Flow rate and velocity
Flow rate Q is the volume passing per second; velocity v is how fast the fluid moves. They are linked by the pipe's cross-section area A:
Q = A × v, with A = π × d² ÷ 4 for a pipe of inside diameter d.
30 L/min (0.0005 m³/s) in a 25 mm pipe: A = π × 0.025² ÷ 4 = 0.000491 m², so v = 0.0005 ÷ 0.000491 = 1.02 m/s. Halving the diameter quadruples the velocity.
Laminar or turbulent
The Reynolds number, Re = ρ × v × d ÷ µ, tells which. Below about 2,300 flow is laminar and smooth; above about 4,000 it is turbulent; between is transitional. Water (ρ = 1,000 kg/m³, µ = 1 mPa·s) at 1.02 m/s in 25 mm: Re = 1,000 × 1.02 × 0.025 ÷ 0.001 = 25,500, fully turbulent, as almost all practical water flow is.
Pressure drop
Friction against the wall costs pressure along the pipe. The Darcy-Weisbach equation gives the loss:
Δp = f × (L ÷ d) × ρ × v² ÷ 2
f is the friction factor: 64 ÷ Re for laminar flow, and for turbulent flow a value from the Colebrook equation that depends on Re and the wall roughness (0.0015 mm for PVC and copper, 0.045 mm for steel, 0.26 mm for cast iron). For the example above in 20 m of PVC, f ≈ 0.025 and Δp = 0.025 × (20 ÷ 0.025) × 1,000 × 1.02² ÷ 2 ≈ 10,400 Pa, about 0.1 bar or 1.06 m of head. Elbows, valves and fittings add more, usually counted as an equivalent length of pipe.
Picking a pipe size
Water supply pipes are usually sized for 1 to 2 m/s: slower pipes cost more, faster ones are noisy, erode fittings and lose too much pressure. Suction lines are kept under 1 m/s to avoid cavitation. Pressure drop rises with the square of velocity, so going one pipe size up often cuts the loss by two thirds.
Calculators
The Pipe Flow Calculator gives velocity, Reynolds number, friction factor and pressure drop from the flow rate, diameter, length and pipe material. The Reynolds Number Calculator does the flow regime on its own, for any fluid.