Derive an expression for equivalent size of pipe in series. A piping system consists of three pipes arranged in series. The lengths of the pipes are 1000m, 800m, 300m and the diameters are 500mm, 400mm and 300mm respectively when they are connected in series. These pipes are to be replaced by a single pipe of length 2100m. Find the diameter of single pipe

Equivalent pipe : The pipe of uniform diameter having loss of head and discharge equal to the loss of head and discharge of a compound pipe, consisting of several pipe of different length and diameters.

Now, Let $L_1$ = Length of pipe 1 and $d_1$ = dia.

$L_2$ = Length …