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0-169

 

 

Ala" Ai‘iALYTICAL ALQD NOz~iOGRAPHICAL SOLUTION FOR THE
OPTIMUM OPEPJiTIOl-J OF TEE} WATER-COOKED

EtE FRI GERAT I ON C Oil-DEN SER

BY

_. I
hafae l B awabe

A THESIS
Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Department of Mechanical Engineering

195M

In the water-cooled vapor-compression refrigeration unit the main
Operational costs, aside from labor, are for power and cooling water.
The relationship between these two is such that, for any given
conditions, the amount of power needed would be inversely proportional
to the amount Of cooling-water used. The more water used, the lower
would be the condensing temperature and consequently less power for
compression would he required, if water is expensive and the amount of
water used is small the condensing temperature would be high and
obviously more power would be needed for the compression of the
refrigerant. If one thinks in terms Of the cost of purchasing the
water and power, the above relationship would immediately suggest that
there must be some Optimum condition at which the total cost Of Operation
is a minimum. That is, given the cost of water and the cost Of power,
a water-cooled refrigeration unit Operating at some suction temperature
would have to Operate at a certain condensing temperature which is the
most economical for these conditions. The amount of water and the
amount of power to be consumed by this unit must balance each other so
that the resulting total cost is a minimum.

The paper prOposeSa completely analytical solution for the Optimum
condensing temperature taking into consideration all the variables
involved. In the derivation of the equations two main assumptions were
made: 1) compression is isentropic, 2) the heat to be removed by the
condenser is the refrigeration-effect plus the theoretical energy added

to the refrigerant by compression. An important part in the derivations

is the proof that, for any suction temperature, the relationship
between the condensing temperature and the compression required is
linear. The solution proposed is in terms of temperatures rather than
pressures and so it is applicable to more than a single refrigerant.
It is shown that the refrigerant used has very little effect on the
sOlution for the optimum condensing temperature. A comparison of
the solution prOpOsed with different methods and solutions for the
same problem by various authors shows its advantages and simplicity..
In addition the paper also presents a nomographic solution for
the Optimum condensing temperature. The nomograph is simple to use
and can be used for any water-cooled compression refrigeration unit
using any of the common commercial refrigerants. This nomograph is
particularly convenient for use by Operators of refrigeration

equipment who do not have a technical education.

References:

Nacintire, H.S.; Egiziggzaiing_Enainaaning, lst rev. ed.
John Wiley & Sons, Inc., New York, 1940, pp. 181-182

Buehler, L.; Economical Use of Condenser water for Ammonia
compression Refrigeration System, Ice and Refrigeration,
Vol. 112, No. 1 (January 1947) po.17

Boehmer, A.P.; Condensing Pressures for Air Conditioning,
Heating. Pipinggand Air Conditioning. Vol. 18, Nos. 9, 10
(September, October fil946]pp.79,94.

I.

II.

III.

Iv.

TABLE OF CONTENTS

 

INTRODUCTION .

DERIVATION OF THE EQUATIONS

0

THE NOMOGRAPHIC SOLUTION .

DISCUSSION AND CONCLUSIONS .

APPENDIX

A. Graphs — Compression vs. Condensing

Temperatures . . . .

B.

BIBLIOGRAPHY .

Table - Values for the Factor m

12

21
26
27

I. INTRODUCTION

The cost of Operation of any industrial piece of equipment is of
prime importance to the engineer, and the problem of achieving Optimum
Operating conditions would usually require very careful analysis of en-
gineering economics. Often, the actual design of equipment must be
directly tied to the initial cost and to the cost of Operation during
the useful life of the equipment. The cost of operation itself is
usually a function of several variables which have to be adjusted so as

to result in minimum eXpenses.

In the water-cooled refrigeration units the main Operational
costs, aside from labor, are for power and cooling water. The relation-
ship between these two is such that, for any given conditions, the amount
of power needed would be inversely prOportional to the amount of cooling
water used. The more water used, the lower would be the condensing
temperature and consequently less power for compression would be re-
quired; if water is expensive and the amount of cooling water used is
small the condensing temperature would be high and obviously more power
would be needed for the compression of the refrigerant. If one thinks
in terms of the cost of purchasing the water and power, the above relation-
ship would immediately suggest that there must be some optimum condition
at which the total cost of Operation is a minimum. That is, given the

cost of water and the cost of power, a water—cooled refrigeration unit

Operating at some suction temperature would have to Operate at a cer-
tain condensing temperature which is the most economical for these
conditions. The amount of water and the amount of power to be consumed
by this unit must balance each other so that the resulting total cost is

a minimum.

The main purpose of this paper is to give a solution for the Op-
timum condensing temperature taking into consideration all the variables
involved. The literature on the subject is quite limited. The problem
has been attached by a few different methods (see reference 1, 2, M,

6 and 8 in the Bibliography), however, these references do not offer a
generalized, complete and accurate solution. The solution prOposed in
this paper is completely analytical and generalized so that it can be
applied to any water-cooled refrigeration unit using any of the most
commonly used refrigerants. In addition, a nomograph for the solution

of the derived equation is given, so thpt an operator of refrigeration
machinery without technical training can easily get a solution and adjust

for the prOper condensing temperature.

 

 

 

II. DERIVATION OF THE EQUATIONS

The actual vapor-compression refrigeration cycle differs from
the theoretical cycle mostly by the amount of the superheat of the
refrigerant in the evaporator and in the lines before entering the com-
pressor, and by the degrees of subcooling in the condenser. The calcur
lations on the cycle here were based on the following assumptions:

1) 10°F superheating of refrigerant before leaving

evaporator.

2) Additional 10°F superheat before entering compressor.

3) 10°F subcooling of the refrigerant before leaving
condenser.

M) The compression is isentrOpic.

The first three assumptions are not essential for the deriva-
tion. but the result obtained could be of more practical value to the
Operating engineer. It will be shown later that the deviations in the
actual refrigeration cycle from the theoretical one would have little
influence on the results obtained, however, the assumption that the

vapor compression is isentrOpic is quite essential.

As it has been stated in the Introduction the principal Opera-
tional costs in a refrigeration plant are those for energy and water
and hence the two quantities to be considered are the compression to
be done by the compressor and the amount of heat to be removed by the
condenser. It is clear that if the energy added to the refrigerant

by compression is known, then the total heat to be removed in the con-

denser is the refrigeration-effect plus this added energy in the
compressor. Some additional heat might be added by the friction in
the cylinders, however, this is usually compensated by the cooling

in the head of the compressor which is done by waste water from the
condenser. The amount of heat that might be added by friction, even
if no cooling of the head is provided for, is usually quite small when
compared with the total heat to be removed by the condenser and it can
be neglected here. If one wishes to include this quantity, which is
usually unknown and at best can only be roughly estimated, it can be
done without any difficulty. The quantity can be added as percentage
of the total heat to be removed and its inclusion bears no consequence

on the equations derived below.

Based on the above assumptions, calculations of the theoretical
compression required per ton-hour were made for different refrigerants
at various Operating conditions and the results were plotted as shown

in Figure l and Figures 1A—5A in the Appendix.

The plots show that. for any given suction temperature within
the range Of normal operating conditions, the rise in the energy re—
quired for compression is linear with the condensing temperature. These
results are quite important for the following derivations since they
show the increase in the energy required per one degree rise in the
condensing temperature is independent of the condensing temperature.

The calculations and the plots were based on suction and condensing

 

        

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temperatures rather than pressures in order to generalize the results

for more than one single refrigerant.

Now let,

A - Cost of power in cents per kw-h

B - Cost of cooling water in cents per 1,000 gallons

6 = Overall compression efficiency in %

tw1 = Temperature of cooling water entering the condenser
in OF

tW2 : Temperature of cooling water when leaving the
condenser in °F

t8 ; Suction or evaporator temperature in 0F

tc : Condensing temperature in 0F

c a Specific heat in Btu.per lb. per OF
m - The increase in energy required for compression
caused by raising the condensing temperature one

OF, in Btu.per OF per ton of refrigeration per hour

All the above quantities are usually known or measurable except

for tc’ tw2 and m. tc is the variable whose solution is sought. tw2
is dependent on tc and an assumption is needed here. An assumption of
5°F terminal temperature difference would be quite satisfactory and this

value is adOpted in this paper, from this tw . to - 5. Any other value
9

b

may be assumed or actually measured and then used in.the equation.

m values are nofiiing but the lepes of the lines in Figures lArSA.in the

Appendix. (Tabulated values for m, for different refrigerants and differ—

ent suction temperature, may be found in Table 1A in the Appendix.)

If tug condensing temperature is to be tc, then the theoretical
compression work necessary per one ton of refrigeration per hour is:
m(tc - ts) Btu, and with.the overall efficiency being e, the energy in-

put is:
m(tc — t3)
3h12( (37100)

 

Kw—h per ton per hour

The total heat to be removed by the condenser is 12,000+m(tc - t8)
Btu per ton per hour; from this the amount of cooling water required is:

12,000+ m(tc - ts) lbs. of water per ton per hour
cp(tw2 - twl)

 

Introducing the costs of electricity and water and substituting for tw

one gets the total cost of Operation for one ton of refrigeration per hour:

_, Am(tc - ts) [12,000...m(tc — t 85113

= cent er ton er hour
3m (e/ioo)“' (to - 5 - 1: VI} 8,330 1’ p

(l) C

 

 

cp was assumed to be equal to unity.

From thermodynamic considerations in order to minimize the overall
cost, 0, the equation should be differentiated.with respect to tc and

equated to zero.
mB(tc-5-tw1)A - [12,000+m(tc-tafls - o

(2) _9_C_ = m 4. '-
dtc 314-12(e/100)‘ 8.330 [£3th 5)]?

solving from this equation for to:

(3) tc = (twl+ 5)t0.o6fiV§_e (twl+ 54,12,000 - 2‘s)

 

The negative sign should be discarded since the condensing temperature

cannot be lower than twi+-5. It will be equal to twl+ 5 if water cost

3:0-

The final equation then, is:

 

u t .-.(t+ 0.06 ..
( ) c ”’1 5)+ “Ea (twf‘ 5+_1_g_1;_b9_g t8)

which is the solution sought for the optimum condensing temperature.

III. TEL NOMOGfiAPHIC SOLUTION

The construction of a nomOgraph with seven variables is not a
simple problem, especially when some of the variables have functional
relationships shch that they are not easily separable as in the above
equation (Eq. h). The details and proof of the construction of the
nomograph presented in this paper (Figure 2), will not be given since
fliis is not the primary concern of the paper. however, a brief outline
of the method might be of interest and that is given here.

The equation

tc = (th5)+0.o6u\E e (twig-5+l2m,000 — t8)

 

is separated in the following manner:

let K = 0.06 X 6 than.

 

to z (twf5)+KVtw]-'|-5+12,000 - t£3
, m

where K now is a variable coefficient of a certain function and it would
be one axis in the nomOgraph to be constructed from this reduced equa-

tion for tc. To get. this axis write _1_c_ - 0.06% and this type of rela-
A

V?

tionship can be easily represented nomographically by the "double"
Z-chart method. In Figure 2, K is the central axis and it is not
graduated since its value is not required and the K axis serves only

as a pivot-line for the continuation of the nomograph.

10

Now, if constant values are assigned to m and t8 the above re-

duced equation bedomes a polynomial in twl of the form:

. fl(X)+K f2(X) - L = 0
where,*
= t
I "l

 

f2(x) - twf5+12,000 - ts
m

I.-.-tc

m and t8 are fixed constants

Polynomials of this form have nomographic representation, how—
ever, f2(x) here has two "variable constants" in it and the most that
one can incorporate within f2(x) for a "net-chart" is one "variable con-
stant". In other words, in the construction of a nomograph for the
variables x, K and L one can assign an additional variable and for each
given value of this added variable a different curve for x results since
f2(x) changes with.different values of this constant that is incorporated
with it. This additional variable is usually called "variable constant"
and the resulting nomograph would have a "network“ between x and this

"variable constant".

In the above reduced equation there are two such "variable constants",
namely, m and t8 and the equation must be reduced.further in order to enable
polynomial nomographic representation. Fortunately, it is possible in
this case to get a good approximate solution when the above equation is
reduced further to include only one "variable constant". Looming at the

values for m in Table 1A. in the Appendix it is seen that the variations

11

in m for different refrigerants at any given suction temperature, t8, are
quite small and an average value would be quite satisfactory. It is
natural than to assume that by assigning a value to t8 the value of m

is fixed too, and henCe m and t3 are considered as one “variable con-
stant". Now, the construction of the "net-chart" nomOgraph is possible,

since f2(x) has been shown to have only one "variable constant".

The last assumption or "reduction" in the equation has the ad-
vantage of making the nomOgraph completely independent from any primary
calculations or finding a value for m, and if one considers tempera-
tures only, the refrigerant circulated in the unit has no influence on

the results.

ri‘he procedure followed in the construction of the nomograph for
the reduced equation is quite lengthy and it is not in.the sc0pe of
fiiis paper to describe this procedure or prove the construction. The
literature on nomography is quite abundant and many authors deal with

representation of polynomials by different methods.

 

 

 

 

 

 

5'

E40
3 A-COST OF ELECTRICITY, CENTS PER KWH.
: 9 s 7 6 5 4 3 2 I .5 .1
L50 EXAMPLE: LL] l I l l l l l l l l I [1111111i1'111 1111 1 I
E A=3 d:
; e=15¢
E 15:607. /
5-60 “65°F /
: 3" ts=30°F /
:_ u]
,: g READ: /
I 1— =93°F
_—70 < t“ f
.. Q:
- 1.1.1
: g I
: 3 t_ 40 j ' - :30
3—80 ”‘2 as
E g % 50 l —40 a): a
1 <7) “<t - o I
— 2: 0: / -50 z
= as he " 9’
390% 2so / /~’//’4’:6O§
:\L E f// ”ff" :70 ES
3 § \‘vv‘im- M-~~~--—-——~—"// :80‘1'
E g .21 l —90
7'003 ”‘ so /
: O 05
1 3» E /
.. <1
: ‘ a 90 1
1—110 5
3 “100 l
3 -4o .0 50 I
E_ t,— SUCTION TEMPEflATUREfF I

120 , ll11'1111l111111111’ I l | ljlllllllll/

1 5 .0 20 30 40 50 so 70 so 90
e-cosr OF WATER.CENTS PER 1,000 GALLONS

516.2. OPTIMUM CONDENSING TEMPERATUREE FOR COMPRESSION REFRIGERATION SYSTEMS

 

   

 

IV. DISCUSSION AhD CONCLUSIOhS

A comparison of the equations derived in this paper with other
equations or solutions, for the same problem, prOposed by different
authors would show best the advantages and the simplicity of the equa—

tions proposed here.

A solution similar, to a certain extent only, to the solution
given above was prOposed by E. J. Macintire (see references 1 and 2).
_ ~ . r156 .
his equation solves for the economical temperaturenof the cooling water
rather than for the optimum condensing temperature or pressure. The
total cost of Operating a refrigeration unit according to this equa-

tion is:

0 = Ame + 0.0012 as
e t
d

The notation is the same as used in this paper except for:

td = economical temperature rise of the cooling water
in OF.
H = the heat to be removed by the condenser in Btu.per

ton per minute.
There are two mistakes in this equation and one of them is an
appreciable one: 1) The difference between the suction temperature and
the condensing temperature (td) has the same numerical value as the

temperature rise in.the cooling water (td)' This situation is practically

13

impossible. Only if the cooling water entered at the same temperature
as the evaporator suction temperature, and also if there were no ter—
minal temperature difference between the condensing temperature and
the water outlet temperature, could this be mathematically correct.
From both a practical and physical standpoint this would be an impos—
sible Operating condition for a refrigeration system. If the td terms,
in the above equation, are intended to be equal and have the defined
value above (of economical water temperature rise), then a fairly large
, part of the electrical cost for Operating the compressor has been left
out of this total cost equation. If the above equation were to repre-
sent the total cost the first term in the equation should be:

mud-t twl-t- 5 - t8)

 

s
2) The second error is in H. The heat to be removed by the con-
denser is assumed to be known and constant or a trial and error solur
tion would be necessary since i is dependent on the varying condensing

temperature. However, the error in here is not too serious, especially

since one can find approximate values for H in the literature.

While this equation for total cost of Operation is considerably
in errOr as noted above in K0. 1, the solution for the economical
water temperature rise yields fairly good values, since most of the
error disappears in the process of differentiating the equation with
respect to td when trying to solve for minimum cost. It is of interest
to note how Often this erroneous equation has appeared in refrigeration

textbooks. It first appeared in this exact form in Macintire's first

1%

edition and in the revised edition of his book and also in the new book
by Macintire and Hutchinson (reference 2). The equation was also picked

by Jordan and Priester in their textbook (see reference 3).

A completely different approach to the problem has been prOposed
by Boehmer (references 6 and 7), but his salution is limited to
"Freon 12" only and for units from 10 to 60 hp. His equation applies
only to relatively high suction temperatures as are encountered in air-
conditioning units and to some extent he relies on manufacturers' data
without allowing for different efficiencies for different units. In ad-
dition, no direct solution for the Optimum condensing pressure or
temperature is possible. The graph prOposed for finding the optimum con—

densing pressure has a limited range of values.

Another earnest attempt to solve the problem for ammonia conden-
sers only, was made by L. Buehler (see references H and 5) and an
elaborate set of equations and graphs has been prOposed by him. The
method is limited to ammonia as a refrigerant and for a relatively small
range of suction temperatures. Different suction temperatures require
different equations and no generalization is possible. In the derivation
of his equation he used manufacturers' data to a great extent and the
equations he arrives at are actually empirical equations rather than

analytical solutions.

Returning now to the solution prOposed in this paper. Of all

the variables involved in the solution for to, the temperature of the

l5

entering cooling water, t has the largest effect. All oflier variables

wl'
change only as the square-root and their effects on tc vary accordingly.
The suction temperature, ts’ has very little influence on tc; this can
be best seen in the nomOgraphic solution (Figure 2) where the curves

for tB are crowded together. This fact might seem a little surprising,
but noticing the lines in Figure l, (and Figures 1A. to 5A.) it is seen
that the different lines for different ta are almost parallel and one

might expect just a linear relationship between t8 and the total cost

of Operation.

The dependence of tc on m and the refrigerant used is not too
significant either. m is actually a measure to how "economical" the
refrigerant is. The variations here are not too big. Table lA. shows
that ammonia and Freon 11 are probably the most "economical" refriger—
ants, since they require less work for compression with rising tc and

this only for 10w evaporator temperatures.

From the above considerations one may safely assume that devia-
tions in the actual refrigeration cycle from the cycle considered here
(see page 3) will have little effect on.the solution for the Optimum
condensing temperature. One may say that the factors that appreciably
affect the solution for optimum Operating conditions are not inherent
within the refrigeration unit itself, but are external to it such as the
costs of water and electricity and in particular the temperature of

the available cooling water.

16

In the same plant, variations in the temperature of the cooling
water may be quite large during the different seasons of the year and
this immediately brings the problem of automatic control for the system.
This phase of the problem requires special investigation by itself and
no solution is being prOposed here. However, an indication as to the
way by which this control might be accomplished is worthwhile mentioning.
Equation 1+, for the condenSing temperature yields at the same time tl'e

economical temperature rise in the cooling water, for, tc - tw+-5
2

 

twg - twl = .oouVE a [<th 5>+ia;9_0_9 - ts]

Since this economical temperature difference depends on tw the
1

problem of control, based on this temperature difference, is not a
simple one, but it can be simplified for an approximate solution. The

radical in the equation is not too sensitive to changes in twl. With

a typical value for m, say m 3 M0 and t3 2 10°F the term 12 000 is ob-
m

viously dominant and variations in t of 10 to 20°F will not change

w 1
the value of the radical appreciably and a seasonal average for twl will
be quite sufficient. The control system then will have to measure the

inlet temperature of the water, t but control the outlet temperature,

wl’

tw2. The economical temperature rise then, is considered as constant.
One cf the most important factors in file derivations given in

this paper was the proof that m is indepenbnt of’the condensing tempera-

ture. This must be modified, since actually it holds true only up to

a certain condensing temperature. This can be best seen in the curves

used to determine the values for m in Figures lA.-5A. in.the Appendix.

17

All the curves are straight lines up to about tc = ll5°F and above this
temperature the lines curve upward. The temperature at which the lines
start to curve is different for different refrigerants as can be seen

in the different plots. For ammonia, for instance, the lines are straight
up to tc = 120°F. The reason for these deviations at high condensing
temperatures could be due to the fact that the refrigerant is at high
superheat conditions, high pressure and temperature, and the amount of
work required to compress it at that region is more than the work needed
at lower temperatures and pressures. The constant entrOpy lines on a

p-h diagram would indicate this.

Fortunately, it is rarely that in a water-cooled condenser it
would be economical to operate at condensing temperature higher than
120°F. Economically speaking, high condensing pressures are advisable
only when electricity rates are extremely cheap or water costs very high.
For most practical purposes the independence of m on tc holds and the
equations derived are definitely applicable for most industrial refrigera-

tion machinery.

The above extensive discussion and derivations might give some
distorted.view as to the importance of operating at the Optimum condensing
temperature. To be sure, it is quite desirable to operate at the ap-
prOpriate conditions, but the optimum solution is not very critical and
one should not exaggerate its necessity. An example will best show the

effect of deviations from the Optimum condensing temperature.

18

Assume:
Refrigerant: Freon 12
t8 = 30°F t, °F

u’IYl - 65
Electric rate,A : 3¢ per kw—h
Cost of water,B a 15¢ per 1,000 gallons

Overall efficiency,e e 60%

Interpolating in Table 1A, m = 33. Substituting in eq. u, or from
the nomograph (Figure 2), one finds tc = 93°F. Equation 1. can be used
now to find the minimum total cost of Operation:

c = W 1&9). + (12.000433) (93-30)] 15 =
3u12 ( b0) (93 - 5 - 65) (8.330)

 

3 3.07i—l.l2 = M.l9¢ per hour per ton.
Now, if the unit Operates at tc = lOO°F the total cost of Opera-

tion is found to be h.25¢ per hour per ton, and if the unit Operates at

tc = 85°F the total cost would be h.32¢ per hour per ton.

These differences are not too large to warrant strict adherence
to the Optimum to, but the differences grow quite fast as the deviation
from the Optimum point gets larger. With large refrigeration units
these differences may amount to large sums in.the long run. The problem
should not be taken very lightly. Many of the refrigeration plants
today Operate without the slightest attention to the problem; either
because the Operators are not aware d? it or because of lack of infor-
mation on how to achieve Optimum conditions. This is especially true

in plants where there is not constant engineering supervision. (There

__-fir——_———_———————fi

 

 

 

19

is some severe criticism in the literature for the neglect of this problem)
With this in mind the nomOgraph presented in this paper was constructed
to facilitate the achievement of a solution by Operators without techni-

cal training.

In conclusion it will be added that, since solutions for the
Optimum condensing temperature are available, it is the duty of the
Operating engineer to try and achieve these Optimum conditions. The
minimum total cost of Operation of a refrigeration plant can be deter-
mined without too much difficulty and it deserves the prOper attention

from the refrigerating engineer.

APPENDIX

 

 

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TABLE 1A

m, THE INCh‘EASE IN ENERGY FOR COIviPh'ESSION CAUSED
BY ONE OF RISE IN THE COiEDEl-ISING ‘I’flVIPFLRATURE -

IN BTU PER °F PER TON PEP. HOUR

 

g

 

Sucticmr
Temperature Ammonia Freon 11 Freon l2 Freon 22 Freon 11h
F

 

—l+o 50 1m 54 5*t 57
-2o 1+2 1+0 1+5 1+6 M9
0 36 36 39 no no
25 31* 31 f 32 32 33

 

 

 

 

 

50 30 27* 30 30 3o

 

10.

ll.

2?

BIBLIOGRAPHY

Macintire, H. 8.; Refrigerating Engineering, lst ed. rev.
John Wiley & Sons, Inc., New York, l9h0, pp. 181-182

 

, and.Hutchinson, F. W.; Refrigerating Engineering,
2nd ed. John Wiley & Sons, Inc., New York, 1950 pp. M904E9l

 

Jordan, R. D., Priester, G. 3.; Refrigeration and Air Conditioning,
Prentice-Hall, Inc., New York, 19N8, pp. EMA-EMS

 

Bushler, L.; Economical Use of Condenser water for Ammonia Com-
pression Refrigeration System, Ice and Refrigeration, Vol. 112,
No. 1, (January 191+?) pp. 17 .

 

, Good Practice in Condenser Operation, Ice and
Refrigeration, Vol. 116, No. 1 (January l9u9), pp. 75-78

 

Boehmer, A. P.; Condensing'Pressures for Air Conditioning,
Heating, Piping and Air Conditioning, Vol. 18, Nos. 9, 10
(September, October, 19M6), pp. 77, 9h

Bushler, L., and Boehmer, A. P.; Economical Use of Condenser
Water in Compression Refrigeration Systems, Refgigeratigg
Engineering. Vol. 57. No. 3 (March l9h9) pp. 251—255

Martin, W. H., and Summers, R. E.; Water-Wise Refrigeration,
Power, Vol. 82, No. 7 (Judy 1938), pp. 72-73

On Nomography:

Levens, A. S.; Nomography, John Wiley & Sons, Inc., New York,

176 pp., lgus

 

Johnson, L. H.; NomOgraphy and Empirical Equations, John Wiley
& Sons, Inc., New York, 150 pp., 1952

Douglass. R. D., and Adams, D. P.; Elements of Nomggraphy,
McGraw-Hill Book Company, Inc., New York 209 pp., 19h7

28

bIBLIOGRAPHY (Continued)

12. Burrows, W. H., The nomographic Representation of Polynomials,
The Journal of Engineering Education, Vol. 30 NO. 5, 19u6,

PP- 351-375

13. Merchant, M. E. and Zlatin, N.; Nomographs for Analysis of
Metal—Cutting Processes.. Mechanical Enggneering. Vol. 67
No. 11 (November 19u5) pp. 737-7Eé

 

 

 

 

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