The reading of pressure metre attached with a closed pipe is 4 . 5 × 10 4 N m - 2 . On opening the valve, water starts flowing and the reading of pressure metre falls to 2 . 0 × 10 4 N m - 2 . The vel

Question

The reading of pressure metre attached with a closed pipe is 4 . 5 × 10 4 N m - 2 . On opening the valve, water starts flowing and the reading of pressure metre falls to 2 . 0 × 10 4 N m - 2 . The velocity of water is found to be V m s - 1 . The value of V is _________.

TestHub · Accepted Answer

The formula to calculate the change in pressure can be written as

$P_{1} - P_{2} = \frac{1}{2} ρ v^{2} . . . (1)$

From equation (1), it follows that

$4.5 \times 10^{4} - 2.0 \times 10^{4} = \frac{1}{2} \times 10^{3} \times v^{2} \Rightarrow 2.5 \times 10^{4} = \frac{1}{2} \times 10^{3} \times v^{2} \Rightarrow v^{2} = 50 \Rightarrow v = \sqrt{50}$

Hence, $V = 50$ .

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