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:

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:

C



- flow coefficient in imperial units

K



- 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

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 ·10}6_{) 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

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 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

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:

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 O_{C, 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

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

t [O_{C] -50 0 50 100 150 200 300 400} Density rho [kg/m3_] 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 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

Dynamic viscosity mi*106 _[Pas]

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

Physical propetries of gases

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

Gas

density Molar weight Gas constant Spec. heat at 20OC and 1 bar Dynamic viscosity

GAS rho M*103 _{R C}

p Cv kapa=Cp/Cv mi*106

[kg/m3_{] [kg/mol] [J/kg*K] [J/kg*K] [J/kg*K] [-]} [Pa*s] - 0OC and 1

bar 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

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

Hydrogen H2 0.08985 2.016 4125 14266 10130 1.407 8.42

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

GAS t [O_{C] 0 100 200 300 400 500 600 700 800} Nitrogen N2 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} Argon Ar 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} lambda*103 _{[W/mK] 16.51 21.17 25.59 29.89 33.96 37.91 39.43} Butane C4H10 cp [kJ/kgK] 1.591 2.026 2.453 2.813 3.127 3.403 3.642 mi*106 _{[Pas] 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} Ethane C2H6 cp [kJ/kgK] 1.647 2.067 2.49 2.87 3.214 3.519 3.787 4.022 4.216 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} Ethylene C2H4 cp [kJ/kgK] 1.406 1.737 2.064 2.394 2.721 3.052 3.382 3.709 4.039 mi*106 _{[Pas] 9.6 12.7 15.6 18.2 20.6 22.8 24.9 26.8 28.7}

lambda*103 _{[W/mK] 16.4 29.54 44.19 59.43 75.71 92.34 108.39 123.3 134.9} Helium He cp [kJ/kgK] 5.204 5.204 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} Oxygen O2 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} Methane CH4 cp [kJ/kgK] 2.165 2.448 2.807 3.175 3.529 3.856 4.153 4.421 4.659 mi*106 _{[Pas] 10.4 13.3 16.1 18.5 20.8 22.7 24.6 26.5 28.2} lambda*103 _{[W/mK] 30.24 41.29 51.87 62.34 72.22 81.88 91.3 100.5 109.3} Propane C3H8 cp [kJ/kgK] 1.549 2.017 2.458 2.834 3.161 3.449 3.697 3.916 4.093 mi*106 _{[Pas] 7.5 10.06 12.48 14.75 17.15 19.4 21.8} lambda*103 _{[W/mK] 15 27.4 41.7 57.9 76 95.8} Propene C3H6 cp [kJ/kgK] 1.426 1.8 2.16 2.476 2.753 2.991 3.2 3.388 3.54 mi*106 _{[Pas] 7.84 10.73 13.4 15.92} lambda*103 _{[W/mK] 14 25.6 38.9 53.7}

Sulfur dioxide SO2 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 42.1}

lambda*103 _{[W/mK] 8.37 12.33 16.63 21.17 25.82 30.7 35.82 41.05 46.29}

Carbon dioxide CO2 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 41.8} lambda*103 _{[W/mK] 14.65 22.79 30.94 39.08 47.22 54.89 62.1 68.85 75.13} Carbon monoxide CO 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 41} lambda*103 _{[W/mK] 23.26 30.12 36.52 42.57 48.5 54.08 59.66 65.01 70.13} Hydrogen H2 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 10.3 12.1 13.9 15.4 16.9 18.3 19.6 21} lambda*103 _{[W/mK] 174.4 216.3 258.2 300.1 341.9 383.8 452.7 467.5 509.4} where is for flue gas:

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