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 Front Cover
 Table of Contents
 Editorial
 Estimation of random error in a...
 Approach to steady-state of a two...
 A projects laboratory for junior...
 Undergraduate use of analog...
 Departmentalized curriculum based...
 A common studies curriculum in...
 The undergraduate curriculum in...
 Solution to previous problem
 Translation of titles
 Back Cover




















Chemical engineering education
http://cee.che.ufl.edu/ ( Journal Site )
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Permanent Link: http://ufdc.ufl.edu/AA00000383/00186
 Material Information
Title: Chemical engineering education
Alternate Title: CEE
Abbreviated Title: Chem. eng. educ.
Physical Description: v. : ill. ; 22-28 cm.
Language: English
Creator: American Society for Engineering Education -- Chemical Engineering Division
Publisher: Chemical Engineering Division, American Society for Engineering Education
Place of Publication: Storrs, Conn
Publication Date: December 1965
Frequency: quarterly[1962-]
annual[ former 1960-1961]
 Subjects
Subjects / Keywords: Chemical engineering -- Study and teaching -- Periodicals   ( lcsh )
 Notes
Citation/Reference: 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 rights reserved by the source institution and holding location.
Resource Identifier: oclc - 01151209
lccn - 70013732
issn - 0009-2479
Classification: lcc - TP165 .C18
ddc - 660/.2/071
System ID: AA00000383:00186

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Table of Contents
    Front Cover
        Front Cover 1
        Front Cover 2
    Table of Contents
        Page 1
    Editorial
        Page 2
    Estimation of random error in a derived quantity
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
    Approach to steady-state of a two stage mixer-settler extractor
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
    A projects laboratory for junior chemical engineers
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
    Undergraduate use of analog computers
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
    Departmentalized curriculum based on chemical change
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
    A common studies curriculum in engineering
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
    The undergraduate curriculum in chemical engineering at Yale
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
    Solution to previous problem
        Page 53
        Page 54
    Translation of titles
        Page 55
        Page 56
    Back Cover
        Back Cover 1
        Back Cover 2
Full Text

THE


JOURNAL


CHEMI


CAL


ENGINEERING


EDUCATION


Volume


Number


December 1965


OF










THE JOURNAL OF CHEMICAL ENGINEERING EDUCATION


Volume 3, Number 2, December 1965

Editor: Robert Lemlich

Associate Editor: Daniel Hershey


Editorial 2

Estimation of Random Error in a Derived Quantity --
D. A. Ratkowsky 3

Approach to Steady-State of a Two Stage Mixer-Settler
Extractor James E. Halligan and Morton Smutz 11

A Projects Laboratory for Junior Chemical Engineers --
Sami Atallah 17

Undergraduate Use of Analog Computers W. E.
Schiesser 22

Departmentalized Curriculum Based on Chemical Change
- William H. Corcoran 32

A Common Studies Curriculum in Engineering Eric
Weger 43

The Undergraduate Curriculum in Chemical Engineering
at Yale Charles A. Walker and John A. Tallmadge 48


Miscellany:

Solution to Previous Problem 53

Translation of Titles 55




The Journal of Chemical Engineering Education is pub-
lished at irregular intervals at the University of Cincinnati,
Cincinnati 21, Ohio, U.S.A. Opinions expressed by contribu-
tors 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.





















WE BOW OUT


As we indicated in our previous issue, this journal
has been suffering from an unusual malady -- a shortage of
publishable material. We have subscribers but we lack a
sufficient number of contributors. As a result our issues
have become too few and far between. Accordingly, we have
regretfully decided to suspend publication.

We do however want to take this final opportunity to
thank our subscribers and contributors, our colleagues and
friends, and our typists and mimeographers for their sup-
port, encouragement, and assistance.

It is our understanding that the Chemical Engineering
Division of the American Society for Engineering Education
is presently taking steps to revitalize their divisional
publication. We wish them success in this endeavor and
urge all our readers to support their efforts.



R. L.








ESTIMATION OF RANDOM ERROR IN A DERIVED QUANTITY


D. A. Ratkowsky
Assistant Professor, Department of Chemical Engineering
The University of British Columbia
Vancouver 8, Canada


------------------------------------------------------------

Abstract: The statistical method for determining the
variance of an arbitrary function of experimentally measured
variables deserves to be more generally employed in under-
graduate laboratory courses to assist the student in evalua-
ting the errors in, and the reliability of,.experimental data.
The statistical method also has an important use in explora-
tory research studies and in process design. In all cases
the method leads to an estimate of the probable error in the
derived quantity, whereas an alternative method gives the
maximum possible error, which generally represents an overly
conservative estimate of the error.

--------------------------------------------

The statistical theory of random errors in a quantity
which is derived from primary experimental observations, is
useful for the estimation of error in at least three classes
of problems:

1) The analysis of experimental error, either in research
or in undergraduate student laboratory classes,

2) Exploratory research studies, to ascertain whether
the method of measuring a particular variable is of
sufficient precision, and

.3) Process design, where experimental error creates an
uncertainty in the magnitude of the quantity to be
designed.

The statistical method for determining the variance of
an arbitrary function of experimentally measured variables
is given in several textbooks (1, 2, 3, 4) which, although
not mentioning chemical engineering specifically in their
titles, may come to the attention of chemical engineers.
There are, however, at least two leading textbooks, both of
which are specifically concerned with applications of mathe-
matical methods to chemical engineering, which do not mention
the statistical method. This statistical method, which en-








ables one to construct confidence intervals for the mean
value of the derived quantity, deserves to be better known
by teachers of chemical engineering, and more generally em-
ployed in undergraduate laboratory courses, to assist in e-
valuating the reliability of the experimental data.
Before presenting the statistical method, it is useful
to first present an alternative method of determining the
propagated error. This method, given in several textbooks
(5, 6) has the weakness that the error it predicts is the
maximum possible error, and takes no account of the possi-
bility of compensating or cancelling errors. It is based
upon the fact that if

U = 0 (xi, x ....... xn) (1)

where x1, x2, ......., x are several directly measured vari-
ables subject to experimental error, then the differential
change in the derived quantity U for a differential change
in each of the measured x's is

S x + ) X + ...... +xn dx (2)


If the errors dxl, dx2, ......., dxn are relatively
small, (so that the terms of higher order in the Taylor ex-
pansion are negligible), then Equation 2 can be reduced to

U = Ax, + 2 + .... + (3)


Illustrative examples of the use of this formula are
given in reference (5), pp. 55-56 and reference (6), pp. 359-
360. One important aspect of the use of Equation 3 is that
the sign of the partial derivative is so chosen that all
terms of Equation 3 have the same sign, that is, the terms
add up in such a way that AU represents the maximum possible
error in the derived variable U. Equation 3 almost certainly
overestimates the error involved in the derived quantity, be-
cause it considers only the simultaneous occurrence of the
most extreme errors and takes no account of the possibility
of compensating errors. The probability of operating at the
most extreme level of error is always small, and becomes van-
ishingly small as one increases the number of primary vari-
ables subject to error. The concept of maximum possible error
is therefore one of limited usefulness.








Statistical techniques lead to a more pertinent measure
of the error in a derived quantity by enabling one to calcu-
late the variance of the mean value of the derived quantity.
The formula to be used is shown below.

If Z = f(xi, x2,.X .., x ) where the x. are indepen-
dent random variables with finite means and finite variances,
then if. the errors-ifn the x. are not too large (so that the
higher order terms of the Taylor expansion can be neglected),
then one can write

2 (,f \2 2 f 2 +(4)
S) + /-x-* ++ ......2 .-2 (4)


The partial derivative of the function f with respect to each
x. is taken with all the remaining x's held constant. The
quantities 6- 2' a- 2 a- 2 represent the variances of
Xu x2 x.:
the respective primary variables xi, x2, ...., x Practical
application of Equation 4 de eds, upon one's ability to de-
termine these variances. The variances are usually determined
from random experimental measurements upon the individual var-
iables. Suppose, for example, that in an experiment to de-
termine the flow rate through a pipe, 5 successive weighing
of the effluent from the pipe during the saie fixed time in-
terval gave values of 97, 102, 99, 104, and 98 pounds respec-
tively. The mean value of the five readings is xj = 100 lbs.
and the best estimate of the variance is ,2 = i3(xi x)2/
(n 1) = 8.5. This, together with similar estimates from
random samples of the other variables, provide the various
variances 2 rx 2 s o- 2 to be used in Equation 4.
x x2 Xn
Sometimes a reading of a particular quantity on an in-
strument or measuring device is very steady, but the limiting
factor to the precision of the reading is the smallest scale
division available on the instrument. Utilizing thexfact
that practically all of the area (actually 99.73),unsder the
curve of the normal (Gaussian) distribution is contained with-
in 3 standard deviations of the mean, then one can consider
36 to be synonymous with the range, and thus from. a manow-
ledge or a guess of the range, it is possible-to'obtain a
reasonable estimate of the standard deviation. Consider a
temperature measurement made with a thermometer ~-i'n which the
smallest scale division is'loC. It seems" reasonable, to as-
sume that the maximum error range obtainable (due'to human
reading error alone) is about 0.50C (or 0.250C). Thus an
estimate of o- would be 0.25 = 0.0833 from which 2 = 0.007.
3 -
Of course, the range may be considerably greater than 0.50C,
due to large fluctuations or instabilities in the temperature.








Here, one would once again require experimentation to obtain
a random sample from which the variance may be estimated.
The previous discussion applies only to steady readings where
the smallest scale division imposes a limiting factor on the
accuracy of the reading.

A special case of Equation 4 occurs when the functional
relation is of the form Z = cxat xa2 ....... x an, where c,
a1, a2, ......, an are constants. Then it is easy to show,
by using Equation 4, that

2 a a 2 + a2 2+ ". + a (5)
X,)n XnX


Presented below are two illustrative problems which will
indicate the uses to which Equation 4 can be put.

Illustr native Example It
Consider an undergraduate laboratory experiment on the
unsteady-state heating of water, starting at room temperature,
in a steam-jacketted open kettle. The apparent overall heat-
transfer coefficient is given by

Mc
U -P dt
a AAt dO
a

where
M = weight of water, lb.

c = heat capacity of water, BTU/lb (OF)

A = area of kettle in contact with water through
which heat transfer can take place, ft2

Ata = apparent temperature difference between steam
and water at any instant, OF

dt/dQ = slope, at any instant, of the curve of water
temperature versus time.

Suppose it is desired tho. determine the value of U and
its precision, at the condition when At = 600F.
a
Since this equation is an example of the special case
quoted above, the expression for the variance of U obtained
with the aid of Equation 5, is









S M +k )2 + + (/+ t


T_: 200 lbs. of water were measured out in 25 lb.
batches. Each batch was.weighed within maximum
error limits of 0.25 lb., i.e. m = 25 0.25 lb.
FL 0.251
Therefore 0 = -- = 0.083 or let & = 0.10
m 3 m
lb. to take into account the loss of water due to
splashing or retention of water in the bucket, etc.,
when transfer to the kettle is being made.

M = mi + mn + ....... + m8

2 = 8' 12 = 0.08 lb2, since the variance

of a sum is the sum of the individual variances.

d : The heat capacity of water is so well known that
OP one can assume that there is no uncertainty in the
knowledge of cp, i.e., a)C 2 = 0.

61: As heating continues, expansion of the water takes
place, causing the wetted area to increase. How-
ever, the term "apparent.heat-transfer coefficient"
implies in fact that this increase in area has been
ignored in favor of using the wetted area at room
temperature. From measurement of the liquid depth,
and a knowledge of the geometry of the kettle, it
is estimated that A = 8.74 ft2 with a maximum un-
certainty of 0.45 ft2.
I" 0.45
Therefore 0.15 ft2
A 3
2 = 0.0225 ft2
A
6 : The temperature difference ta = t tw, where ts
a and tw are the steam and water temperatures, respec-
tively. The temperature of the steam, assumed to
be saturated steam,.was determined from the steam
pressure which was measured using a mercury mano-
meter. The pressure variations were kept within
the maximum error limits of 1 inch Hg, i.e.,
0.5 p.s.i., about a set value of 5 p.s.i.g. The
steam temperature therefore varied between maximum
limits of 1.50F.







Therefore -1.5 = 0.5 2 = 0.25(OF)2
0- 3 ;- "
The water temperature walsmeasured by using the
average value of two thermocouples, each thermocou-
ple indicating between error limits of 0.50F.

t = (1/2)(tw + t)

t 2 = (1/4)(ar 2 + 6(t 2)= (2/4)(0-5)2
wi W2
= 0.0138 (OF)2

Therefore t 2 = 0.25 + 0.01 = 0.26 (OF)2
a

Odt/dQ: The derivative of temperature with respect to time
at the particular time 0 where At = 60F was deter-
mined from the tangent drawn to aaplot of water tem-
perature versus time. From several trials, consid-
ering the various possibilities for drawing a smooth
curve through the points, and considering the preci-
sion of drawing a tangent to a curve, a reasonable
estimate for the derivative dt/dG was 3.0 OF/min
with variance.

adt/dG2 = 0.048 (OF/min)2

The average value of the apparent overall heat transfer
coefficient, Ua, is obtained to be

Ua = 2() (60 = 68.6 BTU/(hr)(ft2)(oF)

and the estimated variance to be

S2 = (6 )2 0.08 0.0225 0.26 0.048
a 68.6 (200) + (8.74)2 (60) + '(30)

= (68.6)2[2 x 10-6 + 2.95 x 104 + 7.22x10-5 +0.00533]

= (4706)(0.00570) = 26.82

au = 5.18
a







Using this value of the standard deviation of U 95%
confidence limits upon U can be constructed. The limits are
1.96 (5.18) = 10.2, the value 1.96 being taken from a tabu-
lation of the normal distribution function.

Thus U a= 68.6 t 10.2 BTU/hr(ft2)(OF), where 10.2 has
the significance of being 95%/ confidence limits about the
mean value 68.6.

The above illustration also shows how Equation 4 can be
useful in exploratory research studies, to help the researcher
decide if a particular measurement is of sufficient precision.
It is seen that by far the biggest contributor to the overall
experimental error is that due to dt/dQ, the contribution be-
ing 0.00533/0.00570 = 93.5%0. Hence, if the purpose of the
research project is to determine U then it is of paramount
importance to establish the temperature vs. time curve accur-
ately, and also to increase the precision in taking the de-
rivative at a particular point on that curve.

The third use of Equation 4 is in process design. Due to
uncertainties in the measured value of certain primary experi-
mental observations, there is going to be an uncertainty in
the derived quantity. Since it is necessary that the unit be-
ing designed be adequate for its task, this uncertainty must
be allowed for in the design. Use of the concept of maximum
possible error results in an overly conservative design. How-
ever, by using the statistical theory of random error, quan-
titatively described by Equation 4, one can base the design
upon, say, the 95%0 confidence limit of the derived quantity.
This will practically always result in an adequate design
without being overly conservative.

Illustrative Example 2:
A countercurrent double-pipe heat exchanger is to be de-
signed to heat 50,000 lb/hr of a liquid from 80 to 1500F.
The specific heat of the liquid is not precisely known but
its mean value can be taken to be cp = 0.85 with .- = 0.04
BTU/lb(F). The overall heat transfer coefficient, U, is es-
timated to be 73 BTU/hr(ft2)(OF) with a = 4. The heating
medium is a liquid of precisely known c which enters at
1800F and leaves at 1200F. Determine tRe required area of the
heat exchanger.

A =e (t2 t) 50,000(0.85)(70)
UAt1 73(34.8) -1170 ft2
UAt 73) (34 )








6" ='A(0.00522)-/2'- 1170(0.0722) = 84.5 ft2

If we wish to be 950/ confident that the exchanger will
have adequate area (aWctually the value calculated will repre-
sent 97.50/ confidence, since in fact a one-tailed test is
being considered), then the design areas should be

A = 1170 + 1.96(84.5) = 1340 ft2

Had the concept of maximum possible error been used in-
stead, the design area would have been in the vicinity of
1530 ft2.

Literature Cited:

1. Volk, W., "Applied Statistics for Engineers" McGraw-
Hill (1958)

2. Davies, 0. L., Editor, "Statistical Methods in Research
and Production" Oliver and Boyd (1957)

3. Parratt, L. G., "Probability and Experimental Errors in
Science", Wiley (1961)

4. Paradine, C. G. and Rivett, B. H. P., "Statistical Me-
thods for Technologists", English U. Press (1960)

5. Mickey, H. S., Sherwood, T. K., and Reed, C. E., "Ap-
lied Mathematics in Chemical Engineering", McGraw-Hill
(1957)
6. Jenson, V. G. and Jeffreys, G. V., "Mathematical Methods
in Chemical Engineering" Academic Press (1963)







APPROACH TO STEADY-STATE OF A TWO STAGE

MIXER-SETTLER EXTRACTOR*



James E. Halligan, Graduate Assistant,and
Morton Smutz, Deputy Director
Institute for Atomic Research and Department of
Chemical Engineering, Iowa State University
Ames, Iowa



Abstract: Under the assumptions of ideal stage behavior,
immiscible solvents, constant flow rates, constant intdrf'ace-
levels, constant distribution coefficients, instantaneous mass
transfer and homogeneous phases, it is possible to solve the
appropriate differential equations simultaneously ak 4expre.ss.
the rate of approach of a mixer-settler extractor to steady-
state as a function of a dimensionless quantityLthat involves
the elapsed time and a quantity related to the system capa-
citance. The particular integral, or steady-state solution,
is the familiar equation for the concentration of a solute in
a stream as a function of the so-called extraction factor.
By introducing solvent extraction theory in this manner, the
student develops a better understanding of the dynamics of the
system and the realization that the steady-state solution is
only a somewhat idealized special case of the general solution.
--------- --------I----- --------------- -----,, ,,,,-,---- --

The Differential Equations:.,. ..
Figure 1 shows a continuous countercurrent two stage
mixer-settler extractor with the light solvent L entering
from the left and the heavy solvent H with solute entering
from the right. Each box represents an ideal stage made up
of a mixer where the two phases are contacted and a settler
where the two phases are allowed to separate. There are many
commercial types of extractors that are designed in this
way (1).

Equations 1 and 2 are solute balances made for each stage
expressing the rate of accumulation of solute as a function
of the rate of solute flowing into and out of the stage.



* Contribution No. 1445; work was performed in the Ames
Laboratory of the U. S. Atomic Energy Commission.







d(VHx, + VLY,)
dt = Loo + H2x2 LY HxI (1)

-.d(VHx2 + VLy)
dt = Liy1 + HFXF L2x2 H2x2 (2)

If the flow rates are assumed constant (L = L2 = L and
H = H2 = H), the distribution coefficient m is assumed con-
stant, and the entering solvent contains no solute, Equation
la and 2a result. The term G is defined as
VH + VLm
S as will be discussed later.


dxj + (1 + E)x x (a)
dt G G: -

dx2 (1 + E)x2 Ex (2a
t G G G + (2a)

Solution of the Equations:
The simultaneous solution of Equations la and 2a provides
a good algebraic work-out and results in Equation 3 for a
stepwise change in x at t = 0. Such a stepwise change may
be thought of as suddenly switching from a solute-free aque-
ous stream to an aqueous feed stream after the extractor has
reached a hydraulic balance with no solute in the system.

d2 x 2(1 + E) dxi r1 + E + E2 x
dt+ G dt + Ux (3)

By inspection one can see the steady-state solution be-
cause 2X and a- will both equal zero. This expression
dt dt
can be verified independently by making steady-state material
balances about the two stages and solving simultaneously.

xF
(X')SS = + E + E (4)

The complementary function can be found by setting the
differential equation equal to zero and solving the resulting
equation.






STAGE I


VL


VH


Ly


HX2


Figure I


STAGE 2


VHL


VH


2.0


Z=t/G

Figure 2


Lyo


HXI


Ly2


HXF





































L.
+ _













X ,
I II I D

SIII III III
______________ 0 .0 0







-(l+EE )t -(l+E+E )t
(x=)CF = CGe G + C2e (.)

The complete solution for xi is the sum of the expres-
sions in Equations 4 and 5. Boundary conditions assumed-,were
that t = 0, xi = 0, and dxl/dt = 0. After considerable alge-
bra, Equation 6 appears.

-(l+E-E)t
xF (1 + E + E+)e G
(x)t 1 + E + E 2E




2E12

If both sides of Equation 6 ar'e divided by the steady-
state value of xi, the fractional approach to steady-state Y
can.. be determined as a function of E, G and t.

-(1+E-Ejt -(l+E+E
- (x,)+. 1 (1 + E + E)e G (1+E-E )e GE
(x-ssa 2E*' S ih 2E


Significance of G:
Figure 2 shows the solution to Equation 7 as a function
of the dimensionless quantity, Z(Z = t/G) with parameters of E.

The significance of G can be seen by multiplying the nu-
merator and denominator of the defining equation by x .

VH + VLm VHi + VLYi (8)
G = =. (8)
H RX i

The numerator represents the amount of solute in stage i at
a given time and the denominator is the amount leaving stage
i per unit time in the aqueous stream. In other words, if
the numerator is relatively large due to large volumes and a
high distribution coefficient, and if the aqueous flow rate







is relatively small, then g~Liich is related to the system
capacitance, will also be large. The fractional approach to
steady-state at a given value of E depends on the ratio of t
to G, as shown in Figure 2.

Sample Prpblem: .
Suppose that one desires to know the fractional approach
to steady-state under the following conditions, choosing any
consistent units for the Variables.

t=l VH =1

L=l VL =

H= m=l

For these conditions, E = 1, G = 2- and Z = 0.5. Figure 2
shows that Y would be 20%/o of its final steady-state value
after t = 1. If, however, VH and VL were each equal to 0.25
instead of unity, Z would equal 2. Figure 2 shows that I
would equal 80% in this case at t = 1.

Discussion:
The same technique has been used to develop similar ex-
pressions for three, four, five and six stage mixer-settlers.
These solutions are no more complicated than those described
in this paper but there is considerably more algebra to do.

Equation la and 2a can be solved simultaneously for x,
as a function of time, using the analog computer wiring dia-
gram shown in Figure 3, but it is not as much fun and the
students learn more electronics and use less of their rusty
sophomore mathematics.


Literature Cited:

1. Treybal, R. E., "Liquid Extraction", McGraw-Hill, (1963).








A PROJECTS LABORATORY FOR JUNIOR .CHEMICAL ENGINEERS*


Sami Atallah
Associate Professor, Department of Chemical Engineering
Tufts University
Medford, Massachusetts


-------------------------------- -----------------

Abstract: This paper describes the operation of an under-
graduate chemical engineering laboratory which is in addition
to the usual unit operations laboratory but is not a substitute
for a research thesis. Small groups of students are assigned
different interesting projects and they are required to search
the literature, build apparatus, keep a record of their labor-
atory activities, and present oral and written reports. This
laboratory achieves several objectives but best of all, it
provides an outlet for the students' creativity and talents.
------ -- -- ------------- ---- -------

If God were to prepare an addendum to his ten command-
ments, this addendum being intended for graduating en-
gineers in general and chemical engineers in particular,
it would probably read something like this:

Thou shalt be well founded in the basic fields of
mathematics, physics and Femistry but

Thou shalt perform engineering work and not be a
pure scientist.

Thou shalt be creative.

Thou shalt have the basic tools to tackle a new
problem and be able to solve it.

Thou shalt have the ability to enlist the help of
others who art more knowledgeable than thou art.

Thou shalt have the ability to use other sources and
devices such as a library or a computer and if
thou shalt find no help, then thou shouldst



Presented at the A.I.Ch.E. annual meeting in Boston, Decem-
ber 1964. Publication release was obtained by the author.







proceed on thine own initiative with confidence
in thyself, and when thou findest a solution,
thou shalt be able to communicate either orally
or in writing whatever thou hast found to thy
colleagues, supervisors and the public.

According to Mayer (1) and Moulton (2), the chemical in-
dustry would say "Amen" to this addendum, and "Hallelujah" if
the word "economically" were added to these commandments. And
in this spirit, about five years ago, the "Projects Laboratory"
was introduced in the normal junior year unit operations course
sequence. It had the following objectives:

1. To provide an outlet for the student's creativity and
talents.

2. To show the student that textbooks are not all there
is to know and thus teach him to use the library and
to search the technical literature.

3. To teach the student the methodology of conducting
an organized experimental study.

4. To familiarize the student with the basic machine
shop practices.

5. To encourage good oral and written presentations.

6. To show the wide variety of interesting problems that
a chemical engineer can get involved with because of
his versatile wide background.

Before presenting the mechanism and mode of operation of
this laboratory and the types of projects pursued, it would
be interesting to show where this laboratory falls in our four
year undergraduate curriculum at Tufts University.

In order to graduate from Tufts, an engineering student
must satisfy the requirements in forty courses of three or
four credit hours each. This requires the average student to
carry five courses each term.

The Freshman year is the same for all engineers. They
take two semesters of chemistry, physics, mathematics, graphics,
and English.

Only students desiring to continue in chemical engineer-
ing must make up their minds at the end of the first.year ....
During the sophomore year a student takes two semesters of
physical chemistry, electric circuits., mathematics, two elec-
tives in the humanities or social studies, a third semester








of physics and his first course in .chemical engihebring stoi-
chiometry.

The Junior and Senior year programs are shown below:

Junior Year
*Unit Operations I 4 *Unit Operations II 4
*Thermodynamics I 3 *Thermodynamics II 3
Organic .Chemistry 4 Chem. Analysis 4
Applied Mechanics 3 Applied Mechanics 4
Hum. or Soc. Study 3 Hum. or Soc. Study 3

Senior Year
*Chem. Eng. Lab. 3 *Chemical Technology 3
Technical Elective. 3 *Plant Design 4
Hum. or Soc. Study 6 Hum. or Soc. Study 6
Free Elective 3 Elective 3

The first projects laboratory is given during the first
term of the junior year as part of the unit operations course.
It is held one afternoon a week. These afternoons are not,
solely devoted to laboratory work. Two afternoons are devoted
to applied mathematics in chemical engineering. Our students
at that point seem to be weak in log-log plotting, graphical
integration, trial and error solutions and slide rule manipu-
lations. An afternoon is devoted to a lecture on the chemical
engineering literature and report preparation. Mimeographed
notes on the literature and sample long form reports (thesis
type) are distributed at that time. Another afternoon is de-
voted to machine shop practice. Occasionally a plant trip or
film may be scheduled. About eight afternoons are spent on
the project.

During the second term, students perform six experiments
in unit operations based on what they have learned during the
first term. These experiments are: distillation, extraction,
fluid flow, insulation testing, heat exchangers and boiling.

During the first semester of the senior year, a student
is given the choice of either doing a B.S. thesis (if he
qualifies with a C+ or better average) or taking the regular
chemical engineering laboratory course. This laboratory
course consists of six weeks of standard experiments in unit
operations i{humidification, drying, evaporation, filtration?
Dorrith.icener and flooding of packed beds). The remainder.
of the coursee is devoted to more sophisticated group projects.
In addition, the students are required to read early in the
term a major portion of Wilson's "Introduction to Scientific
Research" McGraw Hill, paperback edition, and they are quiz-
zed on it periodically and are expected to use what they learn



Courses taught by the department.







from it in their projects.


Operation of the Projects Laboratory:
In general, the laboratory is conducted in the following
manner. The class is divided into 'groups of two and the pro-
jects are assigned to or chosen by these groups. Within
three or four weeks a literature survey is made and a written
theoretical report is prepared by the group. In addition,
one member of the group presents it orally to the class in
8-10 minutes. He is graded by his classmates on: Clarity,
knowledge of the subject, information transfer, extemporane-
ousness, diction and poise. The judging sheets with class
comments are returned to the speaker. Th group then spends
the remainder of the term building an apparatus, running ex-
periments, obtaining data and correlating results. A final
group report (of the thesis type) is handed in at the end of
the term at which time the second member of the group presents
orally the experimental findings and is judged by the class.

Typical Projects:
The following is a list of projects recently assigned to
juniors:

1. Gas Bubbles in Liquids. Study the effect of inlet
conditions on the rate and size of bubbles of air in
water.

2. Recovery of Chemicals from the Lunar Crust. Attempt
to recover the water of crystallization of ores con-
sidered to be on the lunar surface.

3. Rocket Fuel Performance. The performance of a hobby
rocket solid fuel is studied in static firings.
Specific impulse, total impulse, average thrust,
mass ratio, etc., are to be found.

4. Desalination with Solar Energy. Construct a flat
collector and test its efficiency.

In all these projects, the underlined portion was the
title of the initial (theoretical) report. A diagram of the
proposed apparatus was prepared and checked by the instructor
and machinist for feasibility and economy of construction.
Generally, the students assembled the apparatus themselves.
Each group was required to maintain a laboratory data book
which was checked occasionally. The groups met often with
the instructor and sought help from the faculty of other de-
partments.

As one can see from the titles of these projects, they







are not equivalent to research theses. They do not contri-
bute new information to human knowledge (although the author
must confess that he and other faculty members have occasion-
ally used the projects laboratory to test a few research
ideas) but they leave the student with the impression that
he is doing research.

There was no problem in searching for project topics.
Summers spent in an industrial research laboratory, technical
journals, books, other faculty members and the instructor's
current research interests have been the usual sources of ideas.

The students' reaction has been gratifying. In a ques-
tionaire given at the end of the first year that we started
this laboratory, all students indicated that it should be con-
tinued. Some felt that they needed more time. Many worked
after hours and during vacations. We feel that the projects
laboratory encouraged qualified students to choose a B.S.
thesis during the senior year and to do a better job on it.
We feel that it has contributed to the increase in the number
of our students going on to do graduate work (43%/ over'the
past five years) and in general we are sure that this lahora-
tory has made better chemical engineers out of our students.


Literature Cited:

1. Mayer, M. W.. "Industries' Views of Current Chemical En-
fineering Education", paper delivered at the A.S.E.E.
annual meeting, June 1963

2. houlton, R. W., The Trend, 16:No. 4, 4, (Oct. 6, 1964)








UNDERGRADUATE USE OF ANALOG COMPUTERS*


V. E. Schiesser
Associate Professor, Department of Chemical Engineering
Lehigh University
Bethlehem, Pennsylvania




Abstract: Types of problems that can be solved by under-
graduates employing analog computers are examined.


Introduction:
The availability of small electronic analog computers
for use by relatively large numbers of students has brought
about significant changes in undergraduate education in the
Department of Chemical Engineering, Lehigh University. This
paper is a brief account of our experiences in the use of
analog computers in undergraduate education during the last
five years.

Operating Procedure:
Our experience with analog computation.began in 1960
with the purchase of an Electronic Associates, Inc. TR-10 20-
amplifier computer. The initial use of this computer was
somewhat limited because of the lack of programming experience
of the faculty and the unavailability of removable patch pan-
els (i.e. it was necessary to patch a problem directly on the
face of the computer and then remove it before another problem
could be patched). When the manufacturer did finally provide
removable patch panels, the demand for the computer increased
sharply to the point where it was no longer adequate. The
quantity of computing equipment has increased continually to
meet the growing demand and it is anticipated that this trend
will continue for some time in the future, although our future
purchases may be determined to some extent by the recent de-
velopments in digital simulation.

At present 32 patch panels are available for use by any
student in the University. The analog computer laboratory is
open 4 or 5 days a week with supervision and is run on an open-



*Presented at the annual A.I.Ch.E. meeting in Boston, Decem-
ber 1964, Publication release was obtained by the author.









shop basis. A student may obtain a patch panel, cords, bottle
plugs and any other related equipment, patch his problem and
run it on a computer without completing any paperwork. Upon
completion of the problem, the student returns the panel and
components to the central supply area in the laboratory.
Patch panels may be retained for further computation for a
period of time which is determined primarily by the current
demand for additional patch panels to.start new problems.
When this time during which a patch panel may be retained be-
comes too short, additional patch panels are purchased.

Undergraduates are encouraged to use the analog computer
routinely in the solution of assigned problems. The facili-
ties of the computer.laboratory are used extensively in under-
graduate and graduate courses in kinetics and reactor design,
and process dynamics and control, an undergraduate seminar in
mathematical modeling, an introductory sophomore course in
analog and digital computation and a senior projects course.
The Departments of Mechanical Engineering, Electrical Engineer-
ing and Psychology are presently using the analog computer
laboratory and it is anticipated that several other depart-
ments will do so in the near future.

The Advantages of Analog Computation:
Experience has indicated that the following advantages
can be attributed directly to'the availability of small analog
computers:

1. Undergraduates have an opportunity to gain valuable
experience in the mathematical modeling of physical systems.
In deriving the system equations, they must make use of the
basic principles of physics, chemistry and engineering. It
is usually necessary for them to decide which phenomena must
be taken into consideration in their analysis in order to ar-
rive at a realistic model and which phenomena can be dismissed
as unimportant in contributing to the performance of the sys-
tem so as to keep the model within manageable proportions.
The contribution of the analog computer is, of course, that
it enables the student to do something useful and practical
with the model after it has been formulated.

2. The programming of an analog computer, in common
with all computer programming, requires careful problem form-
ulation and attention to detail. On the other hand, the com-
puter enables the student to essentially by-pass the details
of mathematical analysis required to solve the model. He does
not become engulfed in complex mathematical manipulations but
instead can proceed directly to the solution. The analog com-
puter is, of course, particularly valuable for nonlinear prob-
lems for which there are no known analytical methods of solu-
tion. The effects of system nonlinearities are easily assess-








ed and the limitations of a linearized analysis are soon ap-
parent.

3. The student can experiment with the modeled system
and investigate a large number of alternatives in a short per-
iod of time. In a sense he can optimize the system by trial-
and-error experimentation on the computer.

It is therefore not surprising to find that most students
are analog computer enthusiasts, particularly the better stu-
dents who are strongly oriented towards the analytical approach
to engineering problems.

An Example:
The following simple problem in chemical kinetics illus-
trates the procedure for programming a problem for analog com-
puter solution

kl k2
A --> B C

Compute the concentration of A, B and C as a function of time
when initially, A = 1 (mol fraction), B = 0, C = 0*. Consider
three cases: k = 0.1, kg = 1; k, = 0.25, k2 = 0.25;
ki = 1, k2 = 0.1 (sec-).

1. State the equations, initial conditions and parameters.
The equations should be arranged to give the highest order de-
rivatives explicitly.

1.1 First-order kinetics

-dA/dt = kA

dB/dt = kiA k2B

dC/dt = k2B



*We refer to this as the "Piel's Beer" problem
ki k2
Green beer -- Piel's Beer -- Stale beer

The objective then is to catch the "Piel's Beer at its
peak."








1.2 Second-order kinetics


-dA/dt = kiA2

dB/dt = kA2 k2B2

dG/dt = k2B2

Initial conditions: A(0) = 1, B(0) = 0, C(0) = 0
Parameters: I ki = 0.1, k2 = 1
II ki = 0.25, k2 = 0.25
III 'k = 1, k2 = 0.1

2. Magnitude scale the equations. The output of any
operational amplifier in the computer .shbuld not exceed the
reference voltage ( lOv in the case of an EAI TR-10 or TR-
20) or be so small that the computing accuracy is poor. It
is therefore necessary to scale all of the dependent vari-
ables of the equations so as to keep the voltages represen-
ting these variables in the proper range. In this case
scaling is quite easy since the dependent variables are all
mol fractions with a maximum value of 1 which immediately
suggests a scale factor of 10. If square brackets I ] are
used to represent a scaled variable (i.e. a voltage in the
computer), the original equations can be scaled as:

First-order Kinetics

-d[10A]/dt = ki[10A (1)

d[10B]/dt = k,[10A] k [10B] (2)

d[lOC]/dt = k[1OB] (3)

Second-order Kinetics

-d[10A]/dt = kI[10A 2/10 (4)

d[10B]/dt = k,[10A12/10 k2[10B 2/10 (5)








d[lOC]/dt = k2[lOB]2/10 (6)


[loa(o)] = 10

3. Draw the computer circuit diagram. The circuit for
the solution of Equations 1, 2, and 3 is given in Figure 1
and for Equations 4, 5, and 6 in Figure 2.

4. Time scale. In this case the setting of potentio-
meters 1 and 2 (i.e. the values of k, and k2 respectively)
are reasonable and therefore time scaling is not required.
Thus problem time and computer time are the same. If the
rate constants for Case I had been ki = 0.001, k2 = 0.01,
potentiometers 1 and 2 could still be set to 0.1 and 1 re-
spectively and the computer would run 100 times faster than
the physical system. On the other hand if the rate constants
had been k2 = 100, k2 = 1000, potentiometers 1 and 2 could be
set to 0.1 and 1 respectively and the computer would, run 1000
times slower than the physical system. These considerations
can be generalized: The inputs to all integrators can be
changed by a constant factor in order to arrive at reason-
able potentiometer settings and loop gains without changing
the solution. The ratio of problem time to computer time
equals this constant factor. In a sense then, time scaling
takes care of itself quite naturally.

5. Static check. A static check is analogous to a
hand calculation used for debugging a digital computer pro-
gram. It is indispensable for the successful operation of
an analog computer, particularly when the amount of time
each problem is on the computer is to be minimized. The
static check will detect most programming errors and computer
components which are not operating properly.

In the present case, the following voltages should ap-
pear at the outputs of the indicated amplifiers before the
computer is put into operation:

Amplifier Output
1 +10v
2 0
3 0
4 0





Figure 1. Analog Computer Circuit
for Linear Kinetics.


Figure 2. Analog Computer Circuit
for Nonlinear Kinetics.






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I I I I I I I I I I l l


HFA-tH:1fH dTHT:


t I f i I a[li I il l I 1 Il lij


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I I I I I I I I .l I I I I 1 1 I ' "


., ., ., . ... o. . . . I I


1-N


II I 1 II 1 I


iI 1


JEI IIIL
^ _I-_ _ :_ _ -I I
[7 __ I I I I I [ I I A I I I I I I I I i i I I I
L L I I I I ! ! ! !!:! ! !\ I : : I I I I I: I I t I


S : i



__'. '


llallltl]lililll


. . . v -


--L' '' C-U- I- e -- t


_ I .a I l i J I L li a r l i a r n e r s


I I I I I I I I I I I ii I i~i I I r I I I I I II I I I ~ ~-


CL~i


--+-Ll


- 1--


---


0"1


8'0


9'0


V"O


i:


._ 4 .
-E:4-i, ;p ;::
::::_p[ ini:;I-I_


































































O'* 8g0


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29







I F
I I I Ii.

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Ei'
u -i T^


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b::=:::5T:: -:-i ::::,::,
--Ely


l l I I I I I 1 1 I I IF


Tv


OT


KL-;
7LZ

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A more complete check can be made by artificially introducing
an initial condition into each integrator and by summing the
inputs used to form the highest-order derivative in each
equation (the inputs to amplifiers 1 and 2 in this case).
This sum can then be checked against the values of the high-
est-order derivatives computed directly from the system
equations.

6. Run the problem and document the results. Since
it is possible to rapidly generate a large number of solu-
tions in a short period of time, it is essential to document
these solutions as they are obtained. The solutions to the
present problem as they appeared on the xy plotter are given
in Figures 3, 4 and 5.

This kinetics problem is especially simple from the
point of view of magnitude and time scaling. The author
has put together several small linear and nonlinear prob-
lems with detailed solutions which illustrate the more typi-
cal complexities of scaling. These problems are available
upon request.








DEPARTMENTALIZED CURRICULUM BASED ON CHEMICAL CHANGE*


William H. Corcoran
Professor of Chemical Engineering
California Institute of Technology
Pasadena, California


-------------------------------------------------------------

Abstract: Departmentalized curriculum based on chemical
change is defined. Then, better building upon high-school pre-
paration to keep a 4-year undergraduate program in chemical
engineering is discussed. Emphasis is placed upon the need
to prevent proliferation of courses and work in the presence
of the continual acceleration in the growth of knowledge.
Argument is given in favor of teaching principles and develop-
ing abilities to think, with the belief that the best type of
men will aggressively and successfully continue to treat their
own technological gaps. The need for continual analysis of
curricula is reviewed. Suggestions are given for improved
teaching of chemical principles in the early part of the chem-
ical engineering program and for a new attack to chemical en-
gineering design in the senior year.
-------- ---- ------------------------------

In a discussion of a departmentalized curriculum in chem-
ical engineering, or any branch of engineering, the first
thing to consider is what is meant by departmentalized curri-
culum relative to a general engineering curriculum. There
could be many definitions, but one choice would distinguish
between the two by noting that the departmentalized curriculum
would provide the opportunity for the B.S. graduate to be pre-
pared properly for specialized or semi-specialized employment
after four years of undergraduate education. A departmental-
ized curriculum based on chemical change would have 15 to 20
per cent of the program devoted to appropriate courses in
chemistry. The generalized curriculum would not give signi-
ficant specialized preparation, and at least another year of
study would be required to provide the student with the neces-
sary professional tools to begin specialized employment.

After one has considered the meaning of departmentalized
curriculum, the next act could logically be the asking of why
be concerned about that curriculum when a generalized four-



*Presented at the annual A.I.Ch.E. meeting in Boston, Decem-
ber 1964. Publication release was obtained by the author.








year program with one or two years ofj:.graduate study in pro-
fessional subjects would certainly give a sound training for
the first professional degree. The response is threefold:

1. We are less stimulated to significant changes in cur-
ricula if we are just allowed to extend course work.
The four-year program for the first professional de-
gree demands significant and continuous revision in
order to provide the most up-to-date training and
education in a restricted time schedule.

2. Tuition charges in at least the private schools con-
tinue to rise. For example, in 1965-66, the yearly
tuition at the California Institute of Technology
will be $1800. The increase of one or two years in
the program for the first professional degree adds
significant educational expenses for tuition and
other charges.

3. Space needs are always critical in universities. The
addition of 25 to 50 per cent in curriculum time means
increased facilities. Should money be put into that
area or should it be put into efforts on improved
teaching, better linking of research and teaching,
and related fields?

The professional training of a chemical engineer is prob-
ably less tractable in the framework of a generalized curri-
culum for preparatory work than for other engineering profes-
sions. The chemical engineer is marked by his particular
concern with the economic control of chemical reactions for
the benefit of mankind in either defense or non-defense work.
As a chemical engineer, and not just as an engineer, he must
know about the subtleties of chemical reactions that are not
just simply handled by writing chemical rate equations in com-
binations with transport equations to design chemical reactors.
For example, if he is to maximize his ability to program the
best type of knowledge into a computer, it is now desirable
and becoming necessary that he have some understanding of the
movements of electrons in the framework of chemical reactions.
He cannot afford to wait too long in his college work to get
the background that will allow him to think in chemical terms.
That background would include a significant amount of train-
ing in physical chemistry, chemical kinetics, inorganic chem-
istry, and organic chemistry. If that work were left in the
main to the latter professional part of a training program,
more than a year of work after a four-year program would be
necessary for the chemical engineer. The man would be well
trained, no doubt, but in consideration of time and money
would the gain be necessary relative to the needs of the em-
ployer or to those of the man himself in any subsequent gradu-
ate work?








A departmentalized curriculum to prepare a man for spec-
ialized professional performance after four years of under-
graduate work appears to be a continuing possibility. The
possibility seems very desirable in these days of increasing
tuition and of increasing ability of entering freshmen. Rather
than to think that we must increase our training at the under-
graduate level and move toward a generalized engineering pro-
gram in that period of development, we should look closely at
our educational techniques and be willing to make significant
changes in our teaching program in order to provide an educa-
tion in a specialized way in four years. There is a tendency
today to believe that as progress adds to our armamentarium
of technical ideas and methods at a high rate we must communi-
cate a large portion of this fund of knowledge to the student
before he receives even his first degree. Instead of that
concern we should emphasize the development of the thinking
abilities of the student. We should be more selective in our
teaching and spend more time on principles and less time on
technological details. The principles can certainly be taught
in the framework of technology, but the technology really
should serve mainly as a matrix for the development of the an-
alytical abilities of the students. As a student develops his
thinking powers and interest in his own self-education, he
should experience no particular difficulty in continually fill-
ing in the crevices in his knowledge with technical details
that are evolving day by day.

We have not really exploited the abilities of freshmen
entering from the many excellent high schools in the United
States. Even though the students have been exposed to im-
proved courses in mathematics, physics, and chemistry in the
high school, we have not done enough in providing those courses
with an engineering flavor to exploit fully the opportunity to
optimize the preparation of the man who is to become a fresh-
man in an engineering college. The lack of integrated effort
between engineering educators and high-school departments of
science and mathematics is a challenge that is especially di-
rected to us who favor the concept of a departmentalized cur-
riculum based upon chemical change.

The simplest way to focus thoughts on curriculum is to be
specific, and so a four-year program for the near future is
proposed which would continue to provide the high level of
education we have today, would accommodate for the increasing-
ly exciting additions to knowledge and methods, and would al-
low the graduate from that program to work for any chemical
industry and perform well in operations and possibly develop-
ment work or enter graduate work in chemical engineering in
the best schools in the United States. Humanities training
would be about 20 per cent of the curriculum and electives a-
bout 10 per cent.








Table 1 shows the proposed curriculum. The data are
shown for a quarter system with three terms in the academic
year of 9 months. The units noted in the table represent the
total number of class and home hours per.week assigned to the
different subjects. Conversion of units to semester hours is
accomplished by multiplying by 2/9. Over-all percentages of
time devoted to a given area of effort are more meaningful,
and are shown in the summary Table 2. Table 3 gives the cur-
rent program at the California Institute of Technology, and
in Table 4 there is a summary of the details in Table 3.

A comparison of the proposed and current curricula shows
two major changes. First, the new proposal calls for a new
course in chemistry for the first and second years. It would
be a systematized integration of physical chemistry, inorganic
chemistry, and organic chemistry in place of the current se-
parate courses in quantitative chemistry, organic chemistry,
and physical chemistry. Sufficient progress has been made in
the development of quantitative organic chemistry that such
integration seems possible. Not only would the course be
taught to chemical engineers, but strong consideration should
be given to its inclusion in all engineering and science courses
to improve the scientific literacy of the undergraduate. The
second major change is the proposed senior course in chemical
engineering design. In the suggested curriculum, the student
at the end of his junior year would be well trained in many
aspects of applied mathematics and able to move more rapidly
in the parts of design work concerned with applied mechanics
than if the applied mechanics had been taken at a lower level
of training. Therefore there is some logic in suggesting a
significant course in chemical engineering design which would
bring together stoichiometry, industrial chemistry, economics,
applied mechanics, and strength of materials with the student's
knowledge of transport phenomena at a given time in the senior
year.

Electives would be available for the senior year in areas
such as electrical engineering, applied mechanics, and other
technical fields. The electives courses would be selected ac-
cording to the developing interest of the student relative to
graduate school or industrial work. In the suggested curricu-
lum, significant education in principles of chemistry, physics,
mathematics, and engineering would be allowed. Only parts of
current technology would be presented to the chemical engineer
inhis first four years, and they would be more concerned with
explaining principles than with just technological knowledge
for its own sake. The student would be expected to have pre-
pared himself, however, to think clearly in the attack of new
problems and to have the courage to work on these problems even
in the face of failure. His technological development would
be a continuing part of his graduate and subsequent profession-
al study or of his professional work alone.








In summary,.a seven-point program is:suggested for in-
suring a high-quality departmentalized curriculum in chemical
engineering to be given in four years and to have chemical
change as the main basis for its: differentiationfrom general
engineering. The seven points are:

1. Continue with a strong effort to teach why. Worry
less about all technology and focus more on use of
new technology to illustrate old and new principles.

2. Build more carefully upon the greatly improved edu-
cation in high school.

3. Work to introduce more engineering thinking into the
problems and laboratory assignments in high-school
science and mathematics.

4. Introduce more engineering problems and attitudes in-
to the lower-division college courses in mathematics,
physics, and chemistry, and integrate that effort
with the upper-division engineering courses.

5. Introduce a new two-year chemistry course in which
physical chemistry, inorganic chemistry, and organic
chemistry have been systematically combined in place
of the often-used three-year program of separate gen-
eral and quantitative chemistry, organic chemistry,
and physical chemistry.

6. Introduce a third-year course in quantum mechanics
and statistical mechanics with carefully prepared
applications in the gaseous, liquid, and solid states.

7. Build more carefully in the fourth year on the advanced
principles developed in the first three years. Use
fewer units to cover work more intensively. Speci-
fically, introduce a new senior course in chemical
engineering design to encompass work in stoichiometry,
industrial chemistry, economics, applied mechanics,
and strength of materials.

The above steps as they pertain to college work are achievable
even in the presence of 20 per cent of the curriculum devoted
to Humanities and 10 per cent to electives.







Table 1


Proposed Four-Year Undergraduate Course in Chemical Engineering



First Year
(Same for all Science and Engineering Students)

Units per term
1st 2nd 3rd


Mathematics


Physics

Chemistry


English
History

Graphics


Calculus, Vector Algebra,
Analytic Geometry, Infinite
series ...................... 12
Kinematics, Particle Mechanics
and Electric Forces ......... 12
Physical Chemistry, Inorganic
Chemistry, and Organic Chem-
istry ........... ........ ... 12
English Literature 6
History of European Civiliza-
tion .......... ............... 5
Basic Graphics .............. 3


12 12


12


12
6


5 5


47 47


Second Year


History

Mathematics




Physics

Chemistry


History and Government of the
United States ............... 6
Calculus (functions of several
variables), Probability, Vector
Analysis, Group Theory, Differ-
ential Equations, Numerical
Analysis ..................... 12
Electricity, Fields, and Atomic
Structure .................... 12
Physical Chemistry, Inorganic
Chemistry, Organic Chemistry 12
Electives in Science and/or
Engineering ............... 9

51


6 6




12 12

12 12

12 12


9 9

51 51








Table 1. (Continued)


Third Ydar


English
Economics
Electrical
Engineering
Advanced
Physical
Chemistry

Chemical
Engineering
Chemical
Engineering
Mathematics


Advanced Literature *..........
Economic Principles and Problems
Electronics and Circuit Theory ...

Quantum Mechanics, Statistical
Mechanics, Applications to solids,
liquids, and gases (solid state
theory, plasmas, etc.)...........


Computer programming as applied to
chemical engineering problems ....
Chemical Engineering Thermodynamics,
Applied Chemical Thermodynamics ...
Engineering Mathematics, Mathemati-
cal treatment of problems in En-
gineering Chemistry and Physics,
Complex Variables, Series, Partial
Differential Equations, Boundary
Value of Problems, Integral Trans-
forms ........................


Units per term
1st 2nd 3rd
8 8 8
6 6
10 -


10 10


- 3 3


10 10






12 12

49 49


Fourth Year


Humanities Electives ..*..........
Public Affairs ...................


Chemical Transport Phenomena .............
Engineering
Chemical Unit Operations .................
Engineering
Chemical Kinetics .........................
Engineering
Chemical Chemical Engineering Laboratory ..
Engineering
Chemical Chemical Engineering Design (Process
Engineering design and study of strength of ma-
terials and elasticity applied to
process components in framework of
industrial chemistry and economics)
Electives Free Electives ...................


9 9 9
2 2 2
L2 12 -

- 12

9 -

- 9 9


Humanities
History







Table 2

Percentage Distribution of Time in Proposed Four-Year
Undergraduate Program in Chemical Engineering


Area Per Cent of Time

Mathematics 18.0
Physics 12.0
Chemistry 16.9
Chemical Engineering 21.4
Free Electives 5.0
Electrical Engineering 1.7
Science and Engineering Electives 4.5
Graphics 0.5
Humanities 20.0








Table 3


Current Undergraduate Course in Chemical Engineering
at the California Institute of Technology

First Year
(Common to all Curricula)


Units per term
Ist 2nd 3rd


Ma 1 abc Calculus, Vector Algebra, Analytic
Geometry ...........................
Ph 1 abc Kinematics, Particle Mechanics, and
Electric Forces ....................
Ch 1 abc General and Quantitative Chemistry .
En I abc English Literature .................
H 1 abc History of European Civilization ...
Gr 1 Basic Graphics .. ................


12

12
12
6.
5
3

50


12 12


Second Year


H 2 abc History and Government of the United
States .............................
Ma 2 abc Sophomore Mathematics ..............
Ph 2 abc Electricity, Fields, and Atomic
Structure ................. ......
Ch 41 abc Basic Organic Chemistry ...........
Ch 46 ab Basic Organic Chemistry Laboratory .
Electives in Science and/or Engineer-
ing* ........ .. .... .. ..... .......


L2 12
LO 4
6







Table 3 (Cont.)


Third Year


Units per term
1st 2nd 3rd


Advanced Literature .............
Economic Principles and Problems ...
Quantitative Analysis .............
Physical Chemistry .................
Physical Chemistry Laboratory ......
Chemical Engineering Thermodynamic._
Engineering Mathematics ...........


8 8
6
10
9 9
8
9 6
12 12

48 49


Fourth Year


Humanities Electives .............
Public Affairs .....................
Adaptive Design ...................
Industrial Chemistry .............
Applied Chemical Thermodynamics ....
Transport Phenomena ................
Chemical Engineering Laboratory ....
Unit Operations ....................
Electives*...... .. ............ .....


9
2
9
9


12



6-10

47-51


9 9
2 2


9
9
12
9 9
12
6-10 6-10

47-51 47-51


*If an electrical engineering course in electronics and cir-
cuit theory is not elected in the sophomore year, the adviser
will strongly recommend its inclusion in the senior year.


En
Ec
Ch
Ch
Ch
ChE
AM


7abo
4ab
14
21abc
26ab
63ab
95abe


H
ME
ChE
ChE
ChE
ChE
ChE


5abe
55
61ab
64
66ab
67ab
73








Table 4


Percentage Distribution of Time in Current Undergraduate
Program in Chemical Engineering at the California
Institute of Technology


Area
Mathematics
Physics
Chemistry
Chemical Engineering
Free Electives
Mechanical Engineering Design
Science or Engineering Electives
Graphics
Humanities


Per Cent of Time
18.5
12.3
20.3
16.4
5.1
1.5
4.6
0.51
20.5








A COMMON STUDIES CURRICULUM IN ENGINEERING*


Eric Weger
Chairman, Department of Chemical Engineering
Washington University
St. Louis, Missouri

-------------------------------------r------ ----- ---

Abstract: The common studies program in engineering at
Washington University is discussed from the viewpoint of the
chemical engineering curriculum. The courses in engineering
science and applied mathematics taken by all engineering un-
dergraduates are discussed first. The three courses speci-
fically oriented toward chemical engineering are described
and special emphasis is given to a new senior course which
has the objective of acquainting the students with process
design problems.



The Common Studies Program was put into effect in our
Engineering School at Washington University in the fall of
1962. The program is based on the belief that there is a
basic body of knowledge -- in science, mathematics, and the
engineering sciences which anyone in engineering should
possess regardless of their specialty.

The program consists of 79 units (or credits, a unit
being 1 semester hour of a course, or 2- lab hours) of courses.
Of the 79, 52 are taken in the Arts and Sciences College, -
the ones listed as "General" in Table 1. The other 27 are
taken in the field of Engineering Sciences.

As can be seen from Table 2, the curriculum for Chemical
Engineering in the first two years consist solely of common
studies courses. The one exception for Chemical Engineering
students is that they must take a more comprehensive second
semester of general chemistry as a prerequisite to the addi-
tional chemistry they have to take later on. This permits
a choice of a specific engineering field to be put off until
the student is well into his second year. We feel this to be
desirable, since the average incoming freshman usually has no
basis for making an intelligent choice in this matter.



* Presented at the annual A.I.Ch.E. meeting in Boston, Decem-
ber 1964. Publication release was obtained by the author.








One of the fields in'which we thought all engineering
students should obtain a comparable background was applied
mathematics. The details of the common studies program in
mathematics courses can be seen in Table 2. After three
semesters of Calculus given by the Mathematics Department,
the students begin their applied math sequence in the Engi-
neering School.

Two semesters of classical applied mathematics (called
Analysis I and II to appease the mathematicians) present or-
dinary and partial differential equations, vectors, complex
variables, operational methods, Fourier series, etc. The
techniques of "setting up" problems for mathematical solution
are heavily emphasized, especially in the first semester. The
course entitled "Numerical Methods" in the junior year is en-
tirely computer oriented. The students become acquainted with
computer techniques and simple programming. They are encour-
aged in all their subsequent courses to make use of the com-
puter whenever it might be of help to them. They punch their
own programs and batches are run off three times a day on
MWashington University's IBM 7072 computer. The Statistics
course completes the sequence.

,Among the other engineering science common studies courses,
the Thermodynamics course is probably of special interest to
Chemical Engineers. It is, of bourse, not possible nor desir-
able perhaps, to cover some: of;the specifically chemical en-
gineering aspects of thermodynamics in the core course. These
are taken up in the subsequent Elements of Chemical Engineer-
ing Course.

This brings us to the specialized Chemical Engineering
part of the program. First of all, there are, of course,
additional chemistry courses. I might say here that the po-
sition of these courses is not the optimum from our viewpoint.
This is especially so with respect to Physical Chemistry. We
would like to see this in the curriculum somewhere before the
senior year. However, we are constrained by the fact that the
Chemistry Department teaches it definitely on a senior level.
Consequently some of the physical chemistry topics which Chem-
ical Engineering students need for their senior design course
have to be taught by us.V:

There are actually1 nly three undergraduate courses
taught by the Chemical' Engineering Department. The first is
a Transport Phenomena course and its associated laboratory.
This is a full year course. The text by Bird, Stewart, and
Lightfoot is used in the lectures and the laboratory manual
by Crosby is followed to a large extent in the Lab. The next
Chemical Engineering curse is the Elements of Chemical En-
gineering course. 'Thi~ course is a very intensive one semes-







ter presentation of basic stoichiometry, some of the chemical
engineering aspects:of thermodynamics, and the fundamentals of
kinetics. To do all this in one semester, we have allotted 4
lecture hours and a-2- hour problem working session per week
to the course.

The course listed as Process Analysis and Design in the
fourth year of the Chqmical Engineering curriculum is being
taught for the first time during the 1964-65 academic year.
The objective of this course is to acquaint the student with
and give him some practice in the various aspects of chemical
process design. You must keep in mind that up to this point
the student has not been brought into contact with the tradi-
tional unit operations, reactor design, economics, or design
problems. The senior Process Analysis course must, therefore,
cover some of the important aspects of all of these topics.
We have also found it necessary to include some additional
material on vapor-liquid equilibria, estimation of properties
and mass and energy balances.

The design aspect of the course is being handled by taking
up a series of "ease studies". The present plan is to have a-
bout half-a-dozen of these. The problems presented to the
students will he progressively more sophisticated and diffi-
cult. As an example I might cite the first case study which
was handed out to our seniors. It is a project to produce a
"Preliminary Design and Economics Evaluation of Processes for
Producing Cyclohexane from Benzene". Both gas and liquid
phase processes are to be explored. The students, paired in
teams of two and three,have been given about four weeks to
come up with a Tentative Process Report. For this first pro-
ject they are being given a great deal of assistance in loca-
ting sources of property data, outlining of process flow
sheets, etc. In the later studies they will be expected to
do more of this themselves. We are planning case studies to
cover some of the newer aspects of chemical engineering, such
as biochemical and aerothermochemical engineering, as well as
the more traditional processes.

Concurrently with work on their case studies, the students
are attending lectures on continuous and stagewise processes,
reactor design, and process economics. One of the four units
assigned to the course is for one laboratory period or problem
working session per week. This period will be utilized during
the second semester for a ten week series of sessions on pro-
cess control (both lecture and lab) and also some additional
laboratory work with equipment such as distillation columns,
which were not encountered in the Transport Phenomena Labora-
tory.







The big problem in tlis 'cdurse is to present the material
in such a way that it ties in meaningfully with the material
in the basic and engineering sciences which the students have
had in their first three years. I think, on the basis of our
present limited experience, that so far we are succeeding.

In conclusion, I would say that I believe that we have
achieved as good a balance as is possible of analysis and syn-
thesis in our curriculum of chemical engineering courses tied
in with a common studies program. I feel that this curriculum
will be suitable both for the terminal Bachelors man as well
as.the prospective graduate student.





Table 1

Washington University

School of Engineering and Applied Science

Common Studies Program


General
English Composition 6
Chemistry 8
Physics 8
Mathematics 12
Electives*. 18

52

Engineering Sciences
Mechanics 6
Electrical Sciences 7
Thermodynamics 3
Engineering Analysis** 11

27


*Recommended courses include languages, literature, econ-
omics, history, sociology, psychology, philosophy, and
political science.
**Includes statistics and an introduction to digital com-
puters.







Table '2


Washington University

Curriculum in Chemical Engineering


FALL SEMESTER


Phys. 117 Gen. Physics
Math. 116 Calculus I
ECMP 101 Eng. Comp.
Humanity Electives
Phys. Ed., ROTC or Band


Math.
Chem.
Engr.


216 Calculus III
111 Gen. Chem.
213 Networks I


Engr. 231 Mechanics I
Humanity Elective
Phys. Ed., ROTC or Band


FIRST YEAR
Units


4
4
3
3-6
(1)

14-17


SPRING SEMESTER


Phys. 118 Gen. Physics
Math. 215 Calculus II
ECMP 102 Eng. Comp.
Humanity Electives
Phys. Ed., ROTC or Band


SECOND YEAR
4 Engr. 211 Analysis I
5 Chem. 112 Gen. Chem.
3 Engr. 214 Networks II
Engr. 219 Networks Lab.
3 Engr. 232 Mechanics II
3 Humanity Elective
(1) Phys. Ed., ROTC or Band

18


Units

4
4
3
3-6
(1?

14-17


3
5
3
1
3
3
(1)

18.


Tj
365 Num. Methods
320 Thermodynamics
312 Analysis II
367 Transport Phen.
373 Trans. Phen. Lab
241 Quantitative


THIRD YEAR
2 Engr.


Engr.
Engr.
Engr.
Chem.


325 Statistics 3

358 Elems. of Ch.E. 5
368 Transport Phen. 3
374 Trans. Phen. Lab 2
254 Organic 5


FOURTH YEAR


Engr. 477 Proc. Anal. and
Design
Chem. 421 Physical
Chem. 431 Physical Lab.
Humanity Elective
Technical Electives


3
1
0-3
6


Engr. 478 Proc. Anal. and
Design
Chem. 422 Physical
Chem. 432 Physical Lab.
Humanity Elective
Technical Electives


14-17


Total number of units: 133


Engr.
Engr.
Engr.
Engr.
Engr.
Chem.


4
3
1
0-3
6

14-17







THE UNDERGRADUATE CURRICULUM IN CHEMICAL ENGINEERING AT YALE*


Charles A. Walker, Professor
Wnd
John A. Tallmadge, Associate Professor
Department of Engineering and Applied Science
Yale University
New Haven, Connecticut

In a reorganization in July 1962, the Department of En-
gineering and Applied Science was created at Yale to replace
to a large extent the School of Engineering. The degree of
Bachelor of Science is offered by the Department as a part of
Yale College and degrees of Master of Science and Doctor of
Philosophy are offered through the Yale Graduate School.

In making the transition from a School to a Department
it was necessary to adopt the general requirements of Yale
College for the bachelor's degree. These requirements include
as one feature a program for distribution of studies. This
program of distribution requires every student to elect a full-
year course or two term courses in each of the following
fields: (1) English; (2) a foreign language at the second-
year level; (3) history; (4) social studies; (5) the natur-
al sciences; (6) philosophy; (7) a second course in natural
science or mathematics at the second-year level or a course
in literature in a foreign language. Since requirements (5)
and (7) are met automatically by students in Engineering and
Applied Science programs, this means that at least five year
courses of the twenty normally taken must be in fields other
than science, mathematics and engineering. The curriculum is
so arranged that as many as eight-courses may be taken outside
those fields.

Other features of the Yale scene should be borne in mind
in considering the curriculum pattern for chemical engineering.
One of the most important of these is the fact that most of
the students graduating from Yale College receive the degree
of Bachelor of Arts in the humanities. The Class of 1965,
for example, includes about 800 candidates for degrees in the
humanities, 110 for degrees in the natural sciences and 50
for degrees in engineering and applied science. Our students
thus carry on their engineering studies in a community in


*Presented at the annual A.I.Ch.E. meeting in Boston, Decem-
ber 1964. Publication release was obtained by the author a.
+ Current address: Imperial College of Science and Technology,
London, England.







which the humanities are dominant and this has both advantages
and disadvantages. Our students benefit from the high:quality
ofnteaching in the humanities and acquit themselves well in
competition with students in other majors. However, as Astin
[Science, 141, 334-8 (1963)] has pointed out, such an environ-
ment, characteristic of several of the Northeastern men's
colleges, has a decidedly negative effect on the student's
decision to pursue a career.in science and his conclusions
probably also apply to engineering students. That is to say,
it is a characteristic of Yale and other schools in this group
that a Freshman planning to enter the field of science is more
likely to be dissuaded from this choice than he would in other
schools.

A second factor which should be borne in mind is the ori-
entation of Yale students after graduation. Over two-thirds
of Yale graduates enter graduate or professional schools.
For example, 649 of the 956-members of the Class of 1964 en-
tered into advanced study and a sizeable number (280) of these
chose law and business schools. This trend of graduates to
the enterprising professions is also seen among graduates
from programs offered by the Department of Engineering and
Applied Science. Of the graduates of this Department in 1964,
more than one-fourth entered law schools and business schools;
the others were evenly divided between graduate school in en-
gineering and science and industrial positions.

In terms of size, the Department of Engineering and Ap-
plied Science with fifty-three faculty members is somewhat
smaller than the Department of English or the Department of
History and is about the same size as the Department of Physics.
In addition to the 50-70 undergraduate students per year re-
ceiving degrees, this Department also has in residence about
30 candidates for the degree of Master of Science and 120
candidates for the degree of Doctor of Philosophy.

This, then, is the framework within which the program in
chemical engineering is planned and administrated. It is a
program characterized by flexibility, a feature which is con-
sidered to be essential in view of the factors discussed above.

The Department of Engineering and Applied Science is not
formally broken into subgroups representing the traditional
fields of engineering nor into subgroups according to other
patterns such as the engineering sciences. The Department of
some 50 faculty members is small enough that subgroups may
not be as necessary as they would be in schools which have
many more faculty members. This is not to say that subgroups
do not exist. They form naturally according to common inter-
ests but they no longer have formal status. There is, for
example, a natural subgroup of faculty members with primary







interests in chemical engineering and the members of this
subgroup are responsible for activities in our field. Admin-
istratively, we make recommendations regarding our curriculum
and research programs to the larger group. In this regard,
we have the usual problems of communicating with our colleagues
whose work is based in physics-rather than in chemistry.

The Department offers some 50 term courses at the under-
graduate level in the fields of applied mathematics, chemical
engineering, electronics, mechanics of solids and structures,
mechanics of fluids, control systems, communications, solid
state science, etc. These courses are listed by level in
Table 1 in a manner similar to that used in the catalog.
Each student is required to build a four-year program on the
following general scheme:

3 terms of physics
3 terms of mathematics
2 terms of chemistry
16 terms of courses in engineering, applied science, science
10 terms of distributional requirements
6 terms of electives

The selection of courses in engineering and science must
be on a basis to form some coherent pattern but a high degree
of flexibility is allowed. Such a system requires close con-
sultation between the student and his faculty advisors in or-
der to insure that the course plan is in fact a coherent one
and that the student is aware of requirements for admission
to graduate schools and of the requirements of industry and
government for various kinds of positions.

Turning now to the specific case of chemical engineering,
it is expected that the majority of students interested in
this field will plan a curriculum in accord with the pattern
shown in Figure 1. However, we expect that some students will
vary this pattern by substitution within the block of E. and
A. S. courses. For example, a student with strong interests
in applied mathematics or control systems or physics of fluids
could replace some of the suggested courses with others if he
has a strong reason for doing so.

The greatest degree of flexibility comes about, however,
with the eight terms of electives, two of which must be in
engineering or science. The student planning to enter gradu-
ate school would be urged to elect courses in mathematics,
computers, physics of fluids, or a senior project in chemical
engineering. Those planning to enter industry directly might
find it advisable to elect courses in economics or data pro-
cessing or personnel administration.







Thus we feel that we have a core curriculum which can be
tailored to the requirements of students with a variety of in-
terests. It will be recognized, of course, that other insti-
tutions have similar programs. Hence we present this program
not as something new and different but simply as a curriculum
in chemical engineering which seems to us to fit the raquire-
ments of the Yale students of today.

Many aspects of this approach are present in the interim
programs developed for the Classes of 1966 to 1968; the elec-
tive flexibility has applied to all clas:sesfrom 1962 on since
it was adopted for undergraduate engineers in 1959. However,
as the Class of 1969 will be the first to follow this program
for all four years, it is not possible to attempt an overall
evaluation of this curriculum now.


Figure 1

A Suggested Pattern in Chemical Engineering

Term

1 2 3 4 5 6 7 8
1 I
Applied Manentum Separa- Heat Reaction
Mathematics Mathe- and Mass tin- Trans-
I matics Transport Processs fer

Digital
I Physics Computa- Thermodynamics Design
i tion I
SI ____________I
r II
General Organic Physical EAS EAS
Chemistry Chemistry Chemistry elective elective

I I t

English Kistory Philosophy Elective
i I \ *i


Foreign Social ,
Language Science Elective Elective
____________________________________________ _________________________________________________ ___________________________________________________







Table 1


Term Courses Offered by the Department of
Engineering and Applied Science.

Sophomore or Junior Level
Digital Computation
Thermodynamics
Mechanics of Deformable Bodies
Linear Systems
Physical Electronics
Engineering Analysis
Applications of Ordinary Differential Equations
Applications of Partial Differential Equations
Applications of the Complex Variable
Electronic Circuits
Advanced Networks
Advanced Mechanics
Momentum and Mass Transport
Chemical Thermodynamics
Communications, Language, and Machines
Physical Metallurgy
Solid State Science


Senior Level
Case Studies in the Interaction of Engineering and
Society
Probability and Stochastic Processes
Numerical Analysis
Applied Discrete Mathematics
Digital Systems
Quantum Mechanics
Fluid Mechanics
Heat Transfer
Energy Conversion
Structural Mechanics
Elasticity
Electric and Magnetic Fields
Nonlinear Magnetics
Communication Theory
Control Theory
Separation Theory
Reaction Kinetics
Engineering Design
Modern Experimental Techniques
Special Projects


Number
lOa
22a
23b
26a,27b
29b
30a
30b
31b
32a
35a
38a
39b
42a
43b
45
48a
49b


Number
50a,51b

56a
47b
58a
59b
60b
61a,62b
64a
65b
68a
69b
70a
72a
74a
76a,77b
81b
83b
86a,87b
88a,89b
99a,91b









SOLUTION TO THE.PREVIOUS PROBLEM


which appeared in 3: No.1, 33 (1964)


Restatement of Problem:

Consider an infinitely long,, counterflow, water to water,
heat exchanger. Making appropriate.assumptions, prove that
the temperature pinch must occur at the inlet of the stream
with the larger flow rate, and nowhere else along the exchanger.


Solution:

W T
Ta <: ---------- TI




t2 t I,
T





Let us say for the moment that the pinch can occur at
some other location such as shown at the dotted line in the
diagram. Call this pinch temperature T. For convenience,
let all temperatures be absolute (so that they will all be
positive). 'Finally, let W be the larger flow rate, and w the
smaller, so that W >w.

Since each stream consists of water, it is reasonable to
equate the two heat capacities. An energy balance to the
right of the pinch point then gives

W(Ti T) = w(tj T) (1)

or

Ti T w
t, T V

W
But 0 < < 1. Combining with Equation 2 yields


t, T T tI







From this last relationship, either (Ti T) < (ti T) and
both (T. T) and (ti T) are positive, or (T T)<
(T t) and both (T T1) and (T ti) are positive.

Consider the first alternative. Since (TI T) is
positive, TI> T. This means W cools down as it passes
through the exchanger, and so W must be for the hot stream.
(To accept the contrary would obviously violate the Second
Law by having a cold stream cool down further by thermal
contact with a hot stream,) However, canceling T from the
aforementioned inequality which is (TI T) < (t1 T) yields
Ti < ti. This means W is for the cold stream. Obviously,
V cannot represent both the hot stream and the cold stream.
Therefore this first alternative is impossible.

Consider now the second alternative. Here (T Tj) is
positive, so T > TI. This means V warms up as it passes
through the exchanger, and so W must be for the cold stream.
(Again, accepting the contrary would violate the Second Law.)
However, subtracting T from (T T,) < (T tI) which is the
inequality for this alternative, yields -Ti< -ti or TI> ti.
This means W is for the hot stream. Again, W obviously can-
not represent both the cold stream and the hot stream. There-
fore this second alternative is also impossible.

Since there are only two alternatives, and both are im-
possible, the entire situation is impossible. In other words
we cannot say the pinch occurs at some location along the
exchanger. In fact, it cannot even occur at the left-hand
extremity of the exchanger since we could always write Equa-
tion 1 for an energy balance to the right of the pinch.

The pinch must therefore occur at a location to the
right of which we are unable to write an energy balance.
Only the right-hand extremity of the exchanger qualifies.
In other words, the pinch must occur at the inlet of the
stream with the larger flow rate.


R. L.







TRANSLATION OF TITLES


Spanish S. Botero

German H. Zimmer

Current Issue: Volume 3, Number 2, December 1965


Estimation of Random Error in a Derived Quantity. 3

Calculo del error "De Azar" en una cantidad
derivada.

Abschatzung von Random Fehlern in einer ab-
geleiteten Menge.


Approach to Steady-state of a Two Stage Mixer-
Settler Extractor. 11

Aproximacion al estado constant de un ex-
tractor de dos etapas tipo mezclador-sedimentador.

Annaherung zum "Steady-State" in einem zweistufen
"Mixer-Settler" Extractor.


A Projects Laboratory for Junior Chemical Engineers. 17

Un proyecto de laboratories para estudiantes de
tercer ano en ingenieria quimica.

Ein "projects labor" fur Studenten der chemischen
Ingenieurwesen vor dem Vorexamen.


Undergraduate Use of Analog Computers. 22

Uso de "analog" computadores en la universidad.

Gebrauch von Analogrechenmaschinen durch Studenten
erster Semester.


Departmentalized Curriculum Based on Chemical Change. 32

Program para el departamento de ingenieria
quimica basado sobre cambios quimicos.

Studienplan unter Einbeziehung verschiedener
lehrstiihle basierend auf "Chemical Change."







A Common Studies Curriculum in Engineering. 43

Un program de studios comunes en ingenieria.

Ein gemeinsamer Studienplan fMr Ingenieure.


The Undergraduate Curriculum in Chemical Engineering
at Yale. 48

Program de studios basicos para ingenieria
quimica en la universidad de Yale.

Studienplan bis zum Vorexamen fir chemisches In-
genieurwessen an der Yale Universitat.






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I


F
r-









i


























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p















































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