pipe related formulas

8/13/2019 Pipe Related Formulas

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Pipe Related Formulas

1. CROSS SECTIONAL AREA (A) :The cross sectional area expressed in square inches is used in various tubular goods equations. The formulas

described below are based on full sections, exclusive of corner radii.

{1a}Round Tube:A = p! ("# $ d#)

Where:

! "utside iameter, inches d ! #nside iameter, inches

$xample: %alculate the cross sectional area of a &' ".. x .())' wall tube.

! &.))) d ! &.))) * +.())- ! .))) inches

/ ! p0 ( * d(-

/ ! 2.11(0 &.)))( * .)))(-

/ ! 1).+1) inches

{1b} 3quare Tube: / ! ( * d(

Where:

! "utside 4ength, inches d ! #nside 4ength, inches

$xample: %alculate the cross sectional area of a &' ".. x .())' wall tube.

! &.))) d ! &.))) * +.())- ! .))) inches

/ ! ( * d(

/ ! 5 * 2 ! 12

/ ! 12.)) inches(

{1c} 6ectangular Tube: / ! 1 * d1d

Where:

! "utside 4ength, long side, inches

1

! "utside 4ength, short side, inchesd ! #nside 4ength, long side, inches

d1! #nside 4ength, short side, inches

$xample: %alculate the cross sectional area of a

' x ' rectangular tube with .())' wall thic7ness.

! .))' 1! .))' d ! (.))' d1! 2.))'

/ ! 1 * d1d

/ ! .)) .))- * 2.)) (.))- ! 5.))

/ ! 5.)) inches(

+. PLAIN EN" %EI&'T (%pe):The plain end weight expressed in pounds per foot is used in connection with pipe to describe the nominal or specified weight

per foot. This weight does not account for ad8ustments in weight due to end finishing such as upsetting or threading.

{+} %pe= *+, (" $ t)t

Where:

Wpe! plain end weight, calculated to decimal places and rounded to + decimals, pounds0foot ! 3pecified "utside iameter of the 9ipe, inches

t ! 3pecified Wall Thic7ness, inches

$xample: %alculate the plain end weight of pipe having a specified ".. of & inches and a wall thic7ness of .() inches.

Wpe! 1). &.))) * .()- .()

Wpe! 2&.+(1

Wpe! 2&.+ pounds0foot

3. INTERNAL YIELD PRESSURE BURST-RESISTANCE (P):

The internal ;ield pressure or burst resistance of pressure bearing pipe is expressed in pounds0square inch psi-. The .&( factor is to allow for minimum

permissible wall based on /9# criteria for "%T< and line pipe. This factor can be changed based on other applicable specifications regarding minimum

permissible wall thic7ness.

{2} 9 ! ).&( = + >pt0?

Where:

9 ! @inimum #nternal >ield 9ressure Aurst 6esistance- in pounds per square inch, rounded to the nearest 1) psi.

>p! 3pecified @inimum >ield 3trength, pounds per square inch.

t ! Bominal specified- Wall Thic7ness, inches

! Bominal specified- "utside iameter, inches

$xample: %alculate the burst resistance of &' ".. x .()' wall /9# 4) casing.

9 ! ).&( = + >pt0?

9 ! ).&( = +-),)))-.()-0&?

9 ! 1),)) psi

4. PIPE SPECIFICATIONS BASICS

9ressure eterminations:AarlowCs Dormula is commonl; used to determine:

1. #nternal 9ressure at @inimum >ield

+. Eltimate Aursting 9ressure

2. @aximum /llowable Wor7ing 9ressure

. @ill F;drostatic Test 9ressure

This formula is expressed as 9 ! +3t where:

9 ! 9ressure, psig

# ! Bominal wall thic7ness, inches ! "utside iameter, inches

3 ! /llowable 3tress, psi, which depends on the pressure being determined


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To illustrate, assume a piping s;stems (0' ".. x .2&(' wall has a specified minimum ;ield strength 3@>3- of 2(,))) psi and a specified minimum

tensile strength of ),))) psi.

Dor 1. Internal Pressure o- .inimum /ield

3 ! 3@>3 2(,)))- psi and

9 ! +3t ! +-2(,)))-).2&(-

.+( ! 2)2 or 2)) psig rounded to nearest 1) psig-

Dor +. 0ltimate 1urstin2 Pressure

3 ! 3pecified @inimum Tensite 3trength ),))) psi- and

9 ! +3t ! +-),)))-).2&(-

.+( ! (+1& or (++) psig rounded to nearest 1) psig-

Dor 2. .a3imum Allo4able %or5in2 Pressure (.AOP)

3 ! 3@>3 2(,))) psi- reduced b; a design factor, usuall; ).&+ and

9 ! +3t ! +-2(,))) x +-).2&(-

.+( ! +151 or +15) psig rounded to nearest 1) psig-

Dor . .ill '6drostati7 Test Pressure

3 ! 3@>3 2(,))) psi- reduced b; a factor depending on ".. grade ).) for (0' ".. grade A- and

9 ! +3t ! +-2(,))) x ).)-).2&(-

.+( ! 1+ or 12) psig rounded to nearest 1) psig-

%all T8i75ness

AarlowCs Dormula is also useful in determining the wall thic7ness required for a piping s;stem. To illustrate, assume a piping s;stem has been designed with

the following criteria:

1. / wor7ing pressure of +,))) psi 9-

+. The pipe to be used is (0' ".. - specified to /3T@ /(2 grade A 3@>3 * 2(,))) psi-

6earranging AarlowCs Dormula to solve for wall thic7ness gives:

t ! 9 ! +,)))- .+(- ! ).+' wall

+3 +- 2(,)))-

Wall thic7ness has no relation to outside diameter * onl; the inside diameter is affected. Dor example, the outside diameter of a one*inch extra* strong piece

of pipe compared with a one*inch standard weight piece of pipe is identicalG however, the inside diameter of the extra*strong is smaller than the inside

diameter of the standard weight because the wall thic7ness is greater in the extra*strong pipe.

(. W/T$6 #3%F/6


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%ubic Deet of water x 1

area of pipe in sq. inches

/rea of required pipe, the volume and velocit; of water being given ! Bo. cubic feet water x 1

Lelocit; in feet per min.

Drom this area the siIe pipe required ma; be selected from the table of standard pipe dimensions.

/tmospheric pressure at sea level is 1.& pounds per square inch. This pressure with a perfect vacuum will maintain a column of mercur; +5.5 inches or a

column of water 22.5 feet high. This is the theoretical distance that water manu be drawn b; suction. #n practice, however, pumps should not have a total

d;namic suction lift greater that +( feet.

CR0"E OIL

"ne gallon: (,21) grains

"ne barrel oil: + E3 gallons

"ne barrel per hour: .& E3 gallons per minute


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;namic suction head, as determined on test, is the reading of a gage connected to suction noIIle of pump, minus vertical distance from center of gage to

center line of pump. 3uction head, after deducting the various losses, man; be a negative quantit;, in which case a condition equivalent to suction lift will

prevail.

ELOCIT/ 'EA"

The velocit; head sometimes called 'head due to velocit;'- of water moving with a given velocit;, is the equivalent head through which it would have to fall

to acquire the same velocit;: or the head necessar; merel; to accelerate the water. Knowing the velocit;, we can readil; figure the velocit; head from the

simple formula:

h ! L++g

in which 'g' is acceleration due to gravit;, or 2+.1 feet per secondG or 7nowing the head, we can transpose the formula to:

L ! 9; 28

and thus obtain the velocit;.

The velocit; head is a factor in figuring the total d;namic head, but the value is usuall; small, and in most cases negligibleG however, it should be considered

when the total head is low and also when the suction lift is high.

Where the suction and discharge pipes are the same siIe, it is onl; necessar; to include in the total head the velocit; head generated in the suction piping. #f

the discharge piping is of different siIe than the suction piping, which is often the case, then it will be necessar; to use the velocit; in the discharge pipe for

computing the velocit; head rather than the velocit; in the suction pipe.

Lelocit; head should be considered in accurate testing also, as it is part of the total d;namic head and consequentl; affects the dut; accomplished.

#n testing a pump, a vacuum gage or a mercur; column is generall; used for obtained d;namic suction lift. The mercur; column or vacuum gage will show

the velocit; head combined with entrance head, friction head, and static suction lift. "n the discharge side, a pressure gage is usuall; used, but a pressure

gage will not indicate velocit; head and this must, therefore, be obtained either b; calculating the velocit; or ta7ing reading with a 9itometer. #nasmuch as

the velocit; varies considerabl; at different points in the cross section of a stream it is important, in using the 9itometer, to ta7e a number of readings at

different points in the cross section.

/ table, giving the relation between velocit; and velocit; head is printed below:

elo7it6 in -eet per se7ond elo7it6 8ead in -eet elo7it6 in -eet per se7ond elo7it6 8ead in -eet

1 .)+ 5.( 1.)

+ .) 1) 1.((

2 .1 1).( 1.&)

.+( 11 1.&

( .25 11.( +.)(

.( 1+ +.+

& .& 12 +.+

1.)) 1 2.)(

.( 1.1+ 1( 2.()

5 1.+(

NET POSITIE S0CTION 'EA"

B93F stands for 'Bet 9ositive 3uction Fead'. #t is defined as the suction gage reading in feet absolute ta7en on the suction noIIle corrected to pump

centerline, minus the vapor pressure in feet absolute corresponding to the temperature of the liquid, plus velocit; head at this point. When boiling liquids arebeing pumped from a closed vessel B93F is the static liquid head in the vessel above the pump centerline minus entrance and friction losses.

ISCOSIT/

Liscosit; is the internal friction of a liquid tending to reduce flow.

Liscosit; is ascertained b; an instrument termed a Liscosimeter, of which there are several ma7es, viI. 3a;bolt EniversalG TangliabueG $ngler used chiefl;

in %ontinental countries-G 6edwood used in Aritish #sles and %olonies-. #n the Enited 3tates the 3a;bolt and Tangliabue instruments are in general use.

With few exceptions. Liscosit; is expressed as the number of seconds required for a definite volume of fluid under a arbitrar; head to flow through a

standardiIed aperture at constant temperature.

SPECIFIC &RAIT/

3pecific gravit; is the ratio of the weight of an; volume to the weight of an equal volume of some other substance ta7en as a standard at stated

temperatures. Dor solids or liquids, the standard is usuall; water, and for gasses the standard is air or h;drogen.

Doot pounds: Enit of wor7

Forse 9ower F.9.-: 22,))) ft. pounds per minute * & watts * .& 7ilowatts- Enit for measurement of power or rate of wor7

Lolt*amperes: 9roduct of volts and amperes

Kilovolt*/mperes KL/-: 1))) volt*amperes

Watt*hour: 3mall unit of electrical wor7 * watts times hours

Kilowatt*hour KWFr-: 4arge unit of electrical wor7 * 1))) watt*hours

Forse 9ower*hour F9Fr-: Enit of mechanical wor7

To determine the cost of power, for an; specific period of time * wor7ing hours per da;, wee7, month or ;ear:

Bo. of wor7ing hrs, x .& x F.9. motor ! KWFr consumed

$fficienc; of motor at @otor Terminal

KWFr consumed at @otor Terminal x 6ate per KWFr ! Total cost current for time specified

Torque is that force which produces or tends to produce torsion around an axis-. Turning effort. #t ma; be thought of as a twist applied to turn a shaft. #t can

be defined as the push or pull in pounds, along an imaginar; circle of one foot radius which surrounds the shaft, or, in an electric motor, as the pull or drag at

the surface of the armature multiplied b; the radius of the armature, the term being usuall; expressed in foot*pounds or pounds at 1 foot radius-.

3tarting torque is the torque which a motor exerts when starting. #t can be measured directl; b; fastening a piece of belt to +' diameter pulle;, wrapping it

part wa; round and measuring the pounds pull the motor can exert, with a spring balance. #n practice, an; pulle; can be used for torque ! lbs. pull x pulle;

radius in feet. / motor that has a heav; starting torque is one that starts up easil; with a heav; load.

6unning torque is the pull in pounds a motor exerts on a belt running over a pulle; +' in diameter.

Dull load torque is the turning moment required to develop normal horse*power output at normal speed.

The torque of an; motor at an; output with a 7nown speed ma; be determined b; the formula:

T ! Ara7e F.9. x (+()6.9.@.

With a 7nown foot*pounds torque, the horse*power at an; given speed can be determined b; the formula:


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F.9. ! T x 6.9.@.

(+()

F.9. ! T x speed of belt on +'pulle; in feet per minute 22)))

COST OF P0.PIN& %ATER

%ost per 1))) gallons pumped: .15 x power cost per KWFr x head in feet9ump eff. x @otor eff. x )

$xample: 9ower costs .)1 per 7.w.*hourG pump efficienc; is &(JG motor efficienc; is (JG total head is () feet.

.15 x .)1 x () ! M .))+( or 10 of a cent

.&( x .( x )

%ost per hour of pumping:

.)))15 x g.p.m. x head in ft x power cost per KWFr

9ump efficienc; x @otor efficienc;

%ost per acre foot of water:

1.)2+ x head in ft x power per KWFr

9ump efficienc; x @otor efficienc;

9ump efficienc;: g.p.m. x head in feet

25) x b.h.p. to pump-

Fead: 25) x 9ump eff. x b.h.p x g.p.m.

b.h.p. Ara7e horse*power- to pump: @otor efficienc; x h.p. at motor

b.h.p.: g.p.m. x head in feet x 25) x 9ump eff.

g.p.m.: 25) x 9ump eff. x b.h.p. x head in feet

CO.P0TIN& '*P* INP0T FRO. REOLIN& %ATT 'O0R .ETERS

is7 %onstant @ethod-

Kilowatts #nput ! KW in ! K x 6 x 2.) x t

F9 #nput ! F9 in ! K x 6 x 2)) ! .2 x K x 6 x t x & t

K * constant representing number os watt*hours through meter for on revolution of the dis7. Esuall; found on meter nameplate or face of dis7-

6 * number of revolutions of the dis7

t * seconds for 6 revolutions

%ost per 1))) gallons of water:

% ! & x r x F9 in x


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where

A = cross-sectional area of pipe(Square nches)

di= inside dia!eter (inches)

%ei28t o- Empt6 Steel Pipes

Weight of empt; steel pipes can be calculated as

wp= 10."802 t (do- t) (2)

where

wp=wei#ht of steel pipe ($oundsper %oot $ipe)

t = pipe wall thic&ness (nches)

do= outside dia!eter (inches)

%ei28t o- %ater in Pipes -illed 4it8 %ater

Weight of water in pipes filled with water can becalculated as

ww= 0.'05 di2 (')

where

ww= wei#ht of steel pipe filled withwater ($ounds per %oot $ipe)


Outside Sur-a7e Area o- Pipes

"utside surface area of steel pipes can becalculated as

Ao= 0.2"18 do ()

here,Ao= outside area of pipe -per foot (Square %eet)


Inside Sur-a7e Area o- Pipes

#nside surface area of steel pipes can becalculated as


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Ai= 0.2"18 di (5)

where

Ai= inside area of pipe - per foot

(Square %eet)


Area o- t8e .etal

/rea of the metal can be calculated as

A!= 0.785 (do2- di

2) (")

where

A!= area of the !etal (Squareinches)



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