When nozzle area is doubled while head h remains the same, what happens to the ideal discharge Q_th?

• A. It halves
• B. It remains the same
• C. It doubles
• D. It quadruples

Answer: (C)

In an ideal nozzle discharge, the amount of water that can pass per unit time is the product of the exit velocity and the nozzle area. The exit velocity is set by the driving head through Torricelli’s law: v = sqrt(2 g h). If the head h stays the same, the exit velocity remains constant. The discharge rate is Q = A × v, so Q is directly proportional to the nozzle area. Doubling the area therefore doubles the discharge rate. In an ideal case, this linear relationship holds (with real systems you’d include a discharge coefficient, but the fundamental dependence on area remains linear).