An energy$-$efficient system in a water transporting pipe network is of paramount importance in terms of

reducing operating cost. Energy$-$efficient systems consume less electricity to pump water through the network.

This translates to lower operational expenses for water utilities or industries involved in water transportation.

Knowing the pumping power helps in designing and operating the system efficiently. By accurately calculating

the required power, engineers can select appropriately sized pumps and motors, ensuring optimal energy

usage.

Water $(=1000\frac{kg}{m^3},=0\mathrm{.}001(Pa)-s)$ is to be pumped through a $550m$ cast iron pipe of diameter $6cm$

from reservoir $A$ to $B$ at a rate of $160\frac{m^3}{h}.$ Assuming no minor losses $($due to the pipe fittings$),$ calculate the

input power $(kW)$ required by the system to maintain a height of $150m$ between the two reservoirs as shown

in Figure $3.($use Table$-1$ for calculating

Colebrook equation $\frac{1}{\sqrt[\phantom{2}]{f}}$~$=-1\mathrm{.}8log[\frac{6\mathrm{.}9}{Re}+(\frac{\frac{}{D}}{3\mathrm{.}7}{)}^{1\mathrm{.}11}]$