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Q.

A gas flows with a velocity v along a pipe of cross sectional area ‘s’ and bent an angle of 90° at point A. What force does the gas exert on the pipe at ‘A’. If it’s density is ρ?

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a

$\sqrt{2} {SV}^{2} ρ$

b

$\frac{\sqrt{2} SV}{ρ}$

c

$\sqrt{3} \frac{{SV}^{2} ρ}{2}$

d

$\sqrt{3} {SV}^{2} ρ$

answer is B.

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Detailed Solution

Take x-axis along the flow and y-axis perpendicular to it
$\begin{array}{l} V_{inital} = \vec{V}, V_{final} = V \vec{j}; | Δ \vec{V} | = \sqrt{V^{2} + V^{2}} = \sqrt{2} V \\ F = m \frac{Δv}{t} = m \frac{Δv}{t} = ρ \times S \frac{l}{t} \times \sqrt{2} V = \sqrt{2} {SV}^{2} ρ \end{array}$

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