Crane Flow of Fluids

..:;-3 .;:,::J ,~~::Itt. ,~

~

~

FLO

OF FLUIDS

~

THROUGH

~

~

VALVES, FITTINGS, AND PIPE

~ ~ By the Engineering Division

~

:z::::t .:::=:t ..~

--:.:=) Copyright, 1969-Crane Co; .~"

All rights reserved: This publication is fully protected

~

by copyright and nothing that appears in it may be reprinted, either wholly or in part. without special permission .

;::::)

.

~:::::)

.=:,) :::::) :::::::)

.=::.:) CRANE CO.

:::::l

Direct inquiries to 4100 S. Kechi. Aven'ue Chicago, Illinois 60632

Executive Office

300 Park Avenue New York, N.Y. 10022

::::::l ~ ::::')

Technical Paper No. 410

Price $2.50 PR1~TED (rw~lfth

IN U. S. A.

Print.ing-1972)

~""

TablE~ of Contents CHAPTER 2 •_ .....- -_ _.

- - - - - CHAPTER

Theory of Flow in Pipe page

flow of fluid:$ Through Valves and Fittings

Introduction ............... _.. _................................. _.... _....... _.. 1-1 Physical Properties of Fluids_....... _..._... __ .... __ ..... _. __ ..... Viscosity .. '" ...... _.............................. _. __ .. _._ ... _.. _.......... VV' eigh t density ....................................._........ _......... Specific volume .................. _..................................... Sped fic gra \' ity ......................... _.............__ ...............

1-3 1-3

Nature of Flow in PipeLaminar and TurbulenL ................. _.... _.... _... ___ ._ ..... _.. _. IIIean velocity of flow ..................... _.. _......... _........... Reynolds number ............. _.......... _........ ___ ....._........ _... Hydraulic radius ................................ _.....................

1-4 1-4 1-4 1-4

1-2 1-2 1-3

General Energy EquationBernoulli's Theorem ......................................... _._ ........ 1-5 Measurement of Pressure.......... _................................... 1-5 Darcy's FormulaGeneral Equation for Flow of Fluids..................... _.. 1-6 Friction factor _............... _......................................... 1-6 Effect of age and use on pipe friction .................. 1-7 Principles of Co:npressible Flow in Pipe.._............... Complete isothermal equation .. _............................. Simplifiedcornpressible flowgas pipe line formula .. _._ ..................... _....._......... Other commonly used formulas for compressib:.e flow in long pipe lines ........ _....... Comparison of formulas for compressible flow in pipe lines ............ _... _._ ....... Limiting flow of gases and vapors ....... _................

Introduction ...........__ .............................. _........................ Types of Valves and Fittings Used in Pipe Systems ........._..._.........__...................._...... 2-2 Pressure Drop Chargeable to Val ves and Fittings........... _...................................'" 2-2 Crane Flow Tests ............................ _.................. _........ ; 2-3 Relationship of Pressure Drop to Velocity of Flow.. _.... _............. _............................_... 2-7 Resistance Coefficient K, EquivalentLength LID, and Flow.Coefficient Cv ••••••-••••••••••••••••••••••••••••••• 2-8 Relationship of Equivalent Length LID and Resistance Coefficient K to the . Inside Diameter of Connecting Pipe ............. _............ Z-lC Valves with Gradually Increased Ports ....._..:........ _.. 2.:..iD Effect of End Connections ......._.... _..................... _... _... 2-1C Laminar Flow Conditions.. __........_.... _... _........._............ 2'-11

1-7 1-8

Basis for Design of Charts for Determining Equivalent Length, Resistance CoeffiCient, and Flow Coefficient_............................ _.. _........_............ 2_11

1-8

Resistance of Bends ............ _... _..... _............................,., 2-12

1-8 1-8 1-9

Steam-General Discussion ._.......................... _...... _.... 1-10

Other Resistances to Flow...._..............~ ......:_................ 2-13 Flow Through Nozzles and Orifices_...........____.......... 2..lJ Liquids, gases, and vapors ........................... _......... _Z-1:l Maximum flow of compressible:, fluids in a nozzle......................... _..... _... _.............. 22..15 Flow through short tubes .............._............_._ ......... 2-15 Discharge of Fluids Through Valves, Fittings, and Pipe Liquid flow ..._....._.......... _........... _._._ ....._.... _... _... _...... 2-15' Compressible' flow ._ ................_............. __...... _~ ........ _. 2~15

- - - - - - CHAPTER 3

Formulas cmd Nomographs for Flow Through Valves, Fittings, and Pipe

1 - - - - - - - CHAPTER 4

Examples of Flow Problems page

Introduction ........... _............ _.............._................. _....... _ 3-1 Summary of Formulas.. _...................... _............ 3-2 to 3-5 Formulas and Nomographs for Liquid Flow V e10ci ty ...................................................... _......... _.....3-6 Reynolds number; friction factor for clean steel and wrought iron pipe.................... 3-8 Pressure drop for turbulent flow ..... _.: .................... 3-10 Pressure drop for laminar flow .......... _................... 3-12 Flow through nozzles and orifices................ _....... 3-14

;f"~".

10

. -"

'-~""-:l

I

.

Formulas and Nomographs for Compressible Flow Velocity ............................................. _....................... Reynolds number; friction factor for clean steel and wrought iron pipe .................... Pressure drop .......................................................... _. Simplified flow f.ormula ............................................ Flow through nozzles and orifices ........................

I9';ge

Introduction ._ .................................._........... _.................. _ 4'-1 Reynolds Number. and' Friction Factor for Pipe Other than Steel or Wrought Iron .................... 4-1 Determination of Valve Resistance in L, .

LID, K, and Flow Coefficient C•........ _....................... 4-:2 Check Valves-Determination of'Size...................... 4--3 Laminar Flow in' Valves, Fittings, and Pipe, ......... _.. 4-4 Pressure Drop and Velocity in Piping Systems .............. __......................................... ~ Pipe Line Flow Problems ..... _...................................... 4-10

3-16

3-18 3-20 3-22 3-24

Discharge of Fluids from Piping Systems................ 4-:1'2 Flow Through Orifice MeterL .. _............................... 4-15 Application of Hydraulic'Radius to Flow Problems .......................................................... 4-:11 Determination of Boiler ~.apacity ..... - ... -... -............··· 4-:18

APPENDIX A ------------~-----------

APPENDIX B

Engineering Data

Physical Properties of Fluids and Flow Characteri'stics of Valves, Fitfings, and Pipe

page

E-I

Introduction page

Introduction ............................................... ~.................. A-I Physical Properties of Fluids Viscosity of steam .................................. A-2 Viscosity of \vater ................................................ A-3 Viscosity of liquid petroleum products .............. A-3 Viscosity of various liquids ............................... A-4 Viscosity of gases and hydrocarbon vapors ...... A-5 Viscosity of refrigerant vapors .......................... A-5 Physical properties of water.. .................................. A-6 Specific gravity-temperature relationship for petroleum oils ....................... A-7 Weight density and specific gravity of various liquids ................................. A-7 Physical properties of gases ................................... A-8 Volumetric composition and specific gravity of gaseous fuels ........................ A-8 Steam-values of k .................................................. A-9 Weight density and specific volume of gases and vapors ............................... A-lO

Equivalent Volume and 'Weight Flow Rates of Compressible Fluids.......................... B.,..2 Equivalents of Viscosity Absolute ............................................................ ;....... B-3 Kinematic ................................................;................ B-3 Kinematic and Saybolt UniversaL ......... :............ B-4 Kinematic and' Saybolt FuroL. ............................. B'-4 Kinematic, Saybolt Universal, . Saybolt Furol, and Absolute ............................ B-5 Saybolt Universal Viscosity CharL ......................... B-6

!

Equivalents of Degrees API, Degrees Baume, Specific Gravity, Weight Density, and Pounds per Gallon ................ B-1

,I

Steam Data Boiler capacity .....................................................:... B-8 Horsepower of an engine.......................................... B-8 Ranges in steam consumption by prime movers ................................................. B-8

Properties; saturated steam, saturated water _________ A-12

Properties; superheated steam ............................... A-16 Properties; superheated steam, compre,osed water ..... A-19 Vlow Characteristics of )zzles and Orifices Flow coefficient C for nozzles ................................. Flow coefficient C for square edged orifices ........................................ Net expansion factor Y for compressible flow ........................................ Critical pressure ratio, rc for compressible flow ........................................

A-20' A-20 A-21 A-21

Flow Characteristics of Pipe, Valves, and Fittings Net expansion factor Y for compressible flow through pipe to a larger flow area ........ A-22 Relative roughness of pipe materials and friction factor for complete turbulence ............A-23 Friction factors for any type of commercial pipe ............................ A-24 Friction factors for clean commercial steel and wrought iron pipe ........ A-25 Resistance in pipe due to sudden enlargements and contractions............ A-26 Resistance in pipe due to pipe entrance and exit.. ........................ A-26 Resistance of 90 degree bends .............................. A-27 Resistance of miter bends ....................:................. A-27 Types of valves (sectional ilJustrations) ............ A-28 Schedule (thickness) of steel pipe used in obtaining resistance of valves and tittings of various pressure classes ................ A-30 Representative equivalent length ( LID) in pipe diameters of valves and tittings .............. A-30 Equivalent lengths L and LID and resistance coefficient K .............................. A-31 Equivalents of resistance coefficient K and flow coefficient C,...................................... A-32

Power Required for Pumping..................................... B-9 Equivalents (General) Measure ...........................................................:........... vVeight ...............................................................:....... Velocity ...................................................................... Density ........................................................................

B-J 0 B::..! () B-IO B-IO

Physical constants ................................................... 13-10 Temperature ............................................................... B-IO Pretixes ........................................................................ B-IO Liquid measures and weigh t3................................... B-11 Pressure and head ....................................................... B-II Four-Place Logarithms to Base 10............................ B-12 Flow Through Schedule 40 Steel Pipe Water .......................................................................... B-14 Air ................................................................................. B-15 Commercial Wrought Steel Pipe. Data Schedules 10 to 160 ................................................. B-16 Standard, extra strong, and double extra strong...................................... B-18 Stainless Steel Pipe Data Schedules 55, lOS, 40S, and 80S ............................ B-19

APPENDIX C page

Bibliography

C-l

Nomenclature ........................................... 5ee next page

1

I 1

\

Nomendature---------·--~---Unless otherwise stated, all symbols used in this book are defined os follows:

A a

B C Cd

Cv

cross sectional area of pipe or orifice, in square feet cross sectional area of pipe or orifice, in square inches rate of flow in barrels (42 gallons) per hour flow coefficient for orifices and nozzles = discharge coefficient corrected for velocity of approach = Cd / " I-(do/d.)' discharge coefficient for orifices and nozzles flow coefficient for valves: expresses flow rate in gallons per minute of 60 F water with 1.0 psi pressure drop across valve =

D d

,t !,, , t

e

/

g

H h

f f

r

h, hL h", K k

Lm

M MR n

P P'

length of pipe, in feet equ;\'a:ent length of a resistance to flow, in pipe diameters length of pipe, in miles molecular weight univer~al gas constant = 1;44 exponent in equation for polytropic change .(p' \! ~ = constant) pressure. in pounds per square inch gauge pressure, pounds per square inch absolute (see page 1-5 for diagram showing relationship betu:een gauge and absolute pressure)

p' Q q q'

q'. q' • q ..

,

q ..

individual gas constant I

s s. T

Q v pi (6q!:::.P)

internal diameter of pipe, in feet internal diameter of pipe, in inches base of natural logarithm = 2.718 frictio:::! factor in formula hL =/Lv'/D2g acceleration of gravity = 32.2 feet per second per second total head, in feet of fluid static pressure head existing at a point, in feet of fluid total heat of steam, in Btu per pound loss of static pressure head due to fluid flow, in feet of fluid static pressure head, in inches of water resista:.'lce coefficient or velocity head loss in the formula, hL = KV'/2g' ratio of specific heat at constant pressure to specific heat at constant volume = cJ)/c~

L L/D

R

pressure, in pounds per square foot absolute rate of flow. in gallons per minute rate of flow, in cubic feet per second at flowing conditions rate of flow. in cubic feet per second at standard conditions (14.7 psia and 60F) rate of flow. in millions of standard cubic feet per day, MMsefd rate of flow. in cubic feet per hour at standard conditions ('4.7 psia and oaF), scfh rate of flo\\', in cubic feet per minute at flowing conditions rate of flow, in cubic feet per minute at std. conditions (14.7 pSia and 6oF), sefm

v Va v v, Wi W Wa

x Y Z

AfR.'1

544/M

Reynolds number hydraulic radius, in feet critical pressure ra[;o for compressible flo'.' specific gravity of liquids relative to wate:both at standard temperature (60 F) specific gravity of a gas relative to air = the ratio of the molecular weight of ct." gas to that of air absolute temperature. in degrees Rankine (460 + t) temperature, in degrees Fahrenheit specific volume of fluid, in cubic feet pc:-. pound mean velocity of flow, in feet per minute volume. in cubic feet mean velocity of flow, in feet per second sonic (or critical) velOCity of flow of a gas. in feet per second rate of flow, in pounds per hour rate of !low, in pounds per second weight, in pounds percent quality of steam = 100 minus pe, cent of moisture net expansion factor for compressible flow through orifices, nozzles, or pipe potential head or elevation above reference level, in feet

Subscripts indicates orifice or nozzle conditions unless otherwise specified (I) indicates inlet or upstream conditions unless otherwise specified (2) . indicates outlet or downstream conditions unless otherwise specified (100) . refers to 100 feet of pipe

(0)

Greek LeHers L.lta

f:"

differential between two points

Epsilon

•

absol ute roughness or effective height ot pipe wall irregularities, in feet

Rho

P

p'

weight density of fluid, pounds per cubic ft. density of fluid, grams per cubic centimeter

Mu

,

J1. ,

v , v

absolute (dynamic) viscosity, in centipoise absolute viscosity in pound mass per foot second or pou~dal seconds per sq foot absolute viscosity. in slugs per foot sec~mc: or pound force seconds per square 100! kinematic viscosity, in centistokes kinematic visc9sity, square feet per secon

'-'

~

0

= f-

o

"- .1 ';; ., .08 ;;; .06 --

'" .04 I

~. 0

"-

';; 2

'"

~

'" o -

~

f--

.8 .9 1.0

..

P

-

;:;. :::-. 0

1/2

-\1 \"

A\·,

.01

.02

~



f

... ..,

-I C

w

~

l

~

m 0

Q.

e

e

I

~40

I~'" 0

.4

118

en en

C

c

"0 0-

~

100 80

'-.

C>~

-:;

w:: .2

0

:;;

Q.

u..

0

=u"

a::

5

:;:; u

u

7 .:: 6 .,;

~ .4 ~•• 3

c

.02

="

-'= u

B .=

400 300

.03 ~

;; 55 ~

1O~

,

....fI)

.:: 12

12 10

.."

-I

f-

Index 1

m

/:"[>10.

i

['

! .004 -=!.• 003

1

I

'"

Co)

I

1 0' "':

.02

0

'" ",'

"~

., m

a:

.oJ

'"'"

.OOB

'"c'";;; ~

c.

'"

-c c ~

0

0-

'" ., ~

u..

=

~

-=

;;;

';;

e

U-

~

'"

'" ~

c. c.

0

~ ~

"''"

~

I

1/4

g

r:t; ~

'" :::"'

Ii

$

"'

60 -' "C ro 50 e.> 40

:c

"'"

'" 0

0

Z

'";;;

'"ro

0=

'"u

-~

-

0

.E

::;;

~

u ~

10 8

U

~

~

'-'

~

'" 0

"-

~

0

"" I-

.ero

1.0 .8 .6

""

.4

0

I

.3

.:..,

20



Cl

~

CD ~

0

~

'" Q,

>

I

<

,.0

-

,.'"z

!2.. 0

!:!.

Example 2

'<

Given: Air at 400 pounds per square inch gauge and 60 F flows through a I Y2-inch Schedule 40 pipe at the rate of 144,000 cubic feet per hour at standard conditions (14.7 psia and 60 F).

Find: The flow rate in pounds per hour and the velocity in feet per minute. I.

W

2.

P

11 000, using So 2.16

......... page 8-2

1.0

.............

. .... page A-IO

Re~d

Connect

J. 4·

0

n 0 3

... ...!a.

"0 CD

0-

Solution:

3.7

7600

,.n...

u

d' p

p

=

2.16

,--_In_d_cx

W I

=

11000

Y2" Sched

40

CI> "lI'I

c

c.. In

Index.

::J

V = 6 000

-ij'

.."

CI>

3:: c:

;;:

0

z

0 3:: 0

",.,.... x

'" ,.0 0 ~

...,.:x~

0 c :x

" ,.< :;: m

yo ~

~ z

",.

yo

.___._______ Condition of Steam

__. ___~..~lSonable V~.~~it~~s for."!0w._oL~!eam Throu{jh Pip_e_____._____...__ ... Pressure Service Reasonable Velocity ({')

P,ig

(V)

==~=~~ 'b0 ' ."

- -.. ::J

Example 2

Indcx

If

::c

1"1

Example 1

Solution: 1. W

:;.c

"Tl Q

r.

"TI

(For v,>lues of d. see pages B-16 to 8-18)

1

..._. o· ::J

tll

z 0

~ ."

m

n ~

~

Z

m

I

nn

,!

~ D V Uli--il--U U HUH H w

l'

II H II· U ·

I+~*n

Index

I~Z

d

J.I.

.3..,

j

m

.44

I

'1

Internal Pipe Diameter in Inches

.6 .7

_____- - - 3 6 ____

_ - - - - - 24

.R

.9 1.0

~_______ l~

:=::=-:::

~_____

:; e

Re

Co V> -0

10000 8000 1=1 6000 4000 3000 __ 2000

e

"-

"0 I,

V> -0

I

__



=> 0 .c

'::J .::

BOO1_ 600 400 300

i"

200

,=> 0

'

'"

CD

!"

IT

."

0

~

~ ~

~ z

Q .V>

» z 0

.."' ~

-

40J

-0

.,.,.. "",~'...,~,"?~~""'-i"_~~""''''''''',-''''

........."'...~".

IT

0 3: '"c:

I~

.05

Friction Factor for Clean Steel and Wrought Iron Pipe

:J 0 0.. en

.&

-0

V>

...

(q' .)' S,' •.

~

m

-

'"..,

...

"'tJ

..

(For values of d', sec pages 13-16 to 13-18)

i!

I, I

I

W

=

0.0764

$

lI ,I

1 1

I ~ 1

I 1

c: ...

II>

...0 0

q'. S,

~

c

>= V> > z 0

Z 0

"0

~

::I

> '"

0

Cl

Air: For pressure drop, in pounds per square inch per 100 feet of Schedule 40 pipe, for air at 100 psig and 60 F, see page B-15.

1

I

II>

When the flow rate is given in cubic feet per hour at standard conditions (q'.) , use the following equation or the nomograph on page B-2 to convert to pounds per hour (W).

I ~

0

Example 1

n 0 3

Example 2

Given: Natural gas at 250 psig and 60 F flows through an 8-inch Schedule 40 pipe at a rate of 1,200,000 standard cubic feet per hour; its specific gravity is 0.75.

Given: Steam at 600 psig and 850 F flows through a 4inch Schedule 80 steel pipe at' a rate of 30,000 pounds per hour.

Find: The flow rate in pounds per hour and the pressure drop per 100 feet of pipe.

Find: The pressure drop per

Solution:

Solution: /, d 2.

J. 4·

100

feet of pipe.

/,

........ page 13-17

3.826

J1.

0. 02 9

. page A-2

f

0.017

. page 3-19

V

J. 22

.. page 3-17 or A-17

5·

W

=

30 ~-fd-~6

6.

Index

7·

Index ~_ _

2

1

f =

I_V

0,017 1,22

!!!.

69000

.. using S,

= 0.75; page 13-2

2,

J1.

0.011

. , pai:e A-5

J.

f

0.014

" .page 3-1'1

4·

P

1. 0 3

.. paile A-IO

"

~

0

:E ~

::l:

0"

'TI

< >

~

W

~

0

0II>

0

C

..

::I

II>

c: Cl ::l:

:;:m

.'" ~

~ z

Cl

.'" > Z 0

---,

Index

2

Index

1

---/::"P 'OO

II>

::l:

'"

...~

m

Read

Connect

....

"0

...

7.5

Connect

5,

W

=

69 00018-;;

6,

Index

2

7,

Index

_1_ _

1

Rend

S~ 40 pi~

i

Index

2

f =

1

Index

I

0,014

I_~_~~_J /::"P 'OO = 0.68

..,n

>

Z m

.~;::J

3 -21

CHAPTER 3 - fORMULAS AND NOMOGRAPHS fOR HOW THROUGH VALVES, fITIINGS, AND PIPE

CRANE

~

Pressure Drop in Compressible Flow Lines {continued)

~ ;::.;

JOOH Jad spunod 0001 U! 'MOlj

g gg

__

gg g g eo~a.noo:::t"M

80 000 0 ...-fooc.oL..n~('Y)

gC'oJ

0 N

)0

8jBIl-"11

0 _oo(,O'"'"'~~

_~~I.C?~C'"t':?

('oJ

~

C'!

!'I!!IIr1dd!l,1 II! II!!!!!!!!!!!!"'!,! I,I[!,! I I!!!,i!!!!illtddddd,t! i! :'tj,I!!1!I!!!!!,1r1d.!r!' I! jll!t!!!!!!!!!!!

JOpe:l UO!P!J:l- J

Ln~

........

,:,!

~

I!!

I

!

!

~

N

(Y:J

...,,~~

.-

~



![!!!!)!!!

I",!

~

,I! i

!

I

I

!

(op alnpa4JS - ad!d pJBpURlSJ S84JUI U! 'Jaj8WB!O IBU!WON qo ('oJ 0 N

(,Oq-N _ __

0_

00

(,0

U"'>

I

1

I

! I r'IIFIfI I ! ( i i j i l l j i l ' ( I

~

I

!!

J

~

~oor-(,O

""::I'"

i

~

C"')~

)

~ C'J

~ "'$. ............

N

I!

J!

I

~

_

!

[

to:)

.....

~

~

~

_:-;!:

s_"

I

I

-f

I

I

Ililililii\iitljilii\QQ'lllil!ilii(liil\

1.0.......

-~oql':~

cry.........

u:

~

sa4JUI U! 'ad!d )0 Jajawe!o leUJajul--1' ijJUI aJRnbs Jad sPunod U! 'jaa.::l 00 I Jad dOJO aJnssaJd -- oo'cl'i7 L.t1 !!

N

C"')

U"'> Ln(,Or-OOC':l 0 _ _

.......

,I"!I!,!!!!,,!!!!!!!!!!!!I!!

J

0 0 0 N " ~

I f l , I , ! , ! ! ,i"!!!!!ld!I!!I!!!!!!!!!!

..... ><

~----------------.----------------------------------------------------------------

.=

~

~

~

~

g

I'I'I!'I I!i 1!"II'I"j!!! I I r 1 J

ct.

~

q

~

q

punod Jad laa.:l J!qn3 U! 'P!nl:l ZU!MOI:l

)0

~

c-....

I! I

~CJ")CX)

!

!

I

r- :=:1.

I

:::3

::=:I. .==1t

:=D :=:I~

~

==t

The physical properties of many commonly used fluids are required for the solution of flow problems. These properties, compiled from many varied reference sources, are presented in this appendix. The convenience of a condensed presentation of these data will be readily apparent.

I ~

I t

Most texts on the subject of fluid mechanics cover in detail the flow through pipe, but the flow characteristics of valves and fittings are given little, if any, attention, probably because the information has not been available. A means of estimating the resistance coefficients for valves, deviating in minor detail from the standard forms for which the coefficients are known, is presented in Chapter 2 .

~

.

:::::::n i

~ I

The Y net expansion factors for discharge of compressible fluids from piping systems, which are presented here for the first time, provide means for a greatly simplified solution of a heretofore complex problem.

:b~

~

! II

I I

i

A _2

APPENOIX ,,- PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE

CRANE

. 0 f Steam 14 V·ISCOSlty .050

1\\

\\

.048 .046 .044

.040

I

!

:::;

~

.042

,

« \

:

I

Q

.036

l-

a

~

~ I,

~

Vl

Ie

,

';1

......

~

. (/l

~

-- I - - 1 - -

% V - ~~ % 1/ 0 ~ 7~ ll~~~ % ~ \1-"'' ' ' ",,,,,,,/

~

'I

"./"

'V /"

(/l

= « .026

./

V'o\)\)~ '>.\)\)

.~ ~

?f/

/' V' / /~~~ I L/ //%V~/ I

.024

.022

/

~v

I I

0 0/'1~

I

.020

I

, I

I~

.018

;; V'

I I

V

.016 .014

.,V /

\ ~",(J

I

~ .028

I :t

V

V V

,. /

I

~

.030

....

----

----

L,.

.-: .032

:> '"

1860 ...........

.......

c:

u on

2600

-2200-

10..

VI

U

a

'--

1

«

(/l

0.

"-

=>'"

l

Cl.>

'-.....""1

"

~

PSIG 319 1.5 -3000

1-,\ «

I

i

\

'" UJ

.038

I I

...

\

~RESSURE

'-

)

I I

l/

200

I

300

400

500

600

700

800

I 900

1000

1100

1200

t - Temperature, in Degrees Fahrenheit

Example: Viscosity of 600 psig, 8;0 F steam is 0.02Q centipoise.

Adapted from: Philip ). Potter Steam Pou'er Planls, Copyright 1949, The Ronald Press C'..ompany.

CRANE

I

C,H,

CO 2

I

I II

I

l

N, NO N,O 0, SO,

.06754 .07528 I' .04420 I .1037

I I

Heat Capacity Per Cubic Foot at Atmospheric Pressure and 68 F

.350 I .2737 i .897 59.4 I' 1.000 .1725 53.3 .241 .587 90.8 .523 .4064 38.7 .124 .0743 I 1.377 1. 516 .1599 35.1 I .205 .1721 .965 55.2 I .243 I' .3292 .967 55.1 .40 .138 1.25 .754 386. .191 .1365 1. 256 I 42.4 3.42 .0695 1 767. 2.435 .593 .4692 .553 96.4 .24 .2006 1.738 1 30.6 55.2 I .247 .966 .1761 i I .231 1.034 .1648 51.5 .221 .1759 1.518 I' 35.1 .1549 1.103 48.3 .217 .154 24.1 .1230 , I 2.208 II,

I I

k equal to

cplc,

-I

Cp

I'

.07269 .0728 .01039 .09460 .005234 .04163 .1309 .07274 .07788 .1143 .08305 .1663

I

--1--------,-1

I

.1142

I

I

C"

.0185 .0236 .0130 .0181 .0179 .0231 .0077 .0129 .0234 .0183 .0177 .0125 .0291 .0240 .0130 I .0078 .0181 .0129 .0179 .0127 .0247 .0195 .0314 I .0263 .0179 .0128 .0180 .0128 .0253 .0201 .0180 .0129 .0256 .0204

I

1.28 1.40 1.29 1.67 1.28 1.41 1.22 1.66 1.40 1.40 1.26 1.20 1.40 1.40 1.26 1.40 1.25

*\\'eight density values are at atmospheric pressure and 68 F. For yalues at 60 F, multiply by 1.0154.

Volumetric Composition and Specific Gravity of Gaseous Fuels 13 ,

Chemical Composition Percent by Volume

I Ii •

HYdrO-I Carbon Paraffin gen Mon- Hydrocarbons

Type of Gas

I oxide I MethI

r

Natural Gas, Pittsburgh Producer Gas from Bituminous Coal I 14.0 Blast Furnace Gas 1.0 Blue Water Gas from Coke 47.3 Carbureted Water Gas 40.5 Coal Gas (Cont. Vertical Retorts) 54.5

I

II

Coke-Oven Gas Refinery Oil Gas (Vapor Phase) Oil Gas, Pacific Coast

il

46.5 13.1 48.&

ane

27.0 27.5 37.0 34.0 10.9 6.3 1.2 12.7

83.4 3.0 1.3 10.2 24.2 32.1 23.3 26.3

I

Ethane

I

IlluITlinants EthYl-II Benzene ene

I Oxy-

I,

gen

I

I

I

15.8 0.6

21.7

6.1 1.5 3.5 39.6 2.7

2.8 1.3 0.5 1.1

!

Specific Gravity Relative Nitro- Carbon to Air gen DioxS. ide

0.7 0.5 0.2 0.8 1.0 0.3

0.8 50.9 60.0 8.3 2.9 4.4

8.1 3.6

Data on this page reproduced by permission from Mechanical En[!,ineers' Handbook by L. S. Marks. Copyright. May. 1954; McGraw-Hili Book Company. Inc.

4:5 11.5 II 5.4 3.0 3.0 II 2.2 0.1 4.7 II

0.61 0.86 1.02 0.57 0.63 0.42 0.44 0.89 0.47

A-9

APeENDly. A-PHYSICAl PROPERTIES Of flUIDS AND flOW CHARACTERISTICS OF VALVES, FITIINGS. AND PIPE

CRANE

Steam -

Values of

k

Ratio of Specific Heat at Constant Pressure to Specific Heat at Constant Volume

k = epIc.

1.34

~

1.3 2

""'-

"-

§

1.30

c

8. x

L.LJ

.0..

__ £H",!e",o,J - !o-_"i"'_

......r-

g . c

a:>

(/)

I

~o~~ ~o~ I

IOOO~

~o~

""'" 1.26 I"-

;-;::. ~

I

500 F

-

__

I

..

-r-::t,_~ -r-I·h __~ -~OO-L..ro 400 F

---

12 8

!>;os>

300 F

J...l40...ru;.,

....

-

--

~-

.-

--

I---

-......

~

~--

---~-

--

---

~-

~-

::

~

~

~ ~/ - - ~ ~ ~Rl/' - --- ........... \~\\

.//

.J~

I'

~-

1.2 4

'""

\~ t

1.22

I

2

5

10

20

50

100

200

500

pi _ Absolute Pressure, Pounds per Square Incil

For sma'] changes in pressure (or volume) along an isentropic,

pv k = constant

j

::::II ::::=3

::::::'1 . ==:1

.==8

Reprinted from "Thermodynamic Properties of Ste2.m" by J. H. Keenan and F. G. Keyes, 1936 edition, by permission of the publishers, John Wiley &1 Sons, Inc.

~

A - 10

CRANE

APf'f>l ii.0375! .05021 .06.3!l

I'

i i 175

1 200

1'1'

1

I 225

.1477 i .1903 i .233 .275 .318 .361 i ,403 .446 .616 .659 .701 .1421 i .1831 1 .224 ,. 265;'--;"':'c;.30",6o--'---'C'3",4",7-'..-,,3.:,.8:,c8;-,-'...:.-;4",29.-+--,-::~_~~---'C'50:;5:0'2-,'..::.~59;c3;.--;---'C.6C;3.4;;'~"::'767~5 .13691.1764 i .216 .255 .295 .334 .374 .413 .492 .531 .571 .610 .650 .1321 .17021.208 .246 .284 .322 ,361 .399 .'44~95 ".513 .551 .589 .627 .1276 .1644 i .201 .238 .275 .311 .348 .385 ".495 .532 .569 ,606 .1234, .15901.1945 .230 .266 .301 .337 .372 .443 .479, .515 .550 .586 .lI58 1 .1491 .182:-o5c+":.;:2~16:c--~.2c4,~9-+..:.~28;:c3~''':':.;:3~16~.....:.:.3",4",9-+-~:.::o-'--'-'4~16 .449' .483 .516 .550 .1090 1.14051 .1719' .203 .235 .266 .298 .329' .392 0423 .455 .486 .51S .1030 !.1327 : .1624 ', .1921 .222 .252 .281 .311 .370 ADO i .430 .459 .489 .0977 .1258 ' .1540 ! .1821 .210 .238 .267 .295 .323 .351 .379 ,407 .436 .464 .0928 .1196,1 .1464 i .1731 .1999 .227 .253 .280 .307 .334 .360 .387 .414 .441 .0885 i .1140 i .1395' .1649 .1904 .216 .241 .267 .292 .318 .343 .369 .394 ,420 250

I'

300

i

400

500

600

700

2.78 2.74 2.68

3.32 3.27 3.20

3.86 3.80 3.72

4.40 4.33 4.24

,2.63

3.14

3.65

4.16

1

800, 900

1000

psi' psi l~I~I~ ~ ~I~I~ ~ ~ ~ 1. 047 1.185 i l. 3Z3~"'1C'."'46"0"'1c-,1'-.-7"'36;-7-1'2.-'2"'9--+co 2"'.8"4'--:''''3C'.3"'9--''''3'''.'OC94~~4-.4'"9C-:-'''5~.0;;-;5~"'5'-.760OC-

1.026 1.161,1.1.% 1.431',1.70212.24 11.00911.142 '11.V5 1.408: 1.674 2.21 i .986 i 1.116 1.2:-*6 1.376' 1.636 2.16

ii

.968,11.09511.213

li:m: J:g~~ l::i~

1.350 i 1.605

r

2.12

U6f i i:~~; IU~ I ~:~~

tg~ n~

4.95, 5.49 4.87 5.40 4.76 I

4.67

!:g~ ::~~

100 Ii .916: 1.036 ! 1.157 1.2781,1.51912.00 12.48 2.97 3.45 3.93 4.42 lID .1: .900: 1.0181 LU7 1.255,1.492 1.967 2.44 2.92 3.39 3.86 4.34 120 ".884 I 1.001 ! 1.1.;;:17;.-'-01'0'2'73i-4-c1~1:..4o-:6",7-:-;1c:..",93,"3,-1c:2""-o4;:-0c-:-2~'c;:8~6-"_~3.:;.3:;;3--+..:3c:.,,,80~_40'c;2",6-i-7-7' 130 .869 I .984' Li.lI>8 1.213 \1.442 1 1.900 1 2.36 2.82 3.27 3.73 4.19 140 .855'.967 1..05'j 1.193 11.41811.868 1 2.32 2.77 3.22 3.67 4.12 150 .8411 .951! l,.1l!(,2 1.'17311.395,1.83812.28 2.72 3.17 3.61 4.05 175 .807, ,9!411.ll'.l1l 1.127 1.340 i 1.765 I 2.19 2.62 3.04 3.47 3.89 200 .777 I .879 I .982 1.08411.289 I 1.698 (2.11 2.52 2.93 3.34 3.75 225 .7491 .847: .'146 1.044 i 1.242 , 1.636 i 2.03 2.43 2.82 3.21, 3.61 i 4.00 250 .722 .817 ', ""13,' 1.08811.198 1.5791' 1.959 2.34 2.72 3.10' 3.48 3.86 275 .698 .790 .!!lSi .973 i 1.157 11.525 1.893 2.26 2.63 3.00 i 3.36 3.73 i .675 .764 .852 .941 '11.11911.475.1.830 2.19 2.54 2.9013.25 3.61 i 300 1 1 ..",.m~OO","~:..8~8~3~1c:.''OC05~0~1~1~.~3~84~1_",I.~7~1~7772~'0i:5~~2:..3",8o--'~2.~7~2-+-c;.3~'0i:5~~J~.39 , ~3",50__~_.~63~3~1~.,7~16~_ 400 .596' .6751 .;;'53 .8321 .98911.30311.618 1.932 2.25 i 2.56 2.87 3.19450 .5631 .6381 .712 .786 .93411.232,1.529 1.826 2.12 '2.42 2.72 3.01 500 .534 .~£~ i .675 .745 .886 1.16711.449 1.73J 2.01 2.29 2.58 2.86 550 .508 1 " n I ,M1 .708, .84211.110 1.377 1.645 1.912 i 2.18 2.45 2.72 600 .484 i .547 i .611 .675 i .802 I 1.057 1.312 1.567 1.822, 2.08 1 2.33 2.59

I

i

I

I

Air Density Table

The table at the left is calculated for the perfect gas la\\' shown at the top of the page. Correction for supercompressibility, the deviation from the perfect gas law, \\'Quld be less than three percent and has not been applied. The weight density of gases other than air can be determined from this table by multiplying the density listed for air by the specific gravity of the gas relative to air, as listed in the tables on page A-8,

APPENDIX A - PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES. FITTINGS. AND ~

CRANE

A-ll

Weight Density and Specific Volume

Of Gases and Vapors R

continued

8g 0.35

V 0.4

p

60

Index

50 40 30

0.5 15,----1-

20 0.6 ~

0 0

"0

c:: =>

LL. u

0.7

.0

=>

Q:;

Q:;

Q;

u

Cl.

Cl.

D

~

=='" OJ

=>

u

'"

-

~

c::

0.8

0

V>

- C-'>'"

0

0.9

..... ~

-

=>

:.0

a..

u

I

=>

c

~ C-'>



'"I

'"

:0:

~

Cl..

0

I-

100

U

2::l

'" 0

.0

'" ""I

a.

.6 .7

=> C-'>

'"

=u E

:':

=> ""=

""Q:;

"'-

'"

"0

SO

V>

u

'" I

120

Q:;

>

0;,

CQ

c. E

0;>-

Cl

c.

140

E =>

'"

u

'" :0; ro

c

.?5 c'"

>

00

160

U

0

c::-

'-'

180

u.

'" c::

OJ

t 200

OJ

"0

:;;

T

0

a..

co

=> 0

a..

250.34 218.9 945.2 1164.1 0.0170G9 , 16.~. 252.22 220.8 943.9 1164.8 0.017024 17.,1 254.05 222.7 942.7 1165.4 0.017039 18.3 255.84 941.5 1166.0 0.017054 , 224.5 !, 19.:> 257.58 226.3 940.3 1166.6 0.017069 I I - , Steam fables (1967), With perm,:O:Slon of the pubH~hcr, --Ihe American */\bstracted from AS\1E Society of Mechanical Engineers, 345 East 47th Street. New York. New York 10017. 14.696 15.0 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0 31.0 32.0 33.0 34.0

0.3 1..3

I

Steam Cu. ft. per lb.

I

I

I

I

,

I

I

I

I

I

I

I

I

I

26.799 26.290 24.750 23.385 22.168 21.074 20:087 19.190 18.373 17.624 16.936 16.301 15.7138 15.1684 14.6607 14.1869 13.7436 13.3280 12.9376 12.5700 12.2234

{confinued

on

the next page)

(;

C=f:I~

e::r=i

~i

9~~

=::bt

:::::::::s ::=:9 ~

=:$

A-13

APPENDIX A - PI-YSICAl PROPERTIES Of flUIDS AND flOW CHARACTERISTICS OF VAItfft£S, FITTINGS. AND PIPE

CRANE

Properties of Saturated Steam and Saturated Wafer-continued Temperature

Pressure Lbs. per Sq. In. Gage Absolute

P'

35.0 36.0 37.0 38.0 39.0 40.0 41.0 42.0 43.0 44.0 45.0 46.0 47.0 48.0 49.0 50.0 51.0 52.0 53.0 54.0 55.0 56.0 57.0 58.0 59.0 60.0 61.0 62.0 63.0 64.0 65.0 66.0 67.0 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0 76.0 77.0 78.0 79.0 80.0 81.0 82.v 83.0 84.0 85.0 86.0 87.0 88.0 89.0 90.0 91.0 92.0 9.3.0 94.0 %.0 96.0 97.0 98.0 99.0 100.0 101.0 102.0 103.0 104.0 105.0 106.0 107.0 108.0 109.0

I

P

t

I

Degrees F.

20.3 21.3

22.3

259.29 260.95 262.58 264.17 265.72 267.25 268.74

".,+ 23.3 24.3 25.3 26.3

II

I,

28.3 29.3 30.3 31.3 32.3 ~ 33.3 34.3 I 35.3 36.3 37.3 38.3 39.3 40.3 41.3

I I

43.3 44.3 'U 45.3 46.3 47.3 48.3 49.3 50.3 51.3 52.3 53.3 54.3 55.3 56.3 57.3 58.3 59.3 60.3 61.3 62.3 63.3 64.3

I

m." 271.65 273.06 274.44 275.80 277.14 278.45 279.74 281.02 282.27 283.50 284.71 285.90 287.08 288.24

+'' ."

290.50 291.62 292.71 293.79 294.86 295.91 296.95 297.98 298.99 299.99 300.99 301.96 302.93 ;303.89 304.83 ,105.77 ,106.69 ,107.61 ;;08.51 ;;;09.41 310.29 311.17 312.04 312.90 313.75 314.60 315.43 316.26 317.08 3.17.89 3.18.69 3:!9.49

65.3

66.3 67.3 68.3 69.3 70.3 71.3 72.3 73.3 74.3 75.3 76.3 77.3 78.3 79.3 80.3 81.3 82.3 83.3 84.3 85.3 86.3 87.3 88.3 89.3 90.3 91.3 92.3 93.3 94.3

I I I

3:!D.28

I

321.06 321.84 322.61 323.37 324.13 314.88 325.63 32&.36 327.10 327.82 328.54 329.26 329.97 330.67 331.37 33,'.06 332.75 333.44 334.!l

I

I

Btu/lb.

228.0 229.7 231.4 233.0 234.6 236.1 237.7 239.2 240.6 242.1 243.5 244.9 246.2 247.6 248.9 250.2 251.5 252.8 254.0 255.2 256.4 257.6 258.8 259.9 26 I.! 262.2 263.3 264.4 265.5 266.6 267.6 268.7 269.7 270.7 271.7 272.7 273.7 274.7 275.7 276.6 277.6 278.5 279.4 280.3 281.3 282.1 283.0 283.9 284.8 285.7 286.5 287.4 288.2 289.0 289.9 290.7 291.5 292.3 293,1 293.9 294.7 295.5 296.3 297.0 297.8 298.5 299.3 300.0 300.8 301.5 302.2 303.0 303.7 304.4 305.1

Total Heat of Steam

Latent Heat of Evaporation

Heat of the Liquid I

I

I

I

I

I

Specific Volume

h.

i

Btu/lb.

Btu/lb.

~

939.1 938.0 936.9 935.8 934.7 933.6 932.6 931.5 930.5 929.5 928.6 927.6 926.6 925.7 924.8 923.9 923.0 922.1 921.2 920.4 919.5 918.7 917.8 917.0 916.2 915.4 914.6 913.8 913.0 912.3 911.5 910.8 910.0 909.3 908.5 907.8 907.1 906.4 905.7 905.0 904.3 903.6 902.9 902.3 901.6 900.9 900.3 899.6 899.0 898.3 897.7 897.0 896.4 895.8 895.2 894.6 893.9 893.3 892.7 892.1 891.5 891.0 890.4 889.8 889.2 888.6 888.1 887.5 886.9 886.4 885.8 885.2 884.7 884.1 883.6

1167.1 1167.7 1168.2 1168.8 1169.3 1169.8 1170.2 1170.7 I!71.1 1171.6 1172.0 !l72.5 1172.9 1173.3 1173.7 1174.1 1174.5 1174.9 1175.2 1175.6 1175.9 1176.3 1176.6 1177.0 1177.3 1177.6 1177.9 1178.2 1178.6 1178.9 1179.1 1179.4 1179.7 1180.0 1180.3 1180.6 1180.8 118 I.! 1181.4 1181.6 1181.9 1182.1 1182.4 1182.6 1182.8 1183.1 1183.3 1183.5 1183.8 1184.0 1184.2 1I84.4 !l84.6 1184.8 1185.0 1185.3 lI85.5 !l85.7 l!85.9 1186.0 1186.2 1186.4 1186.6 1186.8 1187.0 1187.2 1187.3 1187.5 1187.7 1187.9 !lS8.0 1188.2 1188.4 1188.5 1188.7

I

II

I

I

V

~

I I

Water Cu. ft. per lb.

, I I i

I! I i r,

,\j I ,!

Ir r

I, I

I

O.Oi7083 0.017097 0.017111 0.017124 0.017138 0.017151 0.017164 0.017177 0.017189 0.017202 0.017214 0.017226 0.017238 0.017250 0.017262 0.017274 0.017285 0.017296 0.017307 0.017319 0.017329 0.017340 0.017351 0.017362 0.017372 0.017383 0.017393 0.017403 0.017413 0.017423 0.017433 0.017443 0.017453 0.017463 0.017472 0.017482 0.017491 0.017501 0.017510 0.017519 0.017529 ().017538 0.017547 0.017556 0.017565 ;).017573 (1.017582 0.017591 i).017600 v.017608 (}.017617 fI.017625 0.017634 i).017642 ').017651 0.017659 0.017667 /).017675 0.017684 (;.017692 0.017700 0.017708 0.017716 0.017724 0.017732 (>.017740 0.01775 0.01776 0.01776 0.01777 0.'1l778 0.D1779 0.01779 0.01780 0.01781

I

I I

I

I

I

.

Steam Cu. ft. per lb.

11.8959 11.5860 11.2923 11.0136 10.7487 10.4965 10.2563 10.0272 9.8083 9.5991 9.3988 9.2070 9.0231 8.8465 8.6770 8.5140 8.3571 8.2061 8.0606 7.9203 7.7850 7.6543 7.5280 7.4059 7.2879 7.1736 7.0630 6.9558 6.8519 6.7511 6.6533 6.5584 6.4662 6.3767 6.2896 6.2050 6.1226 6.0425 5.9645 5.8885 5.8144 5.7423 5.6720 5.6034 5.5364 5.4711 5.4074 5.3451 5.2843 5.2249 5.1669 5.1101 5.0546 5.0004 4.947" 4.8953 4.8445 4.7947 4.7459 4.6982 4.6514 4.6055 4.5606 4.5166 4.4734 4.4310 4.3895 4.3487 4.3087 4.2695 4.2309 4.1931 4.1560 4.!l95 4.0837

II I , i

I

II ~

A .. 14 APPENDIX C-'-.'--'-_ __ _

CRANE

A - PHYSICAL PROPERYIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE

Prop'2 iies of Saturated Steam and Saturated Water-continued Y

-------'-

Pressure Lbs. per Sq. In. ___

1

AbSOpl,utc

I

I

Gap!;c 95.3 96.3 97.3 98.~

i I

I i

I

99.c, 100' .0 101.3 102.3 103.3 104.3 105:3 106.3 107.3 108.3 109.3 110.3 111.3 112.3 113.3 114.3

I

,I

I

i

I I

I

I

i !

iI

! I

I I

115.3 116.3 117.3 118.3 119.3 120..3 121.3 122.3 122,.3 124,.3 12S.3 126.3 -, 128.3. 129.3 130.3 131.3 132.3 13,1.3 13'1.3 13S.3 137.3 139.3 141.3 14,1.3 145.3 147.3 149.3 151.3 15:1.3 15';.3 15;i.3 159.3 161.3 16:;.3 16;;.3 167.3 169.3 171.3

~U

,i

II ,

I

!

i

Tcmpcrature

I Ii

--I

==c~=;:==*.===i.. 110.0 111.0 112.0 113.0 114.0 11-~. 0 116.0 117.0 118.0 119.0 120.0 121.0 122.0 123.0 124.0 125.0 126.0 127.0 128.0 129.0 130.0 131.0 132.0 133.0 134.0 135.0 136.0 137.0 138.0 139.0 140.0 141.0 14'-. 0 143.0 144.0 145.0 146.0 147.0 148.0 149.0 150.0 152.0 154.0 156.0 158.0 160.0 162.0 164.0 166.0 168.0 170.0 172.0 174.0 176.0 178.0 180.0 182.0 184.0 186.0 188.0 190.0 192.0 194.0 196.0 198.0 200.0 205.0 210.0 215.0 220.0 225.0 230.0 235.0 240.0 245.0

I

17".3 177.3 179.3 181.3 18:3.3 183.3 190.3 19.1.3 200.3 20:;.3 210.3 215.3 220.3

nu

130.3

I : !

Degrees F.

334.79 335.46 336.12 I 336.78 337.43 33808 I I 338.73 339.37 340.01 340.64 341.27 341.89 342.51 343.13 343.74 344.35 I I 344.95 345.55 346.15 I 346.74 347.33 347.92 l 348.50 349.08 II 349.65 350.23 350.79 351.36 351.92 , 352.48 353.04 353.59 3~4 14 354.69 355.23 355.77 356.31 356.84 357.38 357.91 358.43 359.48 360.51 361.53 362.55 363.55 364.54 365.53 366.50 367.47 368.42 369.37 . 370.31 371.24 372.16 373.08 373.98 374.88 375.77 376.65 377.53 378.40 379.26 II 380.12 380.96 381.80 383.88 385.91 387.91 389.88 391.80 393.70 395.56 397.39 399.19

I

_~~~!b_

I I i

I

I

I,

I

I

Heat of the Liquid

I

I I

I

I

I

, II

!

. I

Ii

I

I I

I

305.8 306.5 307.2 307.9 308.6 3093 309.9 310.6 311.3 311.9 312.6 313.2 313.9 314.5 315.2 315.8 316.4 317.1 317.7 318.3 319.0 319.6 320.2 320.8 321.4 322.0 322.6 323.2 323.8 324.4 325.0 325.5 .>26 1 326.7 327.3 327.8 328.4 329.0 329.5 330.1 330.6 331.8 332.8 333.9 335.0 336.1 337.1 338.2 339.2 340.2 341.2 342.2 343.2 344.2 345.2 346.2 347.2 348.1 349.1 350.0 350.9 351.9 352.8 353.7 354.6 355.5 357.7 359.9 362.1 364.2 366.2 368.3 370.3 372.3 374.2

. Latent Heat Total Heat o f ; of Steam Evaporation! h I g

I I I

I

! !

,I

I

i

I

,

I

I

I I

I I

L I

I

Btu/lb.

Btui!!'.

883.1 882.5 882.0 881.4 880.9 8804 879.9 879.3 878.8 878.3 877.8 877.3 876.8 876.3 875.8 875.3 874.8 874.3 873.8 873.3 872.8 872.3 871.8 871.3 870.8 870.4 869.9 869.4 868.9 868.5 868.0 867.5 8671 866.6 866.2 865.7 865.2 864.8 864.3 863.9 863.4 862.5 861.6 860.8 859.9 859.0 858.2 857.3 856.5 855.6 854.8 853.9 853.1 852.3 851.5 850.7 849.9 849.1 848.3 847.5 846.7 845.9 845.1 844.4 843.6 842.8 840.9 839.1 837.2 835.4 833.6 831.8 830.1 828.4 826.6

1188.9 1189.0 il89.2 1189.3 1189.5 ;; . 11'96 1189.8 1189.9 1190.1 1190.2 1190.4 1190.5 1190.7 1190.8 1190.9 1191.1 1191.2 1191.3 1191.5 1191.6 1191.7 1191.9 1192.0 1192.1 1192.2 1192.4 1192.5 1192.6 1192.7 1192.8 1193.0 1193.1 11932 1193.3 1193.4

,

! I

I ! 1

I

I,

i

II

II

1193.5

I

I

I I I

I

,

1193.6 1193.8 1193.9 1194.0 1194.1 1194.3 1194.5 1194.7 1194.9 1195.1 1195.3 1195.5 1195.7 1195.8 1196.0 1196.2 1196.4 1196.5 1196.7 1196.9 1197.0 1197.2 1197.3 1197.5 1197.6 1197.8 1197.9 1198.1 1198.2 1198.3 1198.7 1199.0 1199.3 1199.6 1199.9 1200.1 1200.4 1200.6 1200.9

Specific Volume

v-

Water

Cu~~per I~.

I

-0"])1782 Tl4-:-048.f-0.01782 4.0138 0.01783 3.9798 0.01784 3.9464 0.01785 3.

...D. 0

0

~

0

:0:

n

til

iii (I) Q

,. ,.n'" :r

~

m

'"'a

::I

n V>

:e

0

0..

g

~

;:

ffi

-

G'I 1"

::I

z

." 'tJ CD

:;;

::r"

::;-

108

'"m::;

fl ::I

10 0

3Z ,.

-. ..

ihP

He - Reynolds Number

i',

6 8

-

",'

... +-

'-1--

f-..

103

3/4

+-\:.....;..,p.-,,=:;13 Ii ..ct:~~:~~

j~1Iff--l·1 I··t.·j·!.·.I··j· ... ,·[·..[·-11.···1... I·I-~~···' ....~~--.,.- .. -..-,-~-~.~-."---------......~~-,~-~,,",,"--

__

~~_·

_ _ _ _ _ • _ _ __

" '-'~..,"""'..._"' •. c,,""_,~,.'...,.,.-

A-26

APPEN[)IX A-PHYSICAL PROPERTIES Of flUIDS AND flOW CHARACTERISTICS OF VALVES, flnINGS, AND PIPE

CRANE

Resistance in Pipe

Resistance Due to Sudden Enlargements and Contractions 20

--

LO 0,9 0,8 ~ I

'"

y

~

0.7

~