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Q.

Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of water is p at a point where the velocity of flow is v, what is the pressure at another point where the velocity of flow is $2 v; ρ$ being the density of water?

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a

$p - \frac{3}{2} ρ v^{2}$

b

$p + \frac{3}{2} ρ v^{2}$

c

$p - 2 ρ v^{2}$

d

$p + 2 ρ v^{2}$

answer is A.

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Detailed Solution

According to Bernoulli's theorem, for a horizontal flow at a height $h$ from ground level,
$p_{1} + \frac{1}{2} ρ v_{1}^{2} + ρ g h = p_{2} + \frac{1}{2} ρ v_{2}^{2} + ρ g h$
or
$p_{2} = p_{1} + \frac{1}{2} ρ (v_{1}^{2} - v_{2}^{2}) = p + \frac{1}{2} ρ \{v^{2} - (2 v)^{2}\} = p - \frac{3}{2} ρ v^{2}$
Hence the correct choice is (a).

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