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Q.

A horizontal pipe of non-uniform cross-section allows water to flow through it with a velocity1 $m s^{- 1}$ when pressure is 50 kPa at a point. If the velocity of flow has to be 2 $m s^{- 1}$ at some other point, the pressure at that point should be

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a

50 kPa

b

100 kPa

c

48.5 kPa

d

24.25 kPa

answer is C.

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Detailed Solution

According to Bernoulli’s equation for horizontal pipe,

$P_{1} + \frac{1}{2} ρ v_{1}^{2} = P_{2} + \frac{1}{2} ρ v_{2}^{2}$

$\Rightarrow$ $P_{1} + \frac{1}{2} ρ (v_{1}^{2} - v_{2}^{2}) = P_{2}$

$\Rightarrow$ $P_{2} = 50 \times 10^{3} + \frac{1}{2} \times 10^{3} \times (1^{2} - 2^{2})$

$\Rightarrow$ $P_{2} = 50 \times 10^{3} - 1.5 \times 10^{3}$

$= 48.5 k P a$

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A horizontal pipe of non-uniform cross-section allows water to flow through it with a velocity1 ms−1 when pressure is 50 kPa at a point. If the velocity of flow has to be 2 ms−1 at some other point, the pressure at that point should be