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Water flows steadily through a horizontal pipe of variable cross-section. If the pressure of water is P at a point where flow speed is v, the pressure at another point, where the flow speed is 2v, is (Take density of water as $ρ$ )

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$P - \frac{3 ρ v^{2}}{2}$

$P - \frac{ρ v^{2}}{2}$

$P - \frac{3 ρ v^{2}}{4}$

$P - ρ v^{2}$

answer is A.

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Detailed Solution

Applying Bernoulli’s theorem,

$p_{1} + \frac{{ρv}_{1}^{2}}{2} = p_{2} + \frac{{ρv}_{2}^{2}}{2}$

$\Rightarrow p_{2} = P + \frac{{ρv}^{2}}{2} - \frac{4 {ρv}^{2}}{2}$

$\Rightarrow p_{2} = P - \frac{3 {ρv}^{2}}{2}$

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