Answer: v = √(2gh).
- A v = √(2gh)
- B v = 2gh
- C v = √(gh)
- D v = gh
Correct answer: A. v = √(2gh)
Explanation: Applying Bernoulli's equation between the top surface and the hole: v = √(2gh). This is identical to the speed of a freely falling object from height h.
Since the same volume of fluid must pass every cross-section per second (continuity), the fluid speeds up where the pipe narrows; Bernoulli's equation then says this faster-moving fluid has lower pressure - the principle behind a venturi meter and an aircraft wing's lift.
Concept context
Pressure, buoyancy, Bernoulli equation, viscosity, and surface tension.