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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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