Question

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 _____ × 10–3 m3s–1.

Answer 1

Using Bernoulli’s equation
$P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho 4v_2^2$

$\frac{3}{2}\rho v^2 = P_1 - P_2$

$⇒$ $v = \sqrt{\frac{2}{3\rho}(P_1 - P_2)}$

$=$ $\sqrt{\frac{2 \times 4500}{3 \times 750}} = 2$ m/sec
So $Q = A1v =$ 24 × 10–3 m3/sec
Answer is 24.