A systemhead curve is hp 15 0030Q2 and a pump characterist

A system-head curve is: h_p = 15 + 0.030Q^2 and a pump characteristic curve is: h_p = 20.0 - 0.080Q^2 Units: h_p rightarrow ft Q rightarrow cfs Calculate the flow rate Q that the pump can provide for this system.

Solution

h_p=15+0.030Q^2---------- 1

h_p=20-0.080Q^{2----------- 2}

^{Solving 1 and 2 --------- 1 - 2}

5 = (0.030+0.08)Q²

Q²=45.45

Q= 6.74 cfs