Question

A pipeline (diameter 0.3 m, length 3 km) carries water from point P to point R (see figure). The piezometric heads at P and R are to be maintained at 100 m and 80 m, respectively. To increase the discharge, a second pipe is added in parallel to the existing pipe from Q to R. The length of the additional pipe is also 2 km. Assume the friction factor, f = 0.04 for all pipes and ignore minor losses.


If there is no restriction on the diameter of the additional pipe, what would be the maximum increase in discharge theoretically possible from this arrangement?

• A. 0%
• B. 50%
• C. 67%
• D. 73%

Answer 1

The correct option is D 73%

If the diameter of additional pipe is very large, the head loss will be zero in it theoretically. Therefore the total head loss will occur between P and Q only


$h_L=\frac{f{L}_{PQ}{Q}_3^2}{12d^5}$

$\Rightarrow 20=\frac{0.04\times 1000\times Q_3^2}{12\times (0.3{)}^5}$

$\Rightarrow Q_3=0.1207m^3/s$

% maximum increase in discharge

$=\left(\frac{Q_3-Q_1}{Q_1}\right)\times 100$

$=\left(\frac{0.1207-0.0697}{0.0697}\right)\times 100$

$=73.17\%=73\%$