Answer: x = 2√(h(H-h)).
- A x = 2√(h(H-h))
- B x = √(2gH)
- C x = √(gh)
- D x = 2H
Correct answer: A. x = 2√(h(H-h))
Explanation: Efflux speed v = √(2gh). Time to fall height (H-h): (H-h) = ½gt², t = √(2(H-h)/g). Range x = vt = √(2gh)×√(2(H-h)/g) = 2√(h(H-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.