The mechanical-energy balance provides a basis for estimating pressure drop owing to friction in fluid flow. For steady flow of an incompressible fluid in a horizontal pipe of constant cross-sectional area, it may be written.

Where ff is the Fanning friction factor, Churchill11 gives the flowing expression for fF for turbulent flow:

Here, Re is the Reynolds number, and (ε/D) is the dimensionless pipe roughness. Turbulent flow obtains for Re > 3,000.
Consider the flow of liquid water at 25oC. For one of the sets of conditions given below, determine (in kg s-1) and ˆ†P / ˆ†L (in kPa m'1). Assume ε / D = 0.0001. Fur liquid water at 25oC, ( = 9% kg m-3 and ( = 9.0 × l0-4 kg m-l s-1. Verify that the flow is turbulent.
D = 2 cm. u = 1 m s-1
D = 5 cm. u = 1 m s-1
D = 2cm, u = 5ms-1
D = 5 cm. u = 5 m s-l

2 f, 0.3305 in | 0.27-+ 09712