How to calculate river discharge
How much water passes a point in one second?
River discharge is the volume of water flowing past a point each second. Multiply cross-sectional area by mean velocity.
Find the area
A cross section is a slice across the river. For a rectangular channel, area is width × depth. A natural channel usually needs several depth measurements.
Use mean velocity
Velocity is speed in a stated direction. Water does not move at the same speed everywhere in a river. Use the mean velocity for the whole cross section when it is supplied.
Worked example
| Invented rectangular channel |
|---|
| Width: 4 m · Depth: 0.5 m · Mean velocity: 0.8 m/s |
- Cross-sectional area = 4 × 0.5 = 2 m².
- Discharge = 2 × 0.8 = 1.6 m³/s.
- This means 1.6 cubic metres of water pass the cross section each second. It is a volume rate, not a depth.
A surface float does not directly measure mean velocity across the whole river. Follow the method supplied in your task. Real river fieldwork needs your teacher’s risk assessment and instructions.
Check you’ve got it
Area stays at 2 m² but mean velocity rises to 1.2 m/s. What is the new discharge?
Check your answer
2 × 1.2 = 2.4 m³/s. That is 0.8 m³/s more than before, a 50% increase.
Try it yourself
Use this new resource. Check your answers, then try another set.
River discharge
Use the explicitly rectangular cross section. The supplied mean velocity represents the whole cross section; it is not an uncorrected surface-float velocity.
| Measurement | Value |
|---|---|
| Width (m) | 6 |
| Uniform depth (m) | 0.3 |
| Mean cross-sectional velocity (m/s) | 0.7 |
Resource description
Idealised fictional rectangular channel