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 The following figure shows a centrifugal pump that is used for pumping water from
one tank to another through a 1,000 ft (including fittings) nominal 4-in. I.D. pipeline. The
performance curve for the pump has been determined and relates the pressure increase ΔP
(psi) across the pump to the flow rate Q (ft3/s) through it:
ΔP = 19.2 − 133.4Q^4.5 and viscosity of water is 1cP

a) Prove that the pressure drop (psi) in the pipeline between points 2 and 3 isgiven closely in terms of the flow rate Q (ft3/s) by:
P2 − P3 = 10.83 + 10,265fFQ^2 where fF is friction factor
b) Determine the flow rate Q (ft3/s).
c) Determine the pressure increase across the pump, ΔP (psi).
d)Determine the Fanning friction factor, fF.