What happens to stream velocity and discharge when the channel becomes narrower?

What happens to stream velocity and discharge when the channel becomes narrower?

• A. Velocity increases, discharge stays the same
• B. Velocity increases, discharge increases
• C. Velocity decreases, discharge stays the same
• D. Velocity stays the same, discharge decreases

Answer: (A)

In open-channel flow, discharge Q equals velocity times cross-sectional area (Q = V × A). Narrowing the channel reduces the cross-sectional area A. If no water is added or removed along that stretch, the same amount of water must pass per second, so the velocity V must increase to keep Q the same. That’s why the correct idea is: velocity increases, discharge stays the same. If water were entering the channel or leaving it along that reach, discharge could change, but narrowing alone changes area and hence forces the velocity to rise while keeping discharge constant.

In open-channel flow, discharge Q equals velocity times cross-sectional area (Q = V × A). Narrowing the channel reduces the cross-sectional area A. If no water is added or removed along that stretch, the same amount of water must pass per second, so the velocity V must increase to keep Q the same. That’s why the correct idea is: velocity increases, discharge stays the same.

If water were entering the channel or leaving it along that reach, discharge could change, but narrowing alone changes area and hence forces the velocity to rise while keeping discharge constant.