KinexiaLEARN PHYSICS

Flow Rate — River Discharge (Worked Example)

Easy
Problem

A river is 20 m wide and 2.0 m deep on average, flowing at 1.5 m/s. What is its discharge (volume flow rate)?

Given

  • width = 20 m

  • depth = 2.0 m

  • v = 1.5 m/s

Find

The discharge Q.

Principle

For a rectangular channel, A = width × depth, then Q = Av.

Formula

Solution

  1. Area: A=20×2.0=40 m2A = 20 \times 2.0 = 40\ \mathrm{m^2}

  2. Substitute: Q=40×1.5Q = 40 \times 1.5

  3. Multiply: Q=60 m3/sQ = 60\ \mathrm{m^3/s}

60 m³/s

Unit check

m² × m/s = m³/s — correct.

What this means physically

60 m³/s — 60 tonnes of water passing every second. Hydrologists measure exactly this to predict floods: rising v or depth multiplies the discharge.

Common mistake

Using surface speed for the average. Friction slows water near the bed, so average v is less than the surface speed — measure at several depths.