Consider an existing pump and pipe system. The diameter, length, and friction

factor of the existing pipe are: $20$ cm$,2500$ m$,$ and $0\mathrm{.}0022,$ respectively. The

static lift for the pumping scheme is equal to $20$ m$.$ The pump characteristic for

the existing pipe is given by hp $=53100$ Q$2$

$,$ where hp $=$ pumping head in m$,$ and

Q $=$ flow rate in m$3/$s$.$ One is interested in increasing the flow rate by $30\%$ by

installing a new pipe with a new pump in parallel to existing system. The new

pipe has a diameter of $25$ cm and f $=0\mathrm{.}0015.$ Determine the power required by

the new pump. Is there a possibility of achieving the same goal of increasing the

discharge capacity of the system in a better way? If you think it is possible, write

a $$brief$$ note on it$.$