20557391-Pressure-Drop-Calculation.doc

8/20/2019 20557391-Pressure-Drop-Calculation.doc

1/13

Pressure drop calculation - theory

In this calculator well known equations have been used. Here you can find all of them for your review.

First of all, pressure drop through the pipe due to friction and local losses can be calculated as follows:

where is:

Dp - pressure drop

rho - fluid density view table Q - volumetric flow rate

D - pipe diameter

lambda - friction coefficient

L - pipe length

sum ksi - the sum of minor losses coefficientTo calculate mass flow rate following equation has been used:

where is:

G - mass flow rateFor pressure drop calculation because of friction, viscosity of fluid has to be known. elation betweendynamic and kinematic viscosity is as follows:

where is:

mi - dynamic viscosity view table

ni - kinematic viscosity view table

!elocity of flowing fluid is calculated based on the continuity equation:

where the cross section of round pipe is:

To find out if the flow is laminar or turbulent, eynolds number must be calculated:

http://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htm


2/13

Friction coefficient for laminar flow is:

for flow in hydraulically smooth pipe "#lasius equation$:

for turbulent flow with e%&'' ''' "(randtl equation$:

for turbulent flow with e)&'' ''' "*arman equation$:

The boundary layer thickness "delta$ can be calculated based on the (randtl equation as:

and when the boundary layer thickness is bigger than pipe roughness and if the flow is turbulent, thanit can be considered as flow in hydraulically smooth pipe and #lasius equation is used.

Pipe diameter calculation - theory

(ipe diameter can be calculated when volumetric flow rate and velocity is known as:

where is:

D - pipe diameter

Q - volumetric flow rate

V - velocity

If mass flow rate is known than diameter can be calculated as:

where is:

G - mass flow rate

rho - fluid density view table

If the flowing fluid is gas than the density can be calculated if pressure, temperature and gas constantis known as:

where is:

p - pressure

T - temperature

http://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htm


3/13

- gas constant view table

It is important to say that the flow rate is depending on the pressure difference between two points.

This calculator is for the calculation if you already know the flow rate. If the flow rate is to becalculated also, than you should use pressure drop calculator.

Control valve sizing calculation

It is well known that for the completely turbulent flow relationship between fluid flow rate andpressure drop follows the power low. Flow coefficient is the proportional constant betweenpressure drop and flow rate and it is determined e+perimentally by valve manufactures. It ise+pressed as the flow rate of water in gpm u.s. "m-h$ for a pressure drop of & psi "& bar$ acrossa flow passage.note: "flow coefficient: v/imperial, *v/metric$

For correct control valve si0ing it is important to calculate flow coefficient using this calculator.1hen flow coefficient is calculated for required flow rate and known pressure drop, selection ofproper control valve can be done by selecting control valve with first bigger flow coefficient.

2lso using this calculator you can calculate ma+imum flow rate through control valve for givenpressure drop and known flow coefficient or valve si0e.

This version of calculator can be used for turbulent flow of water or other incompressible fluid, asviscosity and e+pansion effect is not included. It means that for steam and gas control valve youwill need to use other calculation methods. 2lso, possible flashing and cavitation may reduce thecontrol valve capacity, as it is not treated in this version calculator.

ead about used theory for control valve si0ing calculation

Control valve sizing calculation - theory

ontrol valve si0ing is based on the calculation of flow coefficient for given pressure drop and fluid flowrate. 3ain equation that gives relation between flow rate and pressure drop is:

for imperial units, and:

for metric units, where is:

! v - flow coefficient in imperial units

" v - flow coefficient in metric units

Dp - pressure drop through control valve

Q - fluid flow rate

G - specific gravity view table

http://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/pressuredrop/index.htmhttp://www.pipeflowcalculations.com/controlvalve/theory.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/pressuredrop/index.htmhttp://www.pipeflowcalculations.com/controlvalve/theory.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htm


4/13

ro - relative density view tableFlow coefficient is defined as the proportional constant between pressure drop and flow rate and it isdetermined e+perimentally by valve manufactures. It is e+pressed as the flow rate of water in gpm u.s."m-h$ for a pressure drop of & psi "& bar$ across a flow passage.note: "flow coefficient: v/imperial, *v/metric$elation between volumetric and mass flow rate is calculated using well known equation:

2lso, velocity or pipe diameter can be calculated using following equations:

Venturi tube flow calculation

#ased on the energy conservation low, !enturi tube is one of the easiest to use, not e+pensive andvery accurate instrument for flow rate measuring of water, air, gas or any other fluid in pipesystems.

3easure pressure drop from the inlet to the throat and calculate flow rate using this free calculator.

Flow through !enturi tube calculator can be used for both liquids and gases. Fluid is consideredas incompressible, so density "rho$ and temperature "T$ are constant through tube. 2lso, gas isconsidered as ideal.

ead about used theory in flow through !enturi tube calculation

Venturi tube flow calculation - theory

alculation of flow through the !enturi tube is for incompressible flow, based on the Bernoulliprinciple:

where is:

p / pressurerho / density view table! / velocityg / gravitational constant "4.5& m-s6$0 / geodetic height

2ssumption that pressure lost is negligible:

and:

http://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/venturi/theory.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/venturi/theory.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htm


5/13

and if velocities substituted with flow rate:

where is:

7 / volumetric flow rate8 / diameter

(ressure drop through the !enturi tube because of velocity increase can be calculated as follows:

or:

9+pressing flow rate from the previous equation leads to:

ubstituting:

flow rate can be determined as:

where is coefficient of discharge. The above equation is main one used for flow calculation incalculator.

;ther values are calculated using following equations:

mass flow:

velocities:

http://www.pipeflowcalculations.com/venturi/theory.htm#Coefficient%20of%20discharge%20Chttp://www.pipeflowcalculations.com/venturi/theory.htm#Coefficient%20of%20discharge%20C


6/13

If the calculator is used for gas flow, then gas is considered as incompressible and ideal. 9quation for

ideal gas:

can be used for calculation of temperature T:

as well as density rho:

where is gas constant "-kg* for air$

Coefficient of discharge C

2s fluid e+its a reservoir through a small hole and enters another one, or flows out to the open air,stream lines tend to contract itself, mostly because of inertia. Coefficient of discharge is used toinclude this effect.For the !enturi tubes with diameters in range of 8 < "6'' / &6'' mm$, 86 -8& < "'.? / '.=$ and e8 <"6 @&'A / 6 @&'B$ the coefficient of discharge is < '.45A.In this calculator for coefficient off discharge following equation has been used:

where a, b, and c depend on the type of !enturi tube.

For welded tube, these coefficients are:a


7/13

Orifice plate flow calculation

;rifice plate is used for flow rate measuring in pipe systems. 1ith orifice plate, pressure drop iscreated. #ased on the value of pressure drop, flow rate can be calculated. This instrument is verypractical for large tube diameters and for dirty fluid when turbines are not applicable.

3easure pressure drop from position & to position 6 and calculate flow rate and more with thiseasy to use calculator

;rifice plate calculator can be used for both liquids and gases. Fluid is considered asincompressible, so density "rho$ and temperature "T$ are constant through tube. 2lso, gas isconsidered as ideal.

ead about used theory for flow through orifice calculation.

Orifice plate flow calculation - theory

alculation of flow rate using orifice plate calculator is for incompressible flow, based on theBernoulli principle:

where is:p / pressurerho / density view table! / velocityg / gravitational constant "4.5& m-s6$0 / geodetic height

2ssumption that pressure lost is negligible "pressure drop is obvious and included with coefficient ofdischarge which is introduced bellow$:

and:

and if velocities substituted with flow rate:

http://www.pipeflowcalculations.com/orifice/theory.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htmhttp://www.pipeflowcalculations.com/orifice/theory.htmhttp://www.pipeflowcalculations.com/tables/tablelist.htm


8/13

where is: 7 / volumetric flow rate

8 / diameter(ressure drop through the orifice because of velocity increase can be calculated as follows:

or:

9+pressing flow rate from the previous equation leads to:

ubstituting:

flow rate can be determined as:

where is: / coefficient of dischargee / e+pansion coefficient

oefficient of discharge can be calculated using following equation "I;$:


9/13

where is:beta / diameter relation 86 -8&e8 / eynolds number which can be calculated as follows:

where is:ni / kinematic viscosity view tablemi / dynamic viscosity view table

C& and C6 are functions on tap type and it is:C&


10/13

can be used for calculation of temperature T:

as well as density rho:

Tables of fluid physical propetriesHere you can find the list of available fluid properties tables which can be used in calculators on

this site:8ry airThis table gives values of some dry air physical properties in relation to temperature and pressure.asesThis table gives values of some physical properties of some gasesFlue gasesThis table is for flue gases. It gives values of some physical properties in relation to thetemperature of gases.1aterThis table gives values of some water physical properties in realtion to temperature. Fortemperatures higher than &'' ;, it is for water boiling conditions.teamThis table gives values of some saturated steam physical properties in realtion to temperature.

Physical properties of dry air2vailable tables: dry air gases flue gases water steam

This table gives values of some dry air physical properties in relation to temperature and pressure.

t E; /A' ' A' &'' &A' 6'' '' ?''

8ensity rho Ekg-m

& bar &.AB &.6=A &.'=5 '.46 '.566B '.=AB '.B'=6 '.A&=

A' bar 5.=4? BA.&45 A.4B? ?B.6A ?'.A= B.&5 64.5 6A.=

&'' bar &=A.B?5 &&.B &'=.'= 4&.& =4.BB ='.46 A5.= ?4.=&

6'' bar ?'.? 6A.= 6'A.? &=?. &A6.6 &A.B &&&.5 4A.?&

'' bar ??4. A'.5 655.B 6?B.= 6&B.? &4.? &B'. &=.?

pecific heat cp Ek>-kg*

& bar &.''= &.''B &.''5 &.'&6 &.'&5 &.'6B &.'?B &.B4

A' bar &.6&6 &.&&6 &.'5A &.'=A &.'AA &.'?4 &.'B& &.'5

http://www.pipeflowcalculations.com/tables/dryair.htmhttp://www.pipeflowcalculations.com/tables/gas.htmhttp://www.pipeflowcalculations.com/tables/fluegas.htmhttp://www.pipeflowcalculations.com/tables/water.htmhttp://www.pipeflowcalculations.com/tables/steam.htmhttp://www.pipeflowcalculations.com/tables/dryair.htmhttp://www.pipeflowcalculations.com/tables/gas.htmhttp://www.pipeflowcalculations.com/tables/fluegas.htmhttp://www.pipeflowcalculations.com/tables/water.htmhttp://www.pipeflowcalculations.com/tables/steam.htmhttp://www.pipeflowcalculations.com/tables/dryair.htmhttp://www.pipeflowcalculations.com/tables/gas.htmhttp://www.pipeflowcalculations.com/tables/fluegas.htmhttp://www.pipeflowcalculations.com/tables/water.htmhttp://www.pipeflowcalculations.com/tables/steam.htmhttp://www.pipeflowcalculations.com/tables/dryair.htmhttp://www.pipeflowcalculations.com/tables/gas.htmhttp://www.pipeflowcalculations.com/tables/fluegas.htmhttp://www.pipeflowcalculations.com/tables/water.htmhttp://www.pipeflowcalculations.com/tables/steam.htm


11/13

&'' bar &.? &.6&B &.& &.'4B &.'=5 &.'=6 &.'=A &.'4

6'' bar &.B6 &.B& &.664 &.&B& &.&6B &.&'5 &.'44 &.&'=

'' bar &.B'? &.?'4 &.656 &.6'? &.&B &.&A &.&&= &.&6

8ynamic viscosity miJ&'B E(as

& bar &?.BA &=.6 &4.B& 6&.56 6.46 6A.5A 64.?= 6.=B

A' bar &B.= &4.?6 6'.A= 66.A4 6?.? 6B.? 64.4 .&

&'' bar &5. 6'.6 6&.= 6.? 6A.& 6B.4 '.? .A

6'' bar 66.5 6.B 6?.? 6A.B 6B.5 65.A &.A ?.=

'' bar 65.= 6=.5 6=.A 65.& 65.5 '.& .& B.&

Physical propetries of gases2vailable tables: dry air gases flue gases water steam

This table gives values of some physical properties of some gases.

as

density

3olar

weight

as

constantpec. heat at 6'; and & bar 8ynamic viscosity

2 rho 3J&' p v kapa


12/13

*rypton *r .='5 5.= &''. 6A& &A& &.B= 6.6

Lenon Le A.5A& &&. B.5? &A4 4B. &.= 6&

3ethane H? '.=&= &B.' A&5.5 666A &='' &.& &'.

3ethyl hloride Hl 6.'5 A'.?5 &B?.5 =?& A56 &.65 4.54

Keon Ke '.4''6 6'.&5 ?&&.= &'5 B6' &.B5 64.=

;0one ; 6.66 ?5 &=.? / / &.64 /

(entane AH&6 / =6.& &&A.6 &=&= &A=A &.'4 5.=?

(ropane H5 6.'6 ??.'B &55.5 &5B &BA' &.& =.4A

(ropene HB &.4&? ?6.'A &45.5 &BA &?= &.&= 5.A

ulphur 8io+ide ;6 6.46= B?.'B &64.5 B A' &.6A &&.=

ulphurHydrogen

H6 &.A4 ?.'4 6??.6 &'A4 5'? &. &&.BB

arbon 8io+ide ;6 &.4=B ??.'& &54 5= BA &. &.=

arbon 3ono+ide ; &.6A 65.'& 64= &'?= =A? &.? &B.B

2ir &.64 65.4A 65= &'&' =6' &.? &=.

Hydrogen H6 '.'545A 6.'&B ?&6A &?6BB &'&' &.?'= 5.?6

This table gives values of some physical properties in relation to the temperature of gases.

2 t E; ' &'' 6'' '' ?'' A'' B'' ='' 5''

Kitrogen K6 cp Ek>-kg* &.'4 &.'?6 &.'A6 &.'B4 &.'4& &.&&A &.&4 &.&B& &.&5&

miJ&'B E(as &B.B 6'.5 6?.B 65 &.& .4 B.B 4 ?&.

lambdaJ&' E1-m* 6?.& &.A6 5.A ??.54 A'.=& AA.56 B'.B B?.6 B=.?A

2rgon 2r cp Ek>-kg* '.A66 '.A6& '.A6& '.A6& '.A6& '.A6 '.A6 '.A6 '.A6

miJ&'B E(as 6&.6 6=.& 6.& B.= ?& ?A.66 ?5.=

lambdaJ&' E1-m* &B.A& 6&.&= 6A.A4 64.54 .4B =.4& 4.?

#utane ?H&' cp Ek>-kg* &.A4& 6.'6B 6.?A 6.5& .&6= .?' .B?6

miJ&'B E(as B.5? 4.6B &&.B= &?.' &B.5 &5.=? 6&.'4

lambdaJ&' E1-m* &.6B 6.A B.A6 A&.5= 64.=5 4'.6A &&

9thane 6HB cp Ek>-kg* &.B?= 6.'B= 6.?4 6.5= .6&? .A&4 .=5= ?.'66 ?.6&B

miJ&'B E(as 5.AA &&.A &?.& &B.? &4 6&.? 6.5

lambdaJ&' E1-m* &5 &.= ?=.= BA.4

9thylene 6H? cp Ek>-kg* &.?'B &.== 6.'B? 6.4? 6.=6& .'A6 .56 .='4 ?.'4

miJ&'B E(as 4.B &6.= &A.B &5.6 6'.B 66.5 6?.4 6B.5 65.=

lambdaJ&' E1-m* &B.? 64.A? ??.&4 A4.? =A.=& 46.? &'5.4 &6. &?.4

Helium He cp Ek>-kg* A.6'? A.6'? A.6'? A.6'? A.6'? A.6'? A.6'? A.6'? A.6'?


13/13

miJ&'B E(as &5.=? 66.4B 6B.45 '.5 ?. =.A= ?'.6

lambdaJ&' E1-m* &? &=4.& 6&6.5 6??.6 6=A.B '?.= 6.B

;+ygen ;6 cp Ek>-kg* '.4&A '.4? '.4B '.44A &.'6? &.'?5 &.'B4 &.'5B &.&

miJ&'B E(as &4.6 6?.? 64 .& 6B.4 ?'. ?.A ?B.A ?4.

lambdaJ&' E1-m* 6?.BB 6.4& ?'.= ?5.' AA.'& B&.A6 B=.?A =6.5 ==.B4

3ethane H? cp Ek>-kg* 6.&BA 6.??5 6.5'= .&=A .A64 .5AB ?.&A ?.?6& ?.BA4

miJ&'B E(as &'.? &. &B.& &5.A 6'.5 66.= 6?.B 6B.A 65.6

lambdaJ&' E1-m* '.6? ?&.64 A&.5= B6.? =6.66 5&.55 4&. &''.A &'4.

(ropane H5 cp Ek>-kg* &.A?4 6.'&= 6.?A5 6.5? .&B& .??4 .B4= .4&B ?.'4

miJ&'B E(as =.A &'.'B &6.?5 &?.=A &=.&A &4.? 6&.5

lambdaJ&' E1-m* &A 6=.? ?&.= A=.4 =B 4A.5

(ropene HB cp Ek>-kg* &.?6B &.5 6.&B 6.?=B 6.=A 6.44& .6 .55 .A?

miJ&'B

E(as =.5? &'.= &.? &A.46

lambdaJ&' E1-m* &? 6A.B 5.4 A.=

ulfur dio+ide ;6 cp Ek>-kg* '.B'= '.BB6 '.=&6 '.=A? '.=5 '.5'5 '.56A '.5= '.5A

miJ&'B E(as &6.& &B.& 6' 6.5 6=.A &. A 5.B ?6.&

lambdaJ&' E1-m* 5.= &6. &B.B 6&.&= 6A.56 '.= A.56 ?&.'A ?B.64

arbon dio+ide ;6 cp Ek>-kg* '.5&A '.4&? '.44 &.'A= &.&& &.&AA &.&46 &.66 &.6?4

miJ&'B E(as &.5 &5.? 66.B 6B.? 64.4 .6 B.6 5.& ?&.5

lambdaJ&' E1-m* &?.BA 66.=4 '.4? 4.'5 ?=.66 A?.54 B6.& B5.5A =A.&

arbon mono+ide ; cp Ek>-kg* &.&'? &.'?A &.'A5 &.'5 &.&'B &.&6 &.&A= &.&=4 &.444

miJ&'B E(as &B.B 6'.4 6?.B 6=.5 4 .5 B. 5.= ?&

lambdaJ&' E1-m* 6.6B '.&6 B.A6 ?6.A= ?5.A A?.'5 A4.BB BA.'& ='.&

Hydrogen H6 cp Ek>-kg* &?.&4A &?.??5 &?.A'? &?.A &?.A5& &?.BB6 &?.==4 &?.4 &A.&&A

miJ&'B E(as 5.? &'. &6.& &.4 &A.? &B.4 &5. &4.B 6&

lambdaJ&' E1-m* &=?.? 6&B. 6A5.6 ''.& ?&.4 5.5 ?A6.= ?B=.A A'4.?

where is for flue gas:

• t / temperature

• cp / specific heat

• mi / dynamic viscosity

• lambda / thermal conductivity

20557391-Pressure-Drop-Calculation.doc

Documents

Transcript of 20557391-Pressure-Drop-Calculation.doc