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

The correct answer is 24

Fig.

Using Bernoulli’s equation
$P_1 + \frac{1}{2} \rho v^2 = P_2 + \frac{1}{2} \rho 4v^2$
$\frac{3}{2}ρv^2=P_1−P_2$
⇒$$v = \sqrt{\frac{2(P_1 - P_2)}{3\rho}}
$v = \sqrt\frac{2 \times 4500}{3 \times 750} = 2 \, \text{m/sec}$
So Q = A1v = 24 × 10–3 m3/sec