Question

The cross section of a river channel is approximated by a trapezium. The river has an average channel width of 40 m and average depth of 3 m. If the average flow speed is 2 m/s, the discharge rate is ________ m³/s. \text{[in integer]}

Hint:

The discharge rate is found by multiplying the flow velocity by the cross-sectional area of the river channel.

Answer 1

Correct Answer: 240

The discharge rate \( Q \) is given by the formula:
\[ Q = \text{velocity} \times \text{area} \] The cross-sectional area \( A \) of the trapezium is calculated as: \[ A = \text{width} \times \text{depth} = 40 \, \text{m} \times 3 \, \text{m} = 120 \, \text{m}^2 \] Now, the discharge rate is: \[ Q = 2 \, \text{m/s} \times 120 \, \text{m}^2 = 240 \, \text{m}^3/\text{s} \] Thus, the discharge rate is \( \boxed{240} \, \text{m}^3/\text{s} \).