First slide

Fluid dynamics

Question

A manometer connected to a closed tap reads 3.5 × 10⁵ N/m². When the valve is opened, the reading of manometer falls to 3.0 × 10⁵ N/m², then velocity of flow of water is

Moderate

A

100 m/s
B

10 m/s
C

1 m/s
D

$10 \sqrt{10} m / s$

Solution

Bernoulli's theorem for unit mass of liquid $\frac{P}{ρ} + \frac{1}{2} v^{2} =$ constant
As the liquid starts flowing, it pressure energy decreases $\frac{1}{2} v^{2} = \frac{P_{1} - P_{2}}{ρ} \Rightarrow \frac{1}{2} v^{2} = \frac{3 .5 \times 10^{5} - 3 \times 10^{5}}{10^{3}}$
$\Rightarrow v^{2} = \frac{2 \times 0 .5 \times 10^{5}}{10^{3}} \Rightarrow v^{2} = 100 \Rightarrow v = 10 m / s$

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