A pump is used to deliver $0\mathrm{.}05m\frac{3}{s}$ of water from a reservoir to a pond located at $60m$ height as shown in Figure $3.$ The water is delivered in a commercial cast iron pipe with surface roughness, $$ of $0\mathrm{.}26mm,$ diameter of $0\mathrm{.}2m$ and length of $200m.$

From the data given,

$($a$)$ Show that flow regime is turbulent.

$($b$)$ Calculate the overall losses incurred by the pipe system.

$($c$)$ Obtain the head of pump $($hp$)$ required to accommodate the requirement of the demand.

$($d$)$ Obtain the power required by the pump. $($Use Ws $=Qhp)$

For water, use $=1\mathrm{.}12{10}^{-3}N\frac{s}{m^2}$;$=1000k\frac{g}{m^3}$;$g=9\mathrm{.}81\frac{m}{s^2}$