Pressure Drop Calculation

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 coefficient

To calculate mass flow rate following equation has been used: where is:

 G - mass flow rate

For pressure drop calculation because of friction, viscosity of fluid has to be known. Relation between dynamic and kinematic viscosity is as follows: where is:

 mi - dynamic viscosity view table  ni - kinematic viscosity view table

Velocity 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, Reynolds number must be calculated:

Friction coefficient for laminar flow is:

for flow in hydraulically smooth pipe (Blasius equation):

for turbulent flow with Re<100 000 (Prandtl equation):

for turbulent flow with Re>100 000 (Karman equation):

The boundary layer thickness (delta) can be calculated based on the Prandtl equation as:

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

Pipe diameter calculation - theory

Pipe 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 constant is known as:

where is:

 p - pressure

 T - temperature  R - 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 be calculated 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 and pressure drop follows the power low. Flow coefficient is the proportional constant between pressure drop and flow rate and it is determined experimentally by valve manufactures. It is expressed as the flow rate of water in gpm u.s. (m3/h) for a pressure drop of 1 psi (1 bar) across a flow passage. note: (flow coefficient: Cv-imperial, Kv-metric) For correct control valve sizing it is important to calculate flow coefficient using this calculator. When flow coefficient is calculated for required flow rate and known pressure drop, selection of proper control valve can be done by selecting control valve with first bigger flow coefficient. Also using this calculator you can calculate maximum flow rate through control valve for given pressure drop and known flow coefficient or valve size. This version of calculator can be used for turbulent flow of water or other incompressible fluid, as viscosity and expansion effect is not included. It means that for steam and gas control valve you will need to use other calculation methods. Also, possible flashing and cavitation may reduce the control valve capacity, as it is not treated in this version calculator. Read about used theory for control valve sizing calculation

Control valve sizing calculation - theory

Control valve sizing is based on the calculation of flow coefficient for given pressure drop and fluid flow rate. Main equation that gives relation between flow rate and pressure drop is:

for imperial units, and:

for metric units, where is:

   

Cv - flow coefficient in imperial units Kv - flow coefficient in metric units Dp - pressure drop through control valve Q - fluid flow rate

 G - specific gravity view table  ro - relative density view table

Flow coefficient is defined as the proportional constant between pressure drop and flow rate and it is determined experimentally by valve manufactures. It is expressed as the flow rate of water in gpm u.s. (m3/h) for a pressure drop of 1 psi (1 bar) across a flow passage. note: (flow coefficient: Cv-imperial, Kv-metric) Relation between volumetric and mass flow rate is calculated using well known equation: Also, velocity or pipe diameter can be calculated using following equations:

Venturi tube flow calculation

Based on the energy conservation low, Venturi tube is one of the easiest to use, not expensive and very accurate instrument for flow rate measuring of water, air, gas or any other fluid in pipe systems. Measure pressure drop from the inlet to the throat and calculate flow rate using this free calculator. Flow through Venturi tube calculator can be used for both liquids and gases. Fluid is considered as incompressible, so density (rho) and temperature (T) are constant through tube. Also, gas is considered as ideal. Read about used theory in flow through Venturi tube calculation

Venturi tube flow calculation - theory

Calculation of flow through the Venturi tube is for incompressible flow, based on the Bernoulli principle:

where is: p - pressure rho - density view table V - velocity g - gravitational constant (9.81 m/s2) z - geodetic height Assumption that pressure lost is negligible:

and:

and if velocities substituted with flow rate:

where is: Q - volumetric flow rate D - diameter Pressure drop through the Venturi tube because of velocity increase can be calculated as follows:

or:

Expressing flow rate from the previous equation leads to:

Substituting:

flow rate can be determined as:

where C is coefficient of discharge. The above equation is main one used for flow calculation in calculator. Other values are calculated using following equations: mass flow:

velocities:

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

can be used for calculation of temperature T:

as well as density rho:

where R is gas constant (R=287 J/kgK for air) Coefficient of discharge C As fluid exits 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 C is used to include this effect. For the Venturi tubes with diameters in range of D = (200 - 1200 mm), D2/D1 = (0.4 - 0.7) and ReD = (2 ·105 - 2 ·106) the coefficient of discharge is C = 0.985. In this calculator for coefficient off discharge C following equation has been used:

where a, b, and c depend on the type of Venturi tube. For welded tube, these coefficients are: a=0.70304970 b=0.00490015 c=-0.00024547 For casted tube are: a=0.60892370 b=0.00659844 c=-0.00033123 And for machined are: a=0.49670179 b=0.00873339 c=-0.00044367 Reynolds number on inlet ReD is calculated using well known equation:

Orifice plate flow calculation

Orifice plate is used for flow rate measuring in pipe systems. With orifice plate, pressure drop is created. Based on the value of pressure drop, flow rate can be calculated. This instrument is very practical for large tube diameters and for dirty fluid when turbines are not applicable. Measure pressure drop from position 1 to position 2 and calculate flow rate and more with this easy to use calculator Orifice plate calculator can be used for both liquids and gases. Fluid is considered as incompressible, so density (rho) and temperature (T) are constant through tube. Also, gas is considered as ideal. Read about used theory for flow through orifice calculation.

Orifice plate flow calculation - theory

Calculation of flow rate using orifice plate calculator is for incompressible flow, based on the Bernoulli principle:

where is: p - pressure rho - density view table V - velocity g - gravitational constant (9.81 m/s2) z - geodetic height Assumption that pressure lost is negligible (pressure drop is obvious and included with coefficient of discharge which is introduced bellow):

and:

and if velocities substituted with flow rate:

where is: Q - volumetric flow rate D - diameter Pressure drop through the orifice because of velocity increase can be calculated as follows:

or:

Expressing flow rate from the previous equation leads to:

Substituting:

flow rate can be determined as:

where is: C - coefficient of discharge e - expansion coefficient Coefficient of discharge can be calculated using following equation (ISO):

where is: beta - diameter relation D2/D1 ReD - Reynolds number which can be calculated as follows:

where is: ni - kinematic viscosity view table mi - dynamic viscosity view table L1 and L2 are functions on tap type and it is: L1=L2=0 for corner taps L1=1 L2=0.47 for D & D/2 taps L1=L2=0.0254/D D[m] for 1" taps Expansion coefficient e can be calculated (for gases only):

where is: kappa - isentropic coefficient; kappa = 1.4 for air and other two atom gas molecules view table Other values are calculated using following equations: mass flow:

velocities:

If flowing fluid is gas, then it is considered as incompressible and ideal. Equation for ideal gas:

can be used for calculation of temperature T:

as well as density rho:

Tables of fluid physical propetries Here you can find the list of available fluid properties tables which can be used in calculators on this site: Dry air This table gives values of some dry air physical properties in relation to temperature and pressure. Gases This table gives values of some physical properties of some gases Flue gases This table is for flue gases. It gives values of some physical properties in relation to the temperature of gases. Water This table gives values of some water physical properties in realtion to temperature. For temperatures higher than 100 OC, it is for water boiling conditions. Steam This table gives values of some saturated steam physical properties in realtion to temperature.

Physical properties of dry air Available 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 [OC]

-50

0

50

100

150

200

300

400

1 bar

1.563

1.275

1.078

0.932 0.8226 0.7356 0.6072 0.517

50 bar

83.794

65.198 53.964 46.25 40.57

36.18

29.8

25.37

100 bar

175.648 131.36 107.07 91.13 79.66

70.92

58.37

49.71

200 bar

340.34

253.7

205.4

174.3 152.2

135.6

111.8

95.41

300 bar

449.3

350.8

288.6

246.7 216.4

193.4

160.3

137.4

Density rho [kg/m3]

Specific heat cp [kJ/kgK]

1 bar

1.007

1.006

1.008

1.012 1.018

1.026

1.046

1.69

50 bar

1.212

1.112

1.085

1.075 1.055

1.049

1.061

1.08

100 bar

1.43

1.216

1.133

1.096 1.078

1.072

1.075

1.09

200 bar

1.623

1.361

1.229

1.161 1.126

1.108

1.099

1.107

300 bar

1.604

1.409

1.282

1.204 1.16

1.135

1.117

1.12

1 bar

14.65

17.2

19.61

21.82 23.92

25.85

29.47

32.76

50 bar

16.7

19.42

20.57

22.59 24.4

26.4

29.9

33.1

100 bar

18.3

20.2

21.7

23.4

25.1

26.9

30.4

33.5

200 bar

22.8

23.6

24.4

25.6

26.8

28.5

31.5

34.7

300 bar

28.7

27.8

27.5

28.1

28.8

30.1

33.1

36.1

Dynamic viscosity mi*106 [Pas]

Physical propetries of gases Available tables: dry air gases flue gases water steam This table gives values of some physical properties of some gases.

GAS

Gas density

Molar weight

Gas constant

Spec. heat at 20OC and 1 bar

rho

M*103

R

Cp

[kg/m3]

[kg/mol]

[J/kg*K]

[J/kg*K] [J/kg*K] [-]

[Pa*s] - 0OC and 1 bar

Cv

Dynamic viscosity

kapa=Cp/Cv mi*106

Acethylene

C2H2

1.171

26.04

319.6

1683

1352

1.25

9.35

Ammonia

NH3

0.771

17.03

488.3

2219

1680

1.37

9.18

Argon

Ar

1.782

39.94

208.5

532

322

1.65

20.9

Nitrogen

N2

1.251

28.02

296.7

1047

746

1.4

17

Nitrogen Oxide

NO

1.34

30.01

277.1

975

696

1.38

17.8

Butane

C4H10

2.673

58.12

143.2

1917

1733

1.108

8.1

i-Butane

C4H10

2.668

58.12

143.2

1632

-

-

7.47

Ethane

C2H6

1.357

30.06

276.7

1729

1445

1.2

8.5

Ethylene

C2H4

1.261

28.05

296.6

1528

1222

1.25

9.85

Ethyl Ether

C4H10O -

74.12

112.2

2302

-

-

286

Ethyl Chloride

C2H5Cl -

64.5

129

1340

-

-

9.4

Helium

He

0.178

4.002

2079

5274

3181

1.66

18.8

Chlor

Cl2

3.217

70.91

117.3

481

355

1.36

12

Hydrogen Chloride

HCl

1.639

36.47

228

812

583

1.4

-

Oxygen

O2

1.429

32

259.9

913

653

1.4

20.3

Krypton

Kr

3.708

83.7

100.3

251

151

1.67

23.2

Xenon

Xe

5.851

131.3

63.84

159

96.3

1.7

21

Methane

CH4

0.717

16.03

518.8

2225

1700

1.31

10.3

Methyl Chloride

CH3Cl

2.308

50.48

164.8

741

582

1.28

9.89

Neon

Ne

0.9002

20.18

411.7

1038

620

1.68

29.7

Ozone

O3

2.22

48

173.4

-

-

1.29

-

Pentane

C5H12

-

72.1

115.2

1717

1575

1.09

8.74

Propane

C3H8

2.02

44.06

188.8

1863

1650

1.13

7.95

Propene

C3H6

1.914

42.05

198.8

1635

1437

1.17

8.35

Sulphur Dioxide

SO2

2.927

64.06

129.8

633

503

1.25

11.7

Sulphur Hydrogen

H2S

1.539

34.09

244.2

1059

804

1.3

11.66

Carbon Dioxide

CO2

1.976

44.01

189

837

653

1.3

13.7

Carbon Monoxide CO

1.25

28.01

297

1047

754

1.4

16.6

Air

1.293

28.95

287

1010

720

1.4

17.3

0.08985

2.016

4125

14266

10130

1.407

8.42

Hydrogen

H2

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

Nitrogen

Argon

N2

Ar

t [OC]

0

100

200

300

400

500

600

700

cp [kJ/kgK]

1.039

1.042

1.052

1.069

1.091

1.115

1.139

1.161 1.181

mi*106 [Pas]

16.6

20.8

24.6

28

31.1

33.9

36.6

39

41.3

lambda*103 [W/mK] 24.31

31.52

38.5

44.89

50.71

55.82

60.36

64.2

67.45

cp [kJ/kgK]

0.522

0.521

0.521

0.521

0.521

0.52

0.52

0.52

0.52

mi*106 [Pas]

21.2

27.1

32.1

36.7

41

45.22

48.7

21.17

25.59

29.89

33.96

37.91

39.43

1.591

2.026

2.453

2.813

3.127

3.403

3.642

6.84

9.26

11.67

14.03

16.38

18.74

21.09

lambda*103 [W/mK] 13.26

23.5

36.52

51.87

29.78

90.25

113

cp [kJ/kgK]

1.647

2.067

2.49

2.87

3.214

3.519

3.787

mi*106 [Pas]

8.55

11.5

14.1

16.4

19

21.4

23.8

lambda*103 [W/mK] 18

31.7

47.7

65.9

cp [kJ/kgK]

1.406

1.737

2.064

2.394

2.721

3.052

3.382

3.709 4.039

mi*10 [Pas]

9.6

12.7

15.6

18.2

20.6

22.8

24.9

26.8

lambda*103 [W/mK] 16.51 Butane

C4H10 cp [kJ/kgK] mi*106 [Pas]

Ethane

Ethylene

C2H6

C2H4

6

800

4.022 4.216

28.7

Helium

He

Oxygen

O2

Methane

CH4

lambda*103 [W/mK] 16.4

29.54

44.19

59.43

75.71

92.34

108.39 123.3 134.9

cp [kJ/kgK]

5.204

5.204

5.204

5.204

5.204

5.204

5.204

mi*106 [Pas]

18.74

22.96

26.98

30.8

34.33

37.57

40.32

lambda*103 [W/mK] 143

179.1

212.8

244.2

275.6

304.7

332.6

cp [kJ/kgK]

0.915

0.934

0.963

0.995

1.024

1.048

1.069

1.086 1.1

mi*106 [Pas]

19.2

24.4

29

33.1

26.9

40.3

43.5

46.5

49.3

lambda*103 [W/mK] 24.66

32.91

40.7

48.03

55.01

61.52

67.45

72.8

77.69

cp [kJ/kgK]

2.165

2.448

2.807

3.175

3.529

3.856

4.153

4.421 4.659

mi*10 [Pas]

10.4

13.3

16.1

18.5

20.8

22.7

24.6

26.5

lambda*103 [W/mK] 30.24

41.29

51.87

62.34

72.22

81.88

91.3

100.5 109.3

cp [kJ/kgK]

1.549

2.017

2.458

2.834

3.161

3.449

3.697

3.916 4.093

7.5

10.06

12.48

14.75

17.15

19.4

21.8

lambda*10 [W/mK] 15

27.4

41.7

57.9

76

95.8

cp [kJ/kgK]

1.426

1.8

2.16

2.476

2.753

2.991

3.2

3.388 3.54

mi*10 [Pas]

7.84

10.73

13.4

15.92

lambda*103 [W/mK] 14

25.6

38.9

53.7

cp [kJ/kgK]

0.607

0.662

0.712

0.754

0.783

0.808

0.825

0.837 0.85

mi*106 [Pas]

12.1

16.1

20

23.8

27.5

31.3

35

38.6

lambda*103 [W/mK] 8.37

12.33

16.63

21.17

25.82

30.7

35.82

41.05 46.29

cp [kJ/kgK]

0.815

0.914

0.993

1.057

1.11

1.155

1.192

1.223 1.249

mi*106 [Pas]

13.8

18.4

22.6

26.4

29.9

33.2

36.2

38.1

lambda*103 [W/mK] 14.65

22.79

30.94

39.08

47.22

54.89

62.1

68.85 75.13

cp [kJ/kgK]

1.104

1.045

1.058

1.08

1.106

1.132

1.157

1.179 1.999

mi*106 [Pas]

16.6

20.9

24.6

27.8

39

33.8

36.3

38.7

30.12

36.52

42.57

48.5

54.08

59.66

65.01 70.13

6

Propane

C3H8

mi*106 [Pas] 3

Propene

C3H6

6

Sulfur dioxide

Carbon dioxide

SO2

CO2

Carbon monoxide CO

lambda*103 [W/mK] 23.26 Hydrogen

H2

5.204 5.204

28.2

42.1

41.8

41

cp [kJ/kgK]

14.195 14.448 14.504 14.533 14.581 14.662 14.779 14.93 15.115

mi*106 [Pas]

8.4

lambda*103 [W/mK] 174.4

where is for flue gas:

• • •

t - temperature cp - specific heat mi - dynamic viscosity

•

lambda - thermal conductivity

10.3

12.1

13.9

15.4

16.9

18.3

19.6

21

216.3

258.2

300.1

341.9

383.8

452.7

467.5 509.4