Question $4$

$[15$ Marks$]$

a$.$ Derive the equation for hydraulic energy of a solar PV pumping system in watts $($W$).$

b$.$ After a pumping test, a new borehole in Kitwe, has a safe yield of $0\mathrm{.}5\frac{L}{s}.$ The water requirement for the community is that there are $200$ people each needing $40$ L per day. The static head of the borehole is $50$ m $,$ pressure loss $1$ bar and a drawn down of $15$ m $.$ The average daily insolation at the site is $6$ peak sun hours, array$/$load mismatching factor of $0\mathrm{.}8$ and temperature derating factor for array power loss due to heat of $0\mathrm{.}8.$

i$.$ Determine the particular pump for the application, its operating point and the efficiency at that point from the pump curve in figure $4.$

ii$.$ Calculate the total hydraulic energy and size of PV array $($including cable losses$)$ required for a solar pumping system.

iii. How much water $($in $m^3)$ will the system be able to pump out during the peak sunshine hours.

iv$.$ If the pump is to use an AC motor, what size of inverter is will required.

Figure $4$: Pump and efficiency curves for question $4$