One wants to pump water out from a well with a depth h=\SI5.0m. The pump is on the surface and its water intake pipe (filled with water) has an inner diameter d=\SI16mm and a length that is equal to the depth of the well.
a) How big has to be the power P of the pump to pump water with a flow rate q=\SI30l/min? The efficiency of the pump is η=\SI25\percent.
b) What is the maximal depth hm of the well for which it is possible to pump water from the well with this type of pump?
Assume that besides other forces frictional force is also applied to the water column inside the water, which causes a decrease in the pressure per length l of the pipe Δp=chq2l/d5 where ch=\SI40Pa⋅s2/m2. The density of water ρ=\SI1000kg/m3, gravitational acceleration g=\SI9.8m/s2 and the air pressure p0=\SI100kPa.