Chemical engineering education ( Journal Site )

Material Information

Chemical engineering education
Alternate Title:
Abbreviated Title:
Chem. eng. educ.
Physical Description:
v. : ill. ; 22-28 cm.
American Society for Engineering Education -- Chemical Engineering Division
Chemical Engineering Division, American Society for Engineering Education
Place of Publication:
Storrs, Conn
Publication Date:
annual[ former 1960-1961]


Subjects / Keywords:
Chemical engineering -- Study and teaching -- Periodicals   ( lcsh )
serial   ( sobekcm )
periodical   ( marcgt )


Chemical abstracts
Additional Physical Form:
Also issued online.
Dates or Sequential Designation:
1960-June 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., 1965-1967; Gainesville, Fla., 1968-

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Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
oclc - 01151209
lccn - 70013732
issn - 0009-2479
lcc - TP165 .C18
ddc - 660/.2/071
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Full Text







L/_ _^


Number 2

December 1963



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


Try This One (Problem) 36

Information for Contributors and 26

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.


We are now completing the second year of publication.
Time does indeed seem to fly.

To date, five issues have appeared containing twenty-two
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 two-for-one bonus for 1964 subscribers.

Subscription fees for 1964 are due now. They are still
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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.



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 rate-of-strain 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 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. ROrf-t ^ v

;-See for example Reference 1. This text is recommended
as a fluid-mechanically 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 rate-of-strain 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,


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

2-f-- Ce-2

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,


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

(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

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


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 Y-i ,l +

4 2-43 -413i-vli3 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+


z--(e,. ,- +--i a


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 Navier-Stokes equations.

Literature Cited;

1. Long, R. R., "Mechanics of Solids and Fluids", Prentice-
Hall (1961).


William Squire
Professor, Aero-Space 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


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 non-conforming 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
conversion factor-from 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)


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).

Such quantities do not come within the scope of this

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)


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 i-nm 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.


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

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 (m-l) entries are determined by (m-1)
independent quantities. A set of (m-1) 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
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

Thus, we have
Vmile, hr-1 (.682) = L miles hr-l
(.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

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 acre-ft 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.


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

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,

ft lb Slug

2 -2
Meters sec (10-3)
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", AEDC-TDR 62-6, (Feb. 1962)


Charles E. Dryden*
Department of Chemical Engineering
The Ohio State University
Columbus, Ohio-

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 refracbory-walled 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 sink-source system.

On loan to the Indian Institute of Technology,
Kanpur, India, 1963-1965.

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 grey-body source. The receiving
plane of finite size at a finite distance below and parallel
to the tube plane is considered the grey-body sink. The
source and sink designations can be reversed depending on
the nature of the heat exchange. The well-known 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 sink-source
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 +( -

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 sink-source.

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 heat-receiving surface in the form of a single row
of 4-in, tubes on 9-in. 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 muffle-surface 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 radiant-heat 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 15-ft. squares separated by 10 ft.,
S/D = 1.5 and F12 = 0.550
For 20-ft. 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.


Use of Figures 1 and 2 to obtain directly P12 view
factors for finite geometry, tube-muffle combinations enables
single step computation of the geometric factor by means of
the well-known 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 read-out 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








iLu 0.2


O cT O

C/d Center-to-Center Distance of Tubes in Row
Outside Diameter of Tubes
FIGURE-1. View Factors for One Row of Tubes to a Plane Within
a Refractory Muffle Furnace



F 0.4




1 2 3 4 5 6 7 8
C/ = Center-to-Center 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.80-81, McGraw-Hill (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)
Temperature of muffle = 25600R
Temperature of tubes = 10600R

D = Distance between flour and
tubes, ft.
C = Tube center distance, inches
Fictitious Plane Method:
0( ordinatee of Figure 1 @ S/D=to)
A / A2 = A / A2

F12 = \F (15 ft) x F (20 ft)
ordinatee of Figure 1 @
C/d = l,S/D)

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.) =
q12 x 10

q12 q13 x 100, %



Case No.







0.660 0.660 0,660 0.481
0.433 0.483 0.252 0.349

9.38 10i57





5.46 7.61



0.251 0.347
5.47 7.57

-0.1% -0.07% +0.1% -o.5%

Shorter Communication


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 paper-pencil-slide 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 so-called "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 3-week summer course in "Chemical
Engineering Unit Operations" between the junior and the
senior year.

It is believed that the introduction of a 4-week 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. Computer-assisted courses
should also become a common occurrence during the junior and
senior year.


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)


Full length articles, shorter communications, and letters
to the editor are solicited, Contributions must be original,
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Manuscript typing should be double spaced. Three copies
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should include a brief abstract.

Authors of manuscripts accepted for publication receive
20 reprints free of charge.


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The Journal of Chemical Engineering Education
University of Cincinnati
Cincinnati 21, Ohio


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" -
Prentice-Hall, Inc. (1962)
2. IBM 1620 FORTRAN Reference Manual IBM Publication
C26-5619-0 (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

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

a. Compilers
b. Writing the 1620 FORTRAN program.
c, Operating principles
d. Analysis of the FORTRAN program.
e. The FORTRAN pre-compiler

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


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

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

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 in-sign 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 10-plate column is needed for
the requested separation. The error in decimal point makes
it either a single-plate or 100-plate column. Or a 10 story
house is reduced to a ranch-style 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

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)


Solution to Problem-con't

Cancelling m, substituting equations 1,2, and 5 into 6,
and then integrating, gives

1/2 (161-0.0812R) = 5280 0.00812Rs dX =42.9R2

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


The solution will appear in the next issue.


German Translation by M. Zimmer

Spanish Translation by Saturnino Fanlo

A chronological index for all issues to date is presented

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 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 Third-Year
Students.--Myron Tribus 11

Ensenando Mechanica a estudiantes de Tercer

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.


Ragnarok and the Second Law. 10
Congress in Puerto Rico; Session on Education. 38


Ragnarok y la Segunda Ley
Congress en Puerto Rico; Sesion sobre Educacion


Ragnarok und das Zweite Gesetz
Congress in Puerto Rico; Setzung ueber

Volume 1, Number 2, October 1962

The Postgraduate Curriculum An Approach Through
Critical Path Programming.--L. A. Wenzel 3

El curriculum de post-graduado 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

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

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 Self-Instructed 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.


Brief Note: Problem-Solving Technique. 25
Favorite Classroom Demonstration: Boiling Heat
Transfer --Sami Atallah 38


Nota: Tecnica de solucionar problems
Mi experiment de catedra favorite: Transferencia
de calor en un liquid en ebullicion

Verschiedenes: Problemloesende Technik
Beliebte Unterrichtsvorfuehrung: Hitze-Austausch
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


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



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