A liquid of density 750 kgm-3 flows smoothly through a horizontal pipe that tapers in cross-sectional area from A1 = 1.2 × 10-2 m2 to A2=A12. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ____×10-3m3s-1

Using Bernoulli’s equation p1+12ρv2=p2+12ρ4v232ρv2=p1−p2⇒v=2p1−p23ρ=2×45003×750=2m/secSo Q=A1v=24 x 10-3 m3/sec

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A liquid of density 750 kgm^-3 flows smoothly through a horizontal pipe that tapers in cross-sectional area from A₁ = 1.2 × 10^-2 m² to $A_{2} = \frac{A_{1}}{2}$ . The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ____×10^-3m³s^-1

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answer is 24.

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Detailed Solution

Using Bernoulli’s equation
Question Image
$\begin{array}{l} p_{1} + \frac{1}{2} {ρv}^{2} = p_{2} + \frac{1}{2} ρ 4 v^{2} \\ \frac{3}{2} {ρv}^{2} = p_{1} - p_{2} \\ \Rightarrow v = \sqrt{\frac{2 (p_{1} - p_{2})}{3 ρ}} = \sqrt{\frac{2 \times 4500}{3 \times 750}} = 2 m / \sec \end{array}$
So Q=A₁v=24 x 10^-3 m³/sec

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