If the head h in Q ≈ Cd L sqrt(2 g h) increases by a factor of 4, by what factor does the discharge Q change?

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Multiple Choice

If the head h in Q ≈ Cd L sqrt(2 g h) increases by a factor of 4, by what factor does the discharge Q change?

Explanation:
Discharge is proportional to the square root of the head: Q ∝ sqrt(h), with Cd, L, and g treated as constants. If h increases by a factor of 4, the square root becomes sqrt(4) = 2. So Q doubles: Q2 = Cd L sqrt(2 g (4h)) = 2 Cd L sqrt(2 g h). Therefore the discharge increases by a factor of two.

Discharge is proportional to the square root of the head: Q ∝ sqrt(h), with Cd, L, and g treated as constants. If h increases by a factor of 4, the square root becomes sqrt(4) = 2. So Q doubles: Q2 = Cd L sqrt(2 g (4h)) = 2 Cd L sqrt(2 g h). Therefore the discharge increases by a factor of two.

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