Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2021
Hard
Water flows out from a large tank of cross-sectional area At=1 m² through a small rounded orifice of cross-sectional area Ao=1 cm², located at y=0. Initially the water level, measured from y=0, is H=1 m. The acceleration due to gravity is 9.8 m/s². Neglecting any losses, the time taken by water in the tank to reach a level of y=H/4 is ___ seconds (round off to one decimal place).
2258.9 s(± 3 accepted)
Explanation
At dh/dt = −Ao√(2gh). Integrating: 2√h from H to H/4 = −(Ao/At)√(2g)·t ⟹ t = (At/Ao)·√(H/(2g)) = (1/1e-4)×√(1/19.6) ≈ 2258.9 s.
Source: GATE ME 2021 Session 2 (ME-2) (2021)
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