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Fluid Mechanics Please show work.
Problem 3: (30 points) Figure P.2a shows a pump-piping system in which water at 25°C is pumped from a reservoir whose surface is 4.0 ft above the centerline of the pump inlet. The pump is centrifugal, Taco Model 4013 FI Series with 11.25-in impeller. The pump curve, NPSHequired, and NPSH=-ailable are provided in Figures P.26 and P.2c, respectively. The pump curve approximately follows bellow equation on Fig. P.26 for 11.25-in impeller. H[At] 60 [ft] - 5*10-02 V: flow rate [gallons/min] The piping system from the reservoir to the pump consists of 10.5 ft of cast iron pipe with an ID of 4.0 in and an average inner roughness height of 0.02 in (coefficient of friction f 0.03). There are several minor losses: a sharp-edged inlet (Ki = 0.5), three flanged smooth 90° regular elbows (K1 = 0.3 each), and a fully open flanged globe valve (Ki = 6.0). Unit conversion: 1 f = 7.48 gallon, 1 minute = 60 second, g=32.2 ft²/s (a) Determine flowrate (in gallons/min) at system operating point. (b) Does cavitation occur in this pumping system? If yes, then how does the flowrate, you obtained in part a change? Explain your reason Reservoir Inlet piping system Pump Valve Fig. Pl.a: Pump-piping system