Flow Rate — Water Main (Worked Example)

Given

• d = 0.50 m → r = 0.25 m

• v = 2.0 m/s

Find

The flow rate Q.

Principle

Q = Av for the circular pipe.

Formula

Solution

1. Area: $A = \pi(0.25)^2 = 0.1963\ \mathrm{m^2}$

2. Substitute: $Q = 0.1963 \times 2.0$

3. Multiply: $Q = 0.393\ \mathrm{m^3/s}$

Unit check

m² × m/s = m³/s. Volume per unit time — dimensionally consistent for flow rate.

What this means physically

393 L/s — enough to fill an Olympic pool in about 1.8 hours. City water systems are sized with Q = Av at every pipe.