A swimming pool has a partial-flow filtration system. Water at \(75^{\circ} \mathrm{F}\) is pumped from the pool through the system shown. The pump delivers \(30 \mathrm{gpm}\). The pipe is nominal 3/4-in. PVC (ID \(=0.824\) in.). The pressure loss through the filter is approximately \(\Delta p=0.6 Q^{2}\), where \(\Delta p\) is in psi and \(Q\) is in gpm. Determine the pump pressure and the flow rate through each branch of the system.

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From pool -10 ft- Total length: 20 ft P8.143 Total length: 40 ft Patm Filter