Cloth bag filters are used to remove particulate matter from the gases passing out through several process and boiler stacks in a large industrial plant. The bags become clogged and must be replaced frequently. Since they are quite expensive, rather than being discarded they are emptied washed, and reused. In the washing process, a detergent solution with a specific gravity of 0.96 flows from a storage tank to a washing machine. The liquid effluent from the machine is pumped through a filter to remove dirt, and the cleaned detergent is recycled back to the storage tank. Detergent flows from the storage tank to the washing machine by gravity feed at a rate of 600 L/min. All pipes in the line have 4.0-cm inner diameters. Friction losses are negligible in the line from the tank to the washing machine when the valve is fully opened, and P = 72 J/kg in the return line, which includes the pump and filter.

(a) Calculate the value of the height H (see figure) required to provide the desired flow rate of detergent to the washing machine when the valve is fully opened.

(b) Suppose the pump has an efficiency of 75%, that is, it delivers 75% of its rated value as shaft work. What must the rated value (kW) of the pump be to return 600 L/min of detergent to the storage tank?

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Makeup detergent Filter Pump Dirt Storage tank Bath H Dirty bags Clean bags