Free Water Flow calculator with clear step-by-step results.
Flow rate is cross-sectional area times velocity, and the Darcy-Weisbach relation converts that velocity into friction head loss over the pipe run. The Reynolds number indicates the flow regime: below about 2,300 it is laminar, above 4,000 fully turbulent, which is where the friction factor assumption applies.
Flow rate
Q = pi x (diameter / 2)^2 x velocity
Head loss
h = f x (length / diameter) x velocity^2 / (2 g)
Typically 1-2 m/s for domestic supply. Below 0.5 m/s sediment settles; above about 2.5 m/s noise, erosion and water hammer become problems.
From the Moody chart or the Colebrook equation using Reynolds number and relative roughness. Around 0.02-0.03 is typical for copper and plastic at domestic velocities.