Question

Water flows through two different pipes A and B of the same circular cross-section but at different flow rates. The length of pipe A is 1.0 m and that of pipe B is 2.0 m. The flow in both the pipes is laminar and fully developed. If the frictional head loss across the length of the pipes is same, the ratio of volume flow rates $Q_B/Q_A$ is ________(round off to two decimal places).

• A. 0.5

Answer 1

The correct option is A 0.5
pipe-A $L_A=1m$
pipe-B $L_B=2m$

$d_A=d_B$; $h_{fA}=h_{tB}$

$\frac{32\mu V_A{L}_A}{\rho g{d}_A^2}=\frac{32\mu V_B{L}_B}{\rho g{d}_B^2}$

$\frac{V_B}{V_A}=\frac{d_B^2}{d_A^2}\times \frac{L_A}{L_B}$

Q = AV

$V=\frac{Q}{\frac{\pi }{4}{d}^2}$

$\frac{\frac{Q_B}{\frac{\pi }{4}{d}_B^2}}{\frac{Q_A}{\frac{\pi }{4}{d}_A^2}}=\frac{d_B^2}{d_A^2}\times \frac{L_A}{L_B}$

$\frac{Q_B}{Q_A}=\frac{d_B^4}{d_A^4}\times \frac{L_A}{L_B}=\frac{1}{2}$

$(\therefore Given{d}_A=d_B)$