A team of mechanical engineers has been given the task of designing a piping system for a chemical plant that requires a centrifugal pump to efficiently pump 500 gallons of water per minute (gpm). After searching through Taco's pump catalog, they have chosen the Taco Model 4013 FI Series centrifugal pump with a 16.75-inch impeller. However, before making a purchase, they need to determine if the pump is suitable for their system. The pump they have chosen has a required net positive suction head (NPSHrequired) of 2.8 m. Additionally, the engineers need to raise the temperature to 70C as part of their process, and they want to use the same pump. The engineers' piping system involves pumping water from a large reservoir at a rate of 500 gpm through a 10.5- foot-long pipe with a 4-inch diameter and an average inner roughness of 0.02 in. The reservoir surface is 4.0 ft (Z) above the centerline of the pump inlet (Z2-0), g = 9.81 m/s. The system includes four sharp-edged inlets (r 0), four sharp-edged exits, three 45-degree standard elbows, and one 12-inch radius 90-degree bend. Point 1 represents the reservoir and point 2 represents the location after the pump inlet, with no pump in between. = For all calculations, assume a Reynolds number (Re) of 4.3x105 and a friction factor (f) of 0.0305. (For this question, the values for Re and fhave been provided to expedite the calculations, so there is no need for you to calculate them). For this system, find the required total head loss at 500 gpm flowrate 25 C. Regardless of part a result, if the required total head loss at 500 gpm flow rate is 7.5 m, estimate the pressure required at the pump inlet (NPSHAvailable) at 25 C. c) a) b) In a part of their process, they need to increase the temperature to 70 C, and they want to use the same pump. Estimate the pressure required at the pump inlet (NPSHAvailable). (use 500 gpm flow rate, assume the total headloss 7.5 m regardless of your finding in part a). Compare your findings in part b and c. In which condition (b or c) the selected pump can work without cavitation (assume the selected pump NPSHrequired is 2.8 m (9.18ft)? Explain. At water temperature 70 C, would NPSHrequired increase or decrease? d) e) For water at T= 25 C: p= 997 kg/m, = 8.91104 kg/m.s, pvapor pressure (patm) = 101.3 kPa = 3.169 kPa, atmospheric For water at T-70 C: p=983.3 kg/m, u=4.67x10 kg/m . S, Pvapor = 19940 N/m, atmospheric pressure (patm) = 101300 N/m.