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Churchill Friction Factor Formulae and Calculator

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Churchill Friction Factor Equation and Calculator

This equation for the friction factor was proposed by Stuart Churchill and published in Chemical Engineering magazine in November 1977.

Churchill Friction this is an explicit equation for solving for the friction factor and is expressed as

Equation 1

${\displaystyle f={\lfloor {\left(\frac{8}{Re}\right)}^{12}+\frac{1}{(A+B{)}^{3/2}}\rfloor }^{1/12}}$

Equation 2

${\displaystyle A={[2.457{\log }_e<!--\; \; -->\frac{1}{(7/Re{)}^{0.9}+0.27e/d}]}^{16}}$

Equation 3

${\displaystyle B={\left(\frac{37,530}{Re}\right)}^{16}}$

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 = Reynolds 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