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Pressure drop calculation when flow rate is known for compressible flow
with constant temperature can be calculated as follows:
where is:
p1 - pressure at the start of pipe
p2 - pressure at the end of pipe
Zm - average compressibility coefficient
R=287 J/kgK - gas constant of air
T - air temperature
G - mass flow rate
A - cross section area
lambda - friction coefficient
L - pipe lenght
D - pipe diameter
sum ksi - the sum of minor losses coefficient
Average compressibility coefficient is calculated as:
where is:
Z1 - compressibility coefficient at the start of pipe
Z2 - compressibility coefficient at the end of pipe
Compressibility coefficient for given pressure and temperature is calculated using:
where is:
pr - reduced pressure
Tr - reduced temperature
which are calculated as follows:
Density (rho) of air at given pressure and temperature is calculated using:
Relation between mass and volumetric flow rate is calculated using:
where is:
rhonor - density at normal conditions (p=101325 Pa, T=273.15 K),
Qnor - volume flow rate at normal conditions (p=101325 Pa, T=273.15 K)
Velocity of air is calculated using:
where the cross section of round pipe is:
To find out if the flow is laminar or turbulant, Reynolds number must
be calculated:
where is:
ni = 13.4*10-6mm2/s - kinematic viscosity of air at T=273.15K=const.
Friction coefficient for laminar flow (Re<2320) is:
for flow in hidraulicaly smooth pipe (Blasius equation):
for turbulant flow with Re<100 000 (Prandtl equation):
for turbulant 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 hydraulicaly smooth pipe and Blasius equation is used.
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