Determine the Service and Backwash Rates

The system on site is a pressure sand filter, with a service curve. The filter is backwashed using the feed pump, at a higher flow rate, shown as backwash curve.

Service duty point: 3 m3/h

Backwash duty point: 9 m3/h

Part (a)

What is the speed of the pump to achieve the service and backwash flow rates ?

Part (b)

What would be the best way to control the speed of the pump ? Why ?

Part (C)

The pump is set up as a fixed speed constant pressure system (pump runs once system pressure reaches 550 kPa, turns off, when pressure drops to 450 kPa plant re-starts) to maintain a system pressure of 500 kPa at the discharge of the pump. What would be the service and backwash rates from the pump ?