Discharge per minute in a rectangular river channel: A river 2 m deep and 45 m wide flows at 3 km/h. How much water (in m3) passes a section each minute?

Introduction / Context:Flow rate in a prismatic channel equals cross-sectional area times velocity. Convert the velocity to meters per minute and multiply by area to get discharge per minute.

Given Data / Assumptions:

• Depth = 2 m, Width = 45 m ⇒ Area A = 2 * 45 = 90 m2
• Speed v = 3 km/h = 3000 m/h = 50 m/min

Concept / Approach:

• Discharge per minute Q = A * v (with consistent units).

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 3000 m3: Ignores correct speed conversion.
• 27000 m3: Off by a factor of 6 (hour vs minute confusion).
• 2100 m3: Underestimates due to wrong area or speed.

Common Pitfalls:

• Not converting km/h to m/min correctly.
• Using depth+width instead of depth×width for area.

Final Answer:

4500 m3