First slide

Fluid dynamics

Question

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

Difficult

A

50 kPa
B

100 kPa
C

48.5 kPa
D

24.25 kPa

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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