Example $3.$

Water at and $\{$:${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1\mathrm{.}138{10}^{-3}\frac{kg}{m}*s)$ is to

be charged from reservoir at a rate of $18\frac{L}{s}$ using two horizontal cast

iron pipes $(=0\mathrm{.}00026m)$ connected im series and a pump between

them. The first pipe is $20$ long adn has a $6cm$ diameter, while second

pipe is $35m$ long and has a $4cm$ diameter. The water level in the

reservoir is $30m$ above the centerline of the pipe. The pipe entrance is

sharped$-$edged $(K_L=0\mathrm{.}5)$ and losses associated with the connection of

the pump are negligible. Determine the required pumping head and the

minimum pumping power to maintain the indicated flow rate.