Question

A pipe of 0.7 m diameter has a length of 6 km and connects two reservoirs A and B. The water level in reservoir A is at an elevation 30 m above the water level in reservoir B. Halfway along the pipe line, there is a branch through which water can be supplied to a third reservoir C. The friction factor of the pipe is 0.024. the quantity of water discharged into reservoir C is 0.15 m${}^3$/s. Considering the acceleration due to gravity as 9.81 m/s${}^2$ and neglecting minor losses, the discharge (in m${}^3$/s) into the reservoir B is

• A. 0.572

Answer 1

The correct option is A 0.572

$f=0.024,d=700mm,l=6000m$

$h_f=\frac{fl{Q}^2}{12.1d^5}$

$30=h_{f_1}+h_{f_2}$

$30=\frac{0.024\times 3000\times Q^2}{12.1\times {0.7}^5}+\frac{0.024\times 3000\times (Q-0.15{)}^2}{12.1\times (0.7{)}^5}$

$=35.40Q^2+35.40(Q-0.15{)}^2$

$\therefore Q=0.722m^3/s$

$\therefore Q_B=Q-0.15=0.572m^3/s$