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Q.

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

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a

$\sqrt{\frac{P}{ρ} + v}$

b

$\sqrt{\frac{2 P}{ρ} + v^{2}}$

c

$\sqrt{\frac{P}{ρ} + v^{2}}$

d

$\sqrt{\frac{P}{2 ρ} + v^{2}}$

answer is C.

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Detailed Solution

$P + \frac{1}{2} ρ v^{2} = \frac{P}{2} + \frac{1}{2} ρ V^{2}$

$\Rightarrow V = \sqrt{\frac{P}{ρ} + v^{2}}$

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A fluid is flowing through a horizontal pipe of varying cross – section, with speed vms−1 at a point where the pressure is P pascal. At another point where pressure is P2 pascal its speed is Vms−1. If the density of the fluid is ρkg⁡m−3 and the flow is streamline, then V is equal to