Water enters a large flat-bottomed tank at a rate of 10⁻⁴ m³/s and simultaneously leaks out through a hole of area 1 cm² in the bottom. If the water level in the tank stays constant, what is that steady height?

4 cm
2.9 cm
1.7 cm
5.1 cm

Correct answer: 5.1 cm

Solution

At steady height the inflow equals efflux: Q_in = A*sqrt(2gh). With Q_in = 1e-4 m³/s and A = 1 cm² = 1e-4 m², sqrt(2gh) = 1 m/s, so 2gh = 1, h = 1/(2*9.8) ≈ 0.051 m = 5.1 cm.

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