A completely full cylindrical water tank has height 1.6 m and cross-sectional area 0.5 m². A small hole is present in its side at a height 0.9 m from the bottom. A load of 50 kg is applied on the top surface of water. Take g = 10 m/s² and water density ρ = 1000 kg/m³. The speed of efflux immediately after opening the hole is:
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Question

A completely full cylindrical water tank has height 1.6 m and cross-sectional area 0.5 m². A small hole is present in its side at a height 0.9 m from the bottom. A load of 50 kg is applied on the top surface of water. Take g = 10 m/s² and water density ρ = 1000 kg/m³. The speed of efflux immediately after opening the hole is:

Options

G1 Physics · Accepted Answer

Apply Bernoulli's equation between the top surface and the hole. The extra pressure on the top surface due to the load is ΔP = Mg/A = (50×10)/0.5 = 1000 Pa. Height difference between top surface and hole: H-h = 1.6-0.9 = 0.7 m. Bernoulli gives ΔP + ρg(H-h) = ½ρv². Substitute values: 1000 + 1000×10×0.7 = ½(1000)v². 1000 + 7000 = 500v² ⇒ 8000 = 500v² ⇒ v² = 16 ⇒ v = 4 m/s. Correct option: B.