Problem $4$

A system$-$head curve is:

$h_p=15+0\mathrm{.}030Q^2$

And a pump characteristic curve is:

$h_p=20\mathrm{.}0-0\mathrm{.}080Q^2$

Units: $h_p$ : $ft,Q$ : ccfs

a$.$ Solving both equations for both unknowns, calculate the flow rate Q and the head $h_p$ that the pump can provide for this system.

b$.$ In a spreadsheet, plot five points for each curve and show the operating point and how it matches your answer for part a$.$