Discharge can be calculated using which variables for a rectangular channel?

Discharge can be calculated using which variables for a rectangular channel?

• A. width × depth × velocity
• B. width + depth + velocity
• C. width × velocity ÷ depth
• D. depth × velocity ÷ width

Answer: (A)

Discharge is the volume of water passing a cross-section each second, so it comes from multiplying the cross‑sectional area by the average velocity: Q = A × v. For a rectangular channel, the cross‑sectional area is width × depth, giving Q = width × depth × velocity. This yields the units of cubic meters per second (m^3/s) when width and depth are in meters and velocity in meters per second. For example, a channel 4 m wide, 1.5 m deep, with a flow speed of 2 m/s carries Q = 4 × 1.5 × 2 = 12 m^3/s. The other forms don’t represent volume flow: adding width, depth, and velocity mixes different quantities; multiplying or dividing in those ways does not produce a volumetric flow rate and leads to incorrect units (e.g., m^2/s or m/s).

Discharge is the volume of water passing a cross-section each second, so it comes from multiplying the cross‑sectional area by the average velocity: Q = A × v. For a rectangular channel, the cross‑sectional area is width × depth, giving Q = width × depth × velocity. This yields the units of cubic meters per second (m^3/s) when width and depth are in meters and velocity in meters per second.

For example, a channel 4 m wide, 1.5 m deep, with a flow speed of 2 m/s carries Q = 4 × 1.5 × 2 = 12 m^3/s.

The other forms don’t represent volume flow: adding width, depth, and velocity mixes different quantities; multiplying or dividing in those ways does not produce a volumetric flow rate and leads to incorrect units (e.g., m^2/s or m/s).