What is the standard river discharge equation in metric units?

• A. Discharge (m3/s) = width (m) × depth (m) × velocity (m/s)
• B. Discharge (m3/s) = velocity × depth
• C. Discharge (m3/s) = cross-sectional area × slope
• D. Discharge (m3/s) = width × depth × gravity

Answer: (A)

Discharge is the volume of water passing through a cross-section each second. The standard equation is Q = A × v, where A is the cross-sectional area and v is the average velocity. For a river with a roughly rectangular cross-section, A ≈ width × depth, so Q ≈ width × depth × velocity, which gives units of m^3/s when width and depth are in meters and velocity in m/s. The other forms don’t match the needed dimensions: velocity times depth gives m^2/s (not a volume flow rate), slope or gravity aren’t direct multipliers in this simple discharge formula.