Two pipes of diameter D and d and of equal length L are considered. If the pipes are arranged in parallel, the loss of head for either pipe when a total quantity of water flows through them is h. If the pipes are arranged in series and the same quantity Q flows through them, the loss of head is H. If d= 0.5D, find the percentage of the total flow through each pipe when placed in parallel and the ratio of H to h. Neglect minor losses and assume friction coefficients to be constants.

Solution :

Given :

Length of pipe 1,

$ L_{1}=L$ and its diameter $d_{1}=D$

Length of pipe 2,

$ L_{2}=L$ and its diameter $d_{2}=d$

Total discharge $=Q$

Head loss when pipes are in parallel $=h$

Head loss when pipes are in series $=H$

$d=\frac{D}{2}$ and f is constant

Case 1: …