First slide

Fluid dynamics

Question

A horizontal pipe line carries water in streamline flow. At a point where the cross-sectional area is 10 ${cm}^{2}$ the water velocity is $l {ms}^{- l}$ and pressure is 2000 pa. The pressure of water at another point where the cross-sectional area is 5 ${cm}^{2}$ is

Moderate

A

200 Pa
B

400 Pa
C

500 Pa
D

800 Pa

Solution

Since cross-sectional area is halved, therefore, velocity is doubled.
Now, $P_{1} = 2000 Pa, v_{1} = 1 {ms}^{- 1}$
$P_{2} = ?, v_{2} = 2 {ms}^{- 1}$
Again $P_{2} + \frac{1}{2} \times 1000 \times 2$
= 2000 + $\frac{1}{2} \times 1000 \times 1 \times 1$
or $P_{2} = 2000 + 500 (1 - 4) = 500 Pa$

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