Churchill correlation (friction factor)

Piping Systems
Equivalent length key pipe components
Singularity coefficient key pipe components
Partially filled pipe
Sonic Velocity
Valves types
Valves Cv
Control valve sizing for gases
Pressure safety valves
Colebrook correlation
Churchill correlation
Velocity in pipes
Flow regimes
Orifice calculations

1. Introduction

The friction factor is used to calculate the pressure drop due to the flow of a fluid in a pipe. It represents the interaction in between the fluid and the pipe. There are different ways to calculate it, one can be graphical, using a Moody graph, but for automating calculation it is not practical, thus correlations are required. The Colebrook correlation is usually admitted as being accurate enough for most industrial application but presents a difficulty as it does not explicitly express the friction factor, that is why it may be interesting to consider Churchill equation that allows to directly calculate the friction factor.

Note that the friction factor used here is Darcy (also called Darcy-Wesibach or Moody) friction factor.

2. Churchill equation

Churchill equation
With :
f = Darcy friction factor
D = Pipe diameter (m)
Re = Reynolds number
ε = pipe roughness (m)