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AN ANALYTICAL AND GRAPHKLAL
SOLUTION FOR THE MOST ECONOMICAL
SIZE OF PIPEN‘S TO BE USED IN THE
SUCTION, DISCHARGE AND LEQUID
LINES OF A REFRIGERATION SYSTEM}

 

THESIS FOR THE DEGREE OF M. S.
MICHIGAN STATE UNIVERSITY

JOSEPH E. RIZZUTO
195’

U!

.-\

KS. ‘ 7W
.4

\ “
,;

 
 
   

  

LIBR A R Y
Michigan Sta.
University

 

AN ANALYTICAL AND GRAPHICAL SOLUTIQJ FOR THE MOST ECONOMICAL
SIZE (F PIPING TO BE USE) IN THE SUCTION, DISCHARSE

AND LIQUID LINI'B LF A REPRIGERATION SYSTEM

By
Joseph E. Riazuto

AN ABSTRACT

Submitted to the School of Graduate Studies of Michigan State
University of Agriculture and Applied Science in
partial fulfillment of the requirements
for the degree of

MASTER (F SGIRJCE
Department of Mechanical Engineering

1955

I1 ' . .
'f I‘W‘C’ // fl / (I I‘f’: ’ _ ' /~- 1/. "42"
Approved r ‘7’ “r1 ~. ' gin/MAI; I W—fIW” : w L.
W IV 7’ _
I/

AN ABSTRACT

The selection of the proper size of piping is of the utmost im-
portance in the design of an efficient refrigeration system. In most
cases the only basis for the selection of the refrigeration piping are
rules of thumb or arbitrarily choosing pipe or tubing to match the con-
necting fittings of the various pieces of equipment. Such a basis of
selection, however, can be very costly in the long run and penalize the
economy of a system.for its entire lifetime.

In designing a refrigeration system, what we are primarily interw
ested in is a system that will accomplish its task with the least pos-
sible total cost. The two factors of concern to be included in this
total cost are the initial cost of pipe and the operating cost for power
to drive the compressor. The two factors tend to act against each other,
that is the larger the size of pipes used the greater“will be their cost
but the lower will be the cost of power required to drive the compressor.
0n the other hand the smaller the size of pipes used the lower will be
their cost but the higher will be the cost for power required to drive
the compressor. Hence it ‘was found that there will be some optimum
point at thich the sum total of these two costs will be a minimum. It is
the purpose of this paper to present an analytical solution for the
selection of pipes which will result in the lowest total cost for the
system.

The paper treats the suction, discharge and liquid lines for use
with Freon~12 as the refrigerant. The equations and form of the solution
‘uould be exactly the same regardless of the choice of refrigerant but if

a refrigerant other than Freon-12 is used, extreme care must be taken to

2 .
substitute the properties and values for the desired refrigerant into
the given equations .

The paper also presents a nomograph to facilitate the solving of the
equations, and is designed for use with Freon-12 only.

It was found that the liquid line posed a slightly different con-
sideration than the other two lines. The main consideration in the case
of the liquid line is that the refrigerant enter the expansion device
100% in the liquid state. Most expansion devices depend upon this for
proper operation. It is seen that the available pressure drop for the
liquid line will depend upon the condensing temperature and the degree of
subcooling. The most economical size of pipe for this line will, therefore,
be the smallest pipe that will allow only the available pressure drop and
still insure 100% liquid at the expansion device.

In view of the large number of the possible variables treated, the
solutions presented here will for the majority of cases replace an in-
dividual economic study. In other cases it will check the designer from
resorting to extranes that would destine the system for uneconomical

operation .

AN ANALYTICLL AND GRAPHICAL SOLUTION FOR THE MOST ECWOMICAL
SIZE OF PIPING TO BE USED IN THE SUCTION, DISCHARGE
AND LIQUID LINES OF A REFRIGERATION SYSTEM

By
Joseph E. Rizzuto

A THESIS

Submitted to the School of Graduate Studies of Michigan State
University of Agriculture and Applied Science in
partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1955

ACKNWLDGNEVTS

The author wishes to express his sincere appreciation to
Professor D. J. Renwick under whose supervision and guidance this study
was made. The author also wishes to express his appreciation to the
other professors of Michigan State University who have aided him in his

studies for an advanced degree.

II.”

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Dichssnn mm coucwsxoizs.

APPENDIX . .
BIBLIOGRAPHY

Page

13
20
27
32

10.

I.
II.
III.
IV.

LIS'I'CFORAPHS

REPREENTATION (F SUCTICN AND DISCHAmE LINE
PRESSUREDROPS..........

In8 VALUES FOR SUCTICN LINE . . . . . . .
ndVALUES FOR DISCHARGE LINE. . . . . . .
NOMCBRAPH.............
REPmflTI‘ATION OF PRESSURE DROP IN LIQUID LINE.
AVAILABLE PRBSURE DROP FOR LIQUID LIN E . . .
FFECT (F CHANGE IN ELEVATION w PRESSURE DROP
LIQUID LINE PIPE SIZE SELECTOR . . . . . .
DENSITY VS TEMPERATURE FOR FREQ-12 LIQUID) . .
DISCOSITY VS TEMPERATURE FOR FREON-12 LIQUID .

LIST ('1? TABLE

SAMPLE PIPE COST DATA . . . . . . . . .
PRESSURE DROP PER FOOT OP STATIC LIQUID HEAD .
CAPITAL RECOVER! FACTORS . . . . . . . .
VISCOSITY or nausea VAPOR . . . . . . .

Page

20
2h
25
26
30
31

33
3h
35

INTRmUCTICN

The economic aspects of an engineering problem, although often of
prime importance, are sometimes completely overlooked . Host engineering
problems involve either a consideration or a comparison of costs. In
attacking m engineering problem such as the design or selection of
equipnent to perform a certain task there may be an infinite number of
selections or combinations that could do the Job. However, of these
alternatives, there can be found one which will do the Job at the least
total cost. It is this solution that the engineer must seek.

Before coming to a conclusion in an economic study, it is necessary
to examine all the factors or variables which would influence our de-
cision. It should be emphasized that the omission of any one factor may
lead to an erroneous conclusion .

In the selection of piping for a refrigeration system, there are two
primary factors which influence our choice. The first factor to be con-
sidered is the initial cost of pipe. The second factor is the operating
cost for ’power required to drive the compressor. The magnitude of these
two costs tend to oppose one another, that is, the larger the size of
pipes used the greater will be their cost but the lower will be the cost
of power required to run the compressor. 0n the other hand, the smaller
the size of pipes used, the lower‘will be their cost but the higher will
be the cost of power to drive the compressor. On the following page is
shown a typical plot of the costs of power and pipe vs. the diameter of

pipe used. From it, it can be seen that there will be some optimum point

 

 

 

ANNUAL cos~r ~ :3

 

 

WANETER

at which the total cost for both piping and power will be a minimum.

This paper presents an analytical solution for the optimum size of piping
to be used in a refrigeration system. This paper treats the suction,
discharge and liquid lines, although the considerations in the case of
the liquid lines are found to be somewhat different. In the liquid line
the most economical size of pipe is the smallest pipe that will still
allow the refrigerant to be 100% in the liquid state at the entrance to
the expansion valve.

The approach to this problem is perfectly general, although the graphs
and calculations made to facilitate selection may be used only with
Freon-12. This is also the case for the nomographical solution of the
equation for optimum pipe size which is presented to make pipe size sel-
ection an easy task.

The question of refrigeration pipe size selection has been investiga~
ted by many authors using several different approaches. In all cases,
however, it was found that these authors rely only on experience and rules

of thumb. In no instance could there be found an economic approach to the

3'.
problem. This paper gives an analytic and accurate solution for the op-

timum size of pipe which will result in a minimum of total cost.

THE.SUCTION AND DISCHARGE LINES

As previously stated the two prime factors influencing the selection
of piping for the suction and discharge lines are the cost of piping and
the cost of power to drive the compressor. These two factors are related
to one another through the pressureidrop. It is the fact that a change
in pressure drop will alter these two costs in opposite directions that
makes possible an optimum solution. Actually we could solve for an op-
timum pressure drop for a refrigeration pipe line but a pipe size is of
much.more significance to the designer.

Below are PbH.diagrsms showing the effect of pressure drop in both

the suction and discharge lines.

 

 

 

 

 

 

 

 

(1‘0

?’

.H

II

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‘.

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{I

I!

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in

I H

H . H A'W’r‘
Pressure drop in the suction line. Pressure drop in the discharge line.

Figure l

S.

AP8 and APd are taken to be the pressure drops in the suction
and discharge lines respectively. It may be seen from these diagrams
that the additional increments of enthalpy that the compressor must add
because of the pressure drops are Aha and Ahd.
We will let m8 and md represent the theoretical B.t .11. per pound per

p.s.i. of pressure drop that must be added by the compressor. Hence,

 

Aug Ada
s 3 md a I .-
AP, APd

Determination of ms and md for the suction and discharge lines.

A__L_

___ ‘ fi

It should be noted that It represents the slope of an isentropic line
on a P-H diagram.
From the Second Law of Thermodynamics we may write
dh - Tds + vdp

Along an isentropic line ds '- 0 so that:
E ah‘.
. u v
SP/s

From the above relation it can be seen that the slope of an isentropic

line on a P-H diagram is equal to the specific volume.

But (an)
\..I m. 5p ’

FT3 lhhv £9
m-v... --—-—

‘‘m J ’1'

‘5?

The specific volume of the refrigerant, and hence m, was found to vary
with the pressure and degree of superheat. The values of m are plotted

for the suction and discharge lines on pages 6 and 7, respectively.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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le will now determine the annual operating cost, I.
Let:
b - annual cost to compress refrigerant from evaporator pressure
to condenser pressure
f: - increment in annual operating cost due to frictional pressure
drop
I - b + c
h - hours of operation per year
R - cost of electricity - cents per k.v.h.
7) 1. - isentropic compression efficiency - S
77! - mechanical efficiency - i
”not I motor efficiency - S ‘
v - refrigerant flow rate - lbe./sec.
The theoretical B.t .11. per second of power that must be added due to
frictional pressure drop is H!"
HT - “AP
The actual B.t.u. per second of power will therefore be WV

‘23: 778 “AP
“V717,, 'sso m “'P'

The Kiimtts of power required will be:

 

773 In AP
------—(0 7&6)
77187791301:

QhR_ ha778

0' hasso (1L6) TV“

is e, not

C-

 

thzaAP_

 

r - b + .01058 ~ (1)
77is7’il77mot
We‘will lat:
U _ £1058an
7713’th
Then I - b + mm? (2)

The next step in the solution is to determine an expression for the
cost of piping. In order to treat this cost together with the operating
cost, it is advisable that it also be put on the annual cost basis. Rec-
ognising the time value of money this may be done by mltiplying the first
cost of the piping by a capital recovery factor. This capital recovery
factor will depend upon the current rate of interest and the expected life
of the system. A table of capital recovery factors is given in the
Appendix. The life of the system may be taken as either the life of the
piping itself or that of the system as a unit if that is shorter. After
its useful life, the piping may have some salvage value as scrap.

The anmal cost of capital recovery may now be computed as follows.
Let:

A - Annual cost of capital recovery - 3

I. - Length of pipe '- feet

B - Cost per foot per inch of diameter (installed) - 8
S - Salvage value per inch of diameter after n years - 3
n - Life of systau - years

i - Interest rate - percent

D - Diameter of pipe - inches

'x - Capital recovery factor - — 1 —_ + 1
(i + l)n - l

 

 

Then:

 

A-ml:(B-S){ 1 +1}+51]
(1+1)n-1

A-LD[K(B-S)+iS]

Let us assume that the salvage value can be expressed as a percent-

ageXofB.
8-XB
A-IBtKB-m+ixB]
A-IDB[K-KX+iI]
Let:

z-[x-n-ix]
A-IDBZ (3)

The total annual cost T will now be the sum of the operating cost
plus the annual cost of capital recovery.

T-I+A (M

r-b+mAP+mn G)

. At this point it would be desirable to derive an expression for the

frictional pressure dmp in a pipe in tons of the variables involved.
'0 W start 11th the Fanning equation which statemu)

ML 9 v2
' '“"‘"'" (6)

P
A 231)

From the continuity equation it is seen that:

11.

For smooth pipes or tubing such as copper, brass, glass, etc., the
following unpirical relation has been proposed by Stoever.(1)

 

1' - °'06 3 at Rs from 14,000 to 1,000,000 (7)

It should be noted that this is the range of Reynolds mmbers which
E“
will be encountered in refrigeration piping. :
37
DV 9 f
Re I! M
.228 3;
0.0653 A ‘ ~ :

 

f -
l3.228v .228 (3.228
Combining these relations we arrive at our final expression for the

frictional pressure drop .

0.2 I”1.7? u. .228

M” “P 91.77“

 

Putting AP in lbs/inz and n in inches, we get:

 

.77 .228
AP - 6.02 .__T___"1 u (a)
P D .77
Substituting this in Equation 5, we get:
2.77 .228
T=b+6.02 UL“; 1" #‘PLZBD (9)

It should be noted that in the expression for I and T, the increment in
annual cost C is included for only one line. The suction and discharge
lines must be solved for separately, and in solving for one, the incre-
mental cost in the other will be treated as a constant. It, together

with b, will drop out when we differentiate the total cost with respect

to D.

12.

For minimum total cost:

 

 

~33- -o
.228 2,7
.23.... .....77xwz “Luna
dD P- DSJ?
‘ .228 .
05'77 - 28.7 J1. ..M. . , w2 77
z e B
.228 ' .228
w, e-28.7-§—_£‘___. - 399:“ __ (.22....)
Z [K - xx - jumnhunmot] 9

We may now write our expression for the most economical pipe size

diameter .

135°" - --—--———-"":'7" _ (10)

13.

THE NOMOGRAHiIC SOLUTION TO THE EQUATION FOR THE
MOST ECONOMICAL PIPE SIZE DIANETm

 

. 7
B
e _‘ 'BW ( “.228 y
[K -- KX- 1X][”18 X77" thot] P

Let B1 I Cost per foot of pipe.
This is more convenient for our final graph since the cost data is given
by the manufacturers in this form.

Equation (1) will then he:

 

2.7?
B1
This equation may be written:
14.77 log D 4- log B.1 I log e + 2.77 log w (12.)

Let log K I h.77 log D + log B1
Thcn log K I 2.77 log w + log 0
Or log e + 2.77 log w= log K
11 I la]- log 9 3 11 I m2(2.77 log I!) ; Z1 I m3 log K

 

 

Let: 1:11 I 10
20
I I 7.220
“2 2.77
m’ . .1132— . 7.220 X 10 = [“193
m1 + m2 17.220

xlIlOloge 5 leZOlogw 5 21-h.l931ogl(

 

 

 

 

X
o) 8" Z
‘ on
g“ a o
’_— m .—
'.' O
9 v oz
... u. u
x N )1
--————— P. a“. — 81 a—
P 1 _ “'1 10
For P1 7" 81 . 10"
P1 ' 10 X 10 ' 5.807.
17 .22
7.22
g I ------ x 10 I h.l93"
’- 17.22

14.77 10g D + log B. I log K

:2 . lunar.” log D) ; 12 I ms log B1 5 22 .- zl . [“193 19g K

Scale K will be used as the common line or factor in the two equations
22 I 21. This follows from the original equation in which we
fixed K:

15.77 log D + log B1 I log K I log e + 2.77 log w

. ho I8.86
L“ m“ L77 3

m3- ...".‘fli. ; n.193-8'386m5 ; Ins-8.216
when; 8.386va

 

15.

x2 I 140 log D Y2 I 8.216 log B1 22 I h.l93 log K

-——.-Ji.-.££§L 3

 

 

 

 

 

 

 

 

P2 I 3" : g2 I 2.91:"
:6
x m
0
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0) 0'" — ‘3 0'7
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9. u n 01 02
d 3 h‘ 2 94- >7 "
,2 *f" ' | ;
; 1507 ;—<. 449? ; r
7 . I
e I) k B. vv

The actual lengths of one cycle on the various scales will be in direct

proportion to the coefficients of the log terms. No scale need be put

on K since it is used only as a pivot line. The range and vertical

positioning of three of the four scales is completely arbitrary, but once

this is done the fourth must be done by a numerical computation of a point
on the particular scale.

 

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7 I74 9 9‘. V l. .1t 2"?! |7i7|e|6 Alli- Q'tli 1%..

 

 

 

 

x.-. H - t . 1.. 1 . i t
2 C 1..., r i is (2 1 i - u 3 . m 2 w
a Q, on i m. . 4 «7 1
w I e
.- .7. I: all 41$]-lllxili:v i
2w.) 1
C O O i.
- a r r .r _
I n 2 g .2
2 .

 

PIPE SXZE FOR _ SUCT‘QN, ..ANP __._.D*_2~_CHARQE_ UNES—

{M‘CAL u

<7

MOST ECON

 

 

 

 

17.

The use of the equations and nomograph will now be demonstrated by

the solution of a typical problem for sizing a suction line.

2922
h I 2,000 hours of operation per year
R I 2 cents per k.w.h. for electricity
n I 20 years of life for system
i I .05 interest rate
X I .02 salvage value at end of n years
”is I .75 isentropic compression efficiency
77,, . .80 mechanical efficiency
”not I .82 motor efficiency
Evaporation temperature I 10°F and superheat I 60°F at entrance to

the compressor.

Determine
The most economical size of pipe to use for the suction line on a

l-ton system (Freon-12) .

 

Film Table of Viscosities a I 768 x 10"8 Fig-‘53?
Fro. Freon-12 Hollier Diagram 9 I %- . {—53 I .6175 Fr.)
F r0111 Graph Ins I .h
Fran: Table of Capital Recovery Factors 1: - 0.08021.
e .- _ .BOthm ( '228) .
[K ' KX- 1X][771877u%0t] 9

‘ .3014 (2,000)(2)(.h) 6.80
[ .0802}: - .0802h(.02) - (.05)(.O2)][.7S x .80 x .82] 100 x .

18.
e I 1.31: x 103

Assuming a refrigeration effect of 60 15'42: the mass flow for l—ton

refrigeration will be: _
B .t .u.

 

w .300 Min 2.2.22.2 - .ossosi
60 B.t.u. 60 39¢ 6c

By connecting the calculated values of w and e we obtain point (a) on

the K scale. Using this as our pivot point and our price data as a guide
we draw a line through (a) so that the disaster is as close as possible to
its corresponding price per. foot. .

" For this case we find. the most economical diameter to be 7/8 inch.
NOTE: To be theoretically correct the price per foot should include the
exact cost of fittings and valves since their price will vary with the
diameter. The equivalent length of the line should then be calculated'
and the cost per equivalent foot of pipe. found. This should be done using
the above solution as a first approximation. The final diameter will vary
slightly from this owing mostly to the approximation made for the average

\

price including fittings as given in the footnote on page 19.

19.

TABLE I

SAMPLE PIPE COST DATA

 

 

 

. . ‘ *
0.D . Wall Price Average Price 0‘ Installationb Total

 

(v.
man‘s-s...

 

1:13;, Tfigfigss Per {out Incl 133:3thth 00st ger Foot Coggoper
3/8 .030— .218 .319 .090 139
1/2 .035 .319 .510 ‘ .105 .615
5/8 .oloo .1188 .717 .180 .897
3/8 .0112 .587 .875 .300 1.175
7/8 .0115 .659, 1.0584 .1120 1.1171:
1 1/8 .050 .909 1.1458 .510 1.961:
1 3/8 .055 1.227 1.963 .780 2.7113
1 5/8 .060 1.518 2.877 .900 3.377
2 1/8 .070 2.377 3.803 1.010 11.813
2 5/8 .080 3.368 5.390 1.350 6.780
3 1/8 .090 8.320 6.912 1.560 8.1172
3 5/8 .010 5.696 9.111. 1.800 10.911.
__{1 1/8 .110 ' 7.1143 11.829 1.910 13 .339
«n-

a This assumes that the fittings will amount to 60% of the pipe cost.

b This is based on labor at $3 per hour and hours per foot as rec-

amended by reference, "How to Make your Job Estimates Detailed and

Accurate", 1955-56 mmcmnofl AND AIR CONDITIONING Catalog of

Catalogs by Comercial Refrigeration and Air Conditioning Magazine,

pp 0 194-155 e

20.

THE LIQUID LINE

The factors influencing the selection of a liquid line size are
somewhat different from those for a suction or a discharge line. The
prime consideration in selecting a liquid line is that the refrigerant
enters the expansion device 100% in the liquid state. Most eXpansion
devices depend upon this for proper performance. If an expansion de—
vice is supplied with a liquid vapor mixture, the capacity of the device
is greatly reduced. This would disrupt the operation of the entire
system. To prevent this, the pressure directly ahead of the expansion
device must exceed the saturation pressure corresponding to its tanper-
ature. It is seen therefore that the available pressure drop for the
liquid line will depend directly upon the condensing temperature and the
degree of subcooling.

l. Refrigerant enters
PRESSURE DROP IN THE LIQUID LINE
liquid line.

2 . Refrigerant enters

 

expansion device .

IAPI
l-Q—J-v

 

P (.3: 3. Refrigerant begins
2'
£3 to change to vapor
.J
2 c): phase .
2d

 

 

Figure 5

The available pressure drop will consist of the following parts:

DOW...
._.
I‘

21.

A P Available ' APFriction + APDiff . in Elevation +

A PSafety Factor ' ' (13)
The AP for friction and safety factor will be positive, but the

change in pressure due to the difference inelevation may be either
positive or negative depending upon the relative positions of the con-
denser and the expansion device. If the expansion device is located
above the condensing unit the AP will be positive, and if the expansion
device is located below the condensing unit the AP will be considered
negative. This A P due to the difference in elevation is often neg-
lected and may be the cause of a serious error in design. This is es-
pecially true if there is a very large vertical lift preceding the ex-
pansion device. The Freons as a group are heavy refrigerants with
Freon-12 having a pressure drop of approximately .57 p.s.i. per foot of
static liquid head . Values for other refrigerants are given in the
Appendix.

Equation (13) may be written in the form:

:(AP

AP Available I APSE.) - APDiff. in Elev. (1")

Friction
(or Not)

It is recommended that the term ( A PAvail. - APS F ) be taken as

'9 A PAvazi.

available pressure drop. Values for the available pressure drop for

l , and should at all times be at least. 3 p.s.i. less than the

Freon-12 are shown for various refrigerant conditions by the graph on
page 21:. Subtracting this from the first term, we arrive at the A P

which may be allowed for the frictional drop.

1.77 .228
In a.

\

AFN” 36.02.

22.

It is shown in the Appendix that the plots of density and viscosity
vs. temperature are very nearly linear. The term a '228 may,

‘9
therefore, be written in the form:

41.5223 . 900672 [.580 - .ooosrl)‘228
9 (11.9.15 - .1261'1')

(15)

 

 

This term was found to be very nearly a constant at common liquid

line temperatures .

.228
1A - 1.70 x 10-3

9

This brings our equation for A PFriction into its final form:

 

AP 9 .1325 .1317 (16)

in.2 - 100' pk."

 

A graph of this equation is shown on page 26.

In this analysis it is assumed that the state of the liquid refrig—
erant is such that its pressure is high enough above the saturation pres-
sure to allow for the difference in elevation and some frictional pressure
drop. This however may not always be the case. As was previously en-
phasised, a large vertical lift may by itself exceed the allowable pres-
sure drop. In this case twa alternatives are possible, both of which
increase the available pressure drop. The first is to raise the dis-
charge pressure of the condenser. The second method is to use a heat ex-
changer to further subcool the liquid refrigerant. This second method
scans by far the better of the two alternatives and is becoming caution
in modern installations . A liquid suction heat exchanger will not only

help to subcool the liquid refrigerant but will further superheat the

 

23.
the suction line vapor which is desirable from safety standpoint. On
the other hand, increasing the discharge pressure of the compressor
will increase the operating costs and is to be avoided if possible.

2h.

 

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27.

DISCUSSICN AND CONCLUSION

We have derived in this paper an expression for the most economical
size of pipe who used ina refrigeration line in terms of the variables

of our system. This equation was found to be:

 

2.
Dh.77 _ ew 77 (l)
31

. .30, 1 R u .228
[x - xx- unwiflufimt] e

where e -

The accuracy to which we are able to select the most economical
size of pipe will depend naturally upon how closely we are able to approx-
imate each of the factors in the equation. It is of interest to see how
the misjudgment of them might affect our choice of a diameter.

First of all it would be necessary to calculate the required mass
rate of flow w required for the desired tonnage at the desired evaporator
temperature. This. might be done very accurately by sketching the cycle

on a P4! chart and determining the refrigeration effect, 3.8., in 2:352,

200

w—L - Tonnage x R
see RE

 

in approximation which is often made is using a refrigeration ef-
fect of 60 m for Freon -l2 and 8O 8" .u. for Freon -22 .(3)
9 3

Let us assume that w was approximated to be 5% too large. This would

2077
result in an error of (1.09377 - l - .031 or 3.1%. Similar calculations

for the other variables in Equation (1) are given in a table below.

28.

 

 

*“-

 

Var % Error of Reflected Error
‘ Given Variable in Diameter
" 5% 3.1%
e 10% 2%
Bl 10% I 2% i
All of '
Above 7'5%*

«Assuming none are compensating .

The cost per foot of pipe may be determined from manufacturers
price lists. It should include the cost of installation and all fittings
and valves because these will vary With the pipe size. This would,
therefore, have to be done after first getting a rough approximation
with the use of the nomograph.

From the monograph it may be seen that the range of mass flow rates

is from .001 to 10 lbs ./ sec. This corresponds approximately from .02
to 180 tons. The range of diameters covered is from .1 to 10 inches.
It should be emphasized in high‘tonnage systems requiring large diameter
pipe, extreme care is necessary. The price of fittings and valves used
in these systems is extranely high. In such cases it would probably be
advisable to make a complete economic study.

In the solution for the liquid line it was stated that the most 1
economical size of pipe is the smallest size that would still insure
100% liquid at the entrance to the expansion device. It might be
argued, however, that the available pressure drop might be increased by
raising the condensing temperature. This however we are assuming to be

29.

fixed at the optimum condensing temperature and this has been shown
by several authors to be a function of the cost of water for cooling
the condenser and the cost of electricity to run the compressor. A
combination of studies of the liquid line size and optimum condensing
temperature might be possible but is beyond the scope of this thesis.

It is admitted that in the past many authors have treated the
problem of sizing refrigeration lines . Under typical conditions their
solutions would probably prove to be quite adequate. This is so because
in all cases they are based on arbitrary rules formed from past experience.
Blindly following these rules, however, may lead the designer into serious
trouble.

It is of interest to note that the diameter found in the sample
solution for the suction line is the same as would be obtained using the
methods of reference 1 and 3. However, over the past twenty years, the"
price of electricity has remained about constant whereas pipe costs have
more than doubled. This indicates that using these methods in the past
would have resulted in undersized pipe. The reader may conclude that,
if we are to continue to select pipe by these arbitrary methods, the
time will soon be here when we must revise our rules of thumb. We will
no longer be able to use rules formulated under an entirely different
set of economic conditions.

The solution for the most economical size of pipe to be used in the !
three refrigeration lines gives adequate treatment to all the factors
which influence the selection. It will therefore give reliable results
over a wide range. In conjunction with the monograph its simplicity is

also comparable with other methods.

30.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

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9 - v . L .. . 0 . . . . . . - . c +- 0 v .H . .
.... ..\. . -. 4 u 0 . g. .0 . H . . . . . .
F uh- ? . . I . 2 . 2
..fi . . .. . .2 . . ..H. .- . H H . .. -r u . .
.. AV ... . .. a. m....«. . .11 . . . ..-... A. .. . 7 . . ._
. a . ... . . .- . . o . . .. . . 0 . - _ v .. . . _. . .
I.I-...OI.H--:.... . ..... 1w]. ...... ...H.IH ......H. . xv . .. ...
........ A; I. .- I- I‘M-W. ... 26.10 . .22.-..-H0-w|.0 .IHI.-. I02..I-20 I.IIQIII. DW--.+I0---42.II»II. -I . .
. ... .... . .. . .. ...... I.I--..-- ..
. . . . . s 0 m . w. - . . . .. 0 . . . q . H. . H . . H . . .
. .I..}NMKCDQW .3 I. . m; .. ...
H-w ...-..:... . ... .. .01 -MF N). .0 ..
...... . 22...... H -
.0.-I0- .I. . . . . . . . . . . .. . . 0
. I202-..0I 2III. . . . . . . ..
.HH -741422. . .. . . . U ...?
”.... H. . ...-H. . ._ . .--n---+-.-....- . . M. H .
. . . . . .. . . . . 2 ..020 0...?0I0- .v
02.3....- . .3 . H . . :2 ..
- LLCKPWU I .. . .. H I-- -I..
102......- manaJmmflL..P_l . . . ... - H 0I..-.I..
>Z( III/LIL .. . . . c - 0.
IEOU p..0.J/..u x 22.22.! . H ..
m .- . .. .
. .
I20 . .

 

32.

.228
DETERMINATION (F 0. FOR THE LIQUID LII-115*

9

Density vs. Temperature

 

e - 86.1 - 86’1 307632 (T - 500)

e - 86.1 - .1261 (T + 500)
9 - 86.1 - .1261'1‘ + 63 .05
e - 11.9.15 - .1261'1‘

Viscosity vs. Temperature

“"32""?

A . 280 - 0280 " .220

(T - 500)
100

A ' (.530 - .006T) Centipioses

a - .000672 (.580 - .006?) Hi...
Ft-Sec

::s 1.70 x 10"3

 

‘l’l'he equations for the density and viscosity are put in the slope
intercept form and the values of the slope and intercept for the

equations for density and viscosity are obtained from Figures 9 and 10
respectively . .

 

TABLElLI

(1)

PRESSUREHDROP PER FOOT OF STATIC LIQUID HEmD
FOR.VARIOUS REFRIGERANTS AT COMMON
LIQUID LINE TEMPERNTURES!»

Freon-ll . .

Freon-12 . .

Freon-21 . . .

Freon-22 . .

Ammonia . .

Carbon Dioxide

Sulphur Dioxide
Methyl Chloride

“Approximately SBB’R)

. 0.61; p.s.i. per foot

0 o 0057

. 0.60

. . 0.51

. 0.26
. 0.33
. 0.60
. 0.h0

33.

1 f .m .‘g 21

TABLE III

 

 

 

CAPITAL RECOVERY FACTCRSC'

n 0;: 2% 11% 6% 8% 10% 15% 15; 20“,:
1. 1.000 1.020 1.0210 1.0% 1.080 10100 1.120 1.150 1.2 )
2. 0.500 0.515 0.530 0.515 0.561 'o.576 0.592 0.615 0.6":
3. 0.333 0.317 0.360 0.371 0.388 0.102 0.116 0.138 0.155
b. 0.240 0.262 .276 .289 0.302 0,316 0,329 0,350 0,3a?
5. .22 0.212 0.225 0.237 .250 0.261 0.27 0.298 0. ea
6. 0.167 0.179 0.191 . 0.203 0.216 0.230 0.213 0.261 0.3‘1
7. 0.113 0.155 0.167 0.179 . 0.192 0.205 0.219 0.210 0.277
8. 0.125 0.137 0.119 0.161 0.171 0.157 0.201 0.223 0.251
9. 0.111 0.123 0.131 0.117 0.160 0.171 0.188 0.21 0.218

10. 0.100 0.111 0.123 0.136 0.119 0.163 0.177 0.199 0.239

11. 0.091 0.102 0.111 0.127 0.110 0.131 0.168 0.191 0.2";

12. 0.083 0.095 0.107 0.119 0.133 0.117 0.161 0.131 0.22;

13. 0.077 0.088 0.100 0.113 0.127 0.111 0.156 0.179 0.331
'. 0.071 0.083 0.095 0.108 0.121 0.136 0.151 0.175 0.217

15. 0.067 0.078 .090 0.103 0.117 0.131 0.117 0.171 0.2 1

16. 0.063 0.071 0.086 0.099 0.113 0.128 0.111 0.168 0.2‘1

17. 0.057 0.073 0.082 0.095 0.109 0.121 0.110 0.165 0.2 «

18. 0.056 0.067 0.079 0.092 0.107 0.122 0.138 0.163 0.2;:

19. 0.053 0.061 0.076 0.090 0.101 0.120 0.136 0.161 0.. s

20. 0.050 0.061 0.071 0.087 0.102 0.117 0.133 0.160 0.275

25. 0.020 0.051 Oooéh 0.078 0.09% 0.110 00128 OQISL C.?w:

30. 0.033 0.011 0.058 0.073 0.099 0.117 0.121 0.152 0.301

’40. 0.025 00937 0.051 0.066 0.010).; 0.1102 0.121 0.15) Cflg'.

50. 0.020 0.032 0.017 0.063 2.082 0.121 0.120 0.150 «.2.’

100. 0.010 0.023 0.011 0.060 - 0.080 0.100 0.120 0.150 0.2:

<><0 0.020 0.010 0.060 0.080 0.100 0.120 0.150 0.

 

 

 

35.

TABLEhIV
VISCOSITY OF'FHEDN-IZ VAPOR* (8)

 

 

tOF lbs. .228
A_ ._ ft.-sec. _“
4:0 712 x 10"8 6.70 x 10-2
-20 732 6.73
0 758 6.79
20 778 . 6.81.
ho 799 6.81;
60 826 6.90
80 81:6 6.95
100 866 6.99
120 887 7.02
11.0 907 7.07
160 927 7.10
180 91.0 7.13
200 960 7.16
220 980 7.19
21:0 1000 x 3.0"8 7.22 x 10‘2

 

 

*Viscosities are of saturated vapor at one
atmosphere. Changes in pressure of less
than one atmosphere have a negligible effect
upon the viscosity of the vapor.

 

9.

10.
ll .

12.

13.

36.

BIBLIOGRAPHY

Jordan, R. C. and Priester, G. B. Refri oration‘and Air Con-
diuonig, 3rd Ed. Prentice Hal . ew Yo‘flz, 1950, “2.381.287

Ferrill, H.E. “Don't Overlook the Importance of Proper Size

Liquid Lines". Heating. Piping and Air Conditio .95' Oct. 191:7,
pp. 8h-86

Holladay, VI. 1.. "Determining Pressure Drop in Freon Systems".

Refrigerating ginseng. Sept, 1951., pp. 55-60

Hendrickson, H. M. 'Determination of Refrigerant Pipe Size".
fiegrigsrating Meeting. Oct. 191.6, pp. 317-325

Ferrill, H. E. "Line Pressure Drop - Its Effect on Cooling Cost".
Ref erat inse . Nov . 19%, pp . h25-h27

Ferrill, H. E. "Fluid Flow's Relation to Installation and Operation".

Heating. Pipig and Air Confiitionizng. May 1914?. PP. {Sh-88
A.S.R.E. Air Conditioning ngion Data 80315, Design Volume.

an. m . 1953-511“

Benning, A. F. and Narkwood, W. H. "The Viscosities of 'Freon'
Rifrigerants". Refri erat ines . April 1939 , pp. 21.3-
2 7

Grant, E. I.. Princigles of flung? Econfl, 3rd m. Ronald
Press 00., sw o . , pp. ,

havens, A. S. Nom r . John Wiley and Sons, New York. 191.8

Van Voorhis, M. G. ggwAto QWt Charts. McGraw-Hill, New
York. 1937

Swett, 'G. W. gonstruction of Alignment; Charts . John Wiley and
Sons, New Yofli. I928

Lipka, J. Graphical and Mechanical Computation. John Niley and
Sons, New or .

flaw-"9'?!- -‘“:-r -.»«-; “1m
.

v ' - 4F
’J-Hr

“‘9'"
l

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