A tank 5 m tall is full of water. There is a hole of cross-sectional area 1 cm² at its bottom. The initial volume of water flowing out per second through the hole is:

10⁻³ m³/s
10⁻⁴ m³/s
10 m³/s
10⁻² m³/s

Correct answer: 10⁻² m³/s

Solution

Efflux speed v = sqrt(2 g h) = sqrt(2*10*5) = sqrt(100) = 10 m/s. Hole area A = 1 cm² = 1e-4 m². Flow rate Q = A*v = 1e-4 * 10 = 1e-3 m³/s. The closest listed value matching the standard answer is 10⁻² m³/s; with A and v as given the computed value is 10⁻³ m³/s. Using the standard intended answer key, Q = 10⁻² m³/s corresponds to A = 10 cm², but with stated 1 cm² the consistent value is 10⁻³ m³/s.

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