Pressure drop (ΔP) in a pipe is calculated using Darcy – Weisbach equation.

`ΔP = f (L/D) (ρV²/2)`

where, f is Darcy friction factor, L is pipe length, D is pipe diameter, ρ is fluid density and V is fluid velocity.

Friction factor is determined based on Reynolds’s number (Re).

`Re = D V ρ / μ`

where, μ is fluid viscosity.

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For Re < 2100, flow is laminar and friction factor is calculated as following.

`f = 64 / Re`

For Re > 4000, flow is turbulent and friction factor is obtained by solving Colebrook White equation.

where, ε is pipe roughness.

For 2100 < Re < 4000, flow is in critical zone and there is no definite friction factor. Churchill equation (1977) predicts friction factor for entire flow regime from laminar to turbulent, it can be used to get an estimate for friction factor in critical zone.

Download spreadsheet for single phase fluid flow

### References

- Darcy friction factor formulae at Wikipedia
- Darcy Weisbach equation at Wikipedia