain the true numerical answer. 3. Any error in calculations may cause a deviation from the correct answer. Accordingly, there is no room for any mathematical error in engineering calculations. 4. Errors in engineering work must be discouraged by all possible means. To stress more strongly the undesirability of errors in engineering and to illustrate the serious consequences of error, I usually discuss the following examples.
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1. Er!,O!, in_sign. This is quite a common error but may cause a great deal of confusion. For instance, a cooler is installed instead of a reboiler in the distillation column, a missile, instead of h e ading to the moon, goes to the center of the earth, a promising chemical reaction does not yield any product (error in sign in free energy calc~lations), 5 multiplication, let's say, by 10 instead of by 10, as in the rate of chemical reaction, results in a 1010 error, change of sign in the work term of the mechanical energy balance will result in suction instead of pressure and may re verse the direction of fluid flow in pipes. 2. DiyiE.in_iQSle~d_of ~ultiPliatin. Here the error is of a 2 order where a is the number in question. 3. Er_ro_ ,in_declm~l_poi_gt. Let's suppose that a 10plate column is needed for the requested separation. The error in decimal point makes it either a singleplate or 100plate column $ Or a 10 story house is reduced to a ranchstyle house or enlarged to a 100 story sky scrapere 4. OmisE.in_of lem_iQ ~n_e.9.u~tio_g. This case can readily be illustrated by an omission of reboiler or condenser in the distillation column, the first floor or roof in a house, a span in a bridge, a power house in a plant, etc. 5. DiE_trlin_of j?_e_m_i_!! ~n_e.9.u~tio_g. Distortion of a term will be followed by replacement of the required piece of equipment or material by a different item, such as a condenser on the column by a vacuum pump, a jaw crasher by a pulverizer, water by gasolene, etc. 6. Using log inst~ad of_lQ. The error is evident from the relationship ln a= 2.303 log a 2 'f)
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7. Us2_ of_i_gd2_finit2_ in.!?_e_gr~l. The use of the indefinite integral in calculations., i.e ., neglecting the integration constant., introduces the error equivalent to this constant. No error though if C = o. 8. Re_y_e!_sin_g .!?_he _bi,mi.!?_s_of inte_gr~t_io_g. This error results in the change of sign. 9. Dimension checking in the course of calculations is a highly recommendable practice. It may lead to early discovery of errors. These illustrations, although drastic., are not exaggerated~ They may be useful in explaining to the students the signifi cance of the most common mathematical errors. Try This One If on Earth an astronaut of the future weighs 200 lb with his space suit and small emergency rocket belt, from approximately how large an isolated asteroid (minor planet) of the same density as Earth could he escape with his belt fueled to provide 100 lb of thrust for 10 seconds1 (Solution on following page.) R. L.,
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Solution to Problem on Preceding Page Applying Newton's Law of Gravity to the center of the "in. asses involved, the gravitational acceleration gR at the surface of an asteroid of mass M, radius R, and same density as Earth, is gR = 32.2 ( !L\(RE \ 2 = 32.2 (B._\ 3 (RE \ 2 = 32.2 B._=32.2R=0.00812R ME ) R) RE J R) 3 963 where ME is the Earth 1 s mass and RE is the Earth 1 s radius which is 3963 miles. The gravitational acceleration at a point above the asteroid 1 s surface, X miles from its center, is gx = gR (D 2 = 0.00812 R 3 (2) Xj x_2 Since the rocket belt is small, the change in its mass occasioned by fuel consumption must be even smaller. Therefore, we can take the total mass of 200 lb. as substantially invariant. The net force in poundals exerted on the 200 lb. of mass during thrust is F = 100 X 32.2 200 (3) However, the thrust will be completed near the surface so we can substitute gR for g~ in equation 3, especially since the term will turn out to be only of small influence on the final result. Also, F =ma= mdv/d1 so that Fd1 = mdv. Substituting in the latter and integrating, (3220 200gR)7d~ = 200/dv 0 0 from which the escape velocity in ft/sec is v = 161 l0gR (4) (.5) In order to escape, the kinetic energy imparted must equal the work required to move the mass in questibn from the surface of the asteroid outward against the pull of gravity, theoretically to infinity. Thus, mv 2 = 5260Fx m dX (6) R 31 (1) .. .. ...
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Solution to Problemcon't Cancelling m, substituting equations 1,2, and 5 into 6, and then integrating~ gives 1/2 (1610.0812R) 2 = 5280 / 0.00812R 3 dX =42.9R 2 )<2 Solving equation 7 yields R = 17.2 miles radios. Thus he could escape from an asteroid of up to approximately 34 miles in diameter. Try This One Too A certain neighborhood grocer weighs his pennies 100 at a time, rather than counting them. He claims that because his scale is quite accurate he has 11 never made an error". If the average deviation in the weight of single pennies in circulation is 1%, would the grocer's claim of near infallibility seem plausible? R.L. The solution will appear in the next issue. 32 (7)
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INDEX OF TITLES German Translation by M. Zimmer Spanish Translation by Saturnino Fanlo A chronological index for all issues to date is presented below. As a courtesy to subscribers in other countries, translations of the titles into German and Spanish are included. In the future such translations will be presented at the beginning of each article. Volume 1, Number 1, March 1962 An Integrated Approach to the Teaching of Chemical Engineering [hermodynamics.c. M. Thatcher Un enfo~ue unificado en la ensenanza de Termodinamica on Ingenieria Quimica. Eine Zusammenstellung fuer den Unterricht der Thermodynamik in chemischer Technologie Teaching Statistical Mechanics to ThirdYear Students.Myron Tribus Ensenando Mechanica a estudiantes de Tercer Ano. Unterricht in statistischer Mechanik fuer Studenten im 3. Ausbildungsjahr Chemical Systems Engineering Training Course in a Petrochemical Company.c. J. Huang, T. Q. Eliot, and D.R. Longmire Curso de Entrenamiento de Sistemas de Ingenieria Quimica en una Industria Petroquimica. Eine Vorlesung fuer chemische Systeme in Ingenieurwesen in einer petrochemischen Firma Reaction Selectivity.J. F. Woodham Selectividad de Reaccion. Selektivitaet von Reaktionen Page 3 11 19 26 33
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Shorter Communication: Specialized vs Generalized Engineering Education, a Narrow Viewpoint E. J e Henley Breve Comrnunicacion: Ensenanza de Ingenieria Especializada vs Ingenieria Generalizada, un estrecho punto de vista. Notizen: Spezialisierte oder allgemeine Ausbildung im Ingenieurwesen, ein engbegrenzter Standpunkt. Mi see l lany: Ragnarok and the Second Law. Congress in Puerto Rico; Session on Education. Miscelanea: Ragnarok y la Segunda Ley Congreso en Puerto Rico; Sesion sobre Educacion Verschiedenes: Ragnarok und das Zweite Geset~ Kongress in Puerto Rico; Setzung ueber Erziehungsfragen Volume 1, Number 2, October 1962 The Postgraduate Curriculum An Approach Through Critical Path Programming.L. A. Wenzel El curriculum de postgraduado Un acercamiento usando una trayectoria critica programada. Ein Diplomanden Ausbildungsplan. Eine Ausbildung durch kritische schrittweise Programmierung Teaching Professionalism A seminar Method William Licht Ensenando professionalismo El metodo de Seminaries Das Lehren des Berufsethos. Eine Seminar Methode The Unit Operations Laboratory.R. L. Huntington 34 El laboratorie de Operaciones Unitarias Labormethoden lm halbtechnischen Massstab 35 10 38 3 9 14
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A Nuclear Power Plant Simulator for Educational Purposes.F. T, Dunckhorst and G. Houghton Un simulador de una planta de fuerza nuclear de proposito~ pedagogicos Ein Kernreaktorsimulator fuer Ausbildungswecke The Misuse of the Arithmetic Mean Driving Temperature 20 in a Double Pipe Heat Exchanger.s. Middleman 35 El uso erroneo de la media aritmetica de dif e rencia de temperatura en un intercambiador de calor de doble tubo Der Missbrauch des arithmetischen Mittels der Betriebstemperatur in einem Doppelroehren Hitzeau3tauscher Shorter Communication: The Mole as a Cardinal Number of r1olecular Species.Niels Madsen Breve comrnunicacion: El mol como numero cardinal de especies moleculares Notizen: Das Mol als eine Kardinalzahl fuer Mo le kue larte n Volume 2, Number L, June 1963 Chemical Engineering Education in Western Europe,Allen N. Smith Ensenanza de Ingenieria Quimica en Europa Occidental. Chemische Technologie Ausbildung in West Europa Chemical Engineering Education in the u.s.s.R. Nathan Gilbert Ensenanza de Ingenieria Quimica en la Union Sovietica Chemische Tecbnologie Ausbildung in USSR 3 12 35
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Chemical Engineering: Its Past, Present and Future.Gerald Houghton Ingenieria Quimica: Pasado, Presente y Future 0hemische Technologie, ihre Vergangenheit, Gegenwart und Zukunft 18 A SelfInstructed Program to Simplify Computations. J. s. Ratcliffe 26 Un programa autodidacta para simplificar calculos Ein selbstgelehrtes Brograrnrn zur Vereinfachung von Berechnungen. Shorter Corrrrnuniaation: The Analogy Between Chemical and Dimensional Equation.William Squire Breve Comunicacion: Analogia entre Equaciones quimicas y dimensionales Notizen: Die Analogie zwischen chemischen und dimensionalen Gleichungen. Mi see llany: Brief Note: ProblemSolving Technique. Favorite Classroom Demonstration: Boiling Heat TransferoSami Atallah Miscelanea: 36 Nota: Tecnica de solucionar problemas Mi e.xperimento de catedra favorito: Transferencia de calor en un liquido en ebullicion Verschiedenes: Problemloesende Technik Beliebte Unterrichtsvorfuehrung: HitzeAustausch in einem kochenden Medium. 33 25 38
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( I
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Volume 2, Number 2, December 1963 Interpretation of Viscous Stress in a Newtonian Fluid.Dr. R. E. Rosensweig Interpretacion del esfuerzo de viscosidad en un flujo Newtoniano Interpreation von viskosem stress in einer Newton'schen Fluessigkeit Conversion Factors.William Squire Factores de Conversion Umrechnungsfaktoren Radiant Heat Exchange to Tubes in Enclosed Muffle Furnaces,.Charles E. Dryden Transferencia de calor por radiacion a tubes encerrados en hornos mufla Hitzeaustansch durch Strahlung zu Rohren in gesohlossenen muffelefen. The Role of Computer Training in Undergraduate Engineering Curricula.R. s. Ramalho La importancia del entrenamiento en el uso de 11 Computers 11 en los curricula de Ingenieria Die Rolle der Computer Ausbildung im Technologie Studium fuer Anfaenger There are no "Small" Mathematical Errors in Engineering Work.L. s. Kowalczyk No existen "pequenos" errores matematicos en los calculos de Ingenieria Es gibt keine nkleinen 11 mathematischen Fehler in der Technologie. 10 16 22 26 37
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