Water flows under gravity between an impounding reservoir and a service reservoir, through a $1000$ m long pipe of $220$ mm diameter and ks $=0\mathrm{.}13$ mm$.$ The difference in level of the water surfaces in the reservoirs is $110$ m and the operating flow rate is $285$ l$/$s$.$ Assume

u $=1\backslash$times $106$

m$2/$s$.$

Immediate future demands will necessitate an increase in the maximum flow rate between the $2$ reservoirs of $20\%.$ A pump will be used to boost the flow in the existing main. Electricity supply is available and the pump motor will run at $1500$ rev$/$min $($rpm$).$