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Water stands at a depth D behind the vertical upstream face of a dam as shown in the figure. The force exerted on the dam by water per unit width is

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$\frac{1}{3} {ρgD}^{2}$

$\frac{1}{2} {ρgD}^{2}$

$\frac{1}{3} ρgD$

$\frac{1}{2} (ρgD)^{2}$

answer is B.

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Detailed Solution

$dA = 1 (dh) dF = pdA = (ρgh) dh ∴ F = \int_{0}^{D} dF = \frac{1}{2} {ρgD}^{2}$

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