Question

A single pipe of length 1500 m and diameter 60 cm connects two reservoirs having a difference of 20 m in their water levels. The pipe is to be replaced by two pipes of the same length and equal diameter 'd' to convey 25% more discharge under the same head loss. If the friction factor is assumed to be the same for all the pipes, the value of 'd' is approximately equal to which of the following options?

• A. 37.5 cm
• B. 40.0 cm
• C. 45.0 cm
• D. 50.0 cm

Answer 1

The correct option is D 50.0 cm


For single pipe

$h_F=\frac{8fL{Q}_1^2}{{\pi }^{2}g{D}^5}$

$L=1500m,D=0.6m$
$h_F=20m$

$Q_1=\frac{0.112}{\sqrt{f}}$ ...(i)


In case of double pipe discharge is increased by 25% than that of previous case hence,

$2Q_2=1.25Q_1$

$20=\frac{8f\times 1500\times (0.625Q_1{)}^2}{9.81\times {\pi }^2\times d^5}$

$\frac{f{Q}_1^2}{d^5}=0.413$

$Q_1^2=\frac{0.413d^5}{f}$

$Q_1=\frac{0.642d^{5/2}}{\sqrt{f}}$ ...(ii)

From eq. (i) and (ii), we get
$d=49.7cm\simeq 50cm$