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A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms^-1 at a point where the pressure is P pascal. At another point where pressure is $\frac{P}{2}$ pascal, its speed is V ms^-1. If the density of the fluid is $ρ$ kgm^-3 and the flow is streamline, then V is equal to

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$\sqrt{\frac{P}{ρ} + v}$

$\sqrt{\frac{2 P}{ρ} + v^{2}}$

$\sqrt{\frac{P}{2 ρ} + v^{2}}$

$\sqrt{\frac{P}{ρ} + v^{2}}$

answer is D.

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Detailed Solution

$P + \frac{1}{2} {ρv}^{2} = \frac{P}{2} + \frac{1}{2} {ρV}^{2}$
From this we get $V = \sqrt{\frac{P}{ρ} + v^{2}}$

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