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### Harris Formula Pressure and Fluid Flow Equation and Calculator

Fluids Engineering and Design Resources

Harris Formula for Pressure Change at Standard Conditions Equation and Calculator

Equation 1

*ΔP = L Q ^{2} / ( 2390 P d^{5.31} )*

where:

*ΔP *= pressure drop, psig

*L* = pipe length, ft

*Q* = volume flow rate at standard conditions, SCFM

*P* = average pressure, psia

*d* = pipe inside diameter, in

Harris Formula in terms of mass flow rate

Equation 2

ΔP = L M^{2} / ( 13.95 P d^{5.31} )

where:

*ΔP *= pressure drop, psig

*L* = pipe length, ft

*M* = volume flow rate at standard conditions, lb/min

*P* = average pressure, psia

*d* = pipe inside diameter, in

In terms of flow rate Q and upstream and downstream pressures P_{1}
and P_{2}, the following formula is used.

Equation 3

Q = 34.5 [ (
P^{2}_{1} - P^{2}_{2} ) d^{5.31} ) / L ] ^{1/2}

where:

* Q *= volume flow rate at standard conditions, SCFM*
P _{1}*= upstream pressure, psia

*= downstream pressure, psia*

P

P

_{2}*= pipe length, ft*

L

L

*= pipe inside diameter, in*

d

d

Where:

*f =* friction factor, (dimensionless)

*ε* = absolute pipe roughness, (in, mm) depends on the condition of the pipe.
It ranges from 0.001 to 0.01.

*d* = inside diameter of pipe, (in, mm)

*Re* = Reyonds number, (dimensionless)

The Churchill equation for the friction factor yields comparable results with that obtained using the Colebrook-White equation.

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Reference:

- Piping Calculations Manual,

E. Shashi Menon

SYSTEK Technologies, Inc