1.      In the system shown schematically below, water is supplied to a spray nozzle by a gear pump with a constant output of 20 US gpm. The flow rate of water discharged through the nozzle is controlled by manipulating the flow of water re-circulated around the pump using a proportional-plus-integral controller. The set point of the controller is normally 14 US gpm but can vary between 9 and 18 US gpm. The flow sensor has a range of 0-20 US gpm and responds instantaneously to flow variations. The control valve has a C_V of 3 US gpm/psi^1/2, a time constant of 2 seconds, a linear installed characteristic and is current-to-close.

(a) What should be the action of She controller (reverse or direct)? Why?

(b) Would it be better to eliminate the recirculation loop and install the control valve immediately downstream of the pump? Why?

(c) If the pump discharge pressure is 100 psig when the control valve is closed, show that the flow rate across the nozzle is 8 US gpm when the control valve is wide open,

Notes: The valve and nozzle are the only significant flow resistances in this system. You may also assume that the pump suction port and the spray leaving the nozzle are at atmospheric pressure. The nozzle behaves as an orifice.

(d) What are the outputs of the controller and flow transmitter (in %) when the set point is 12 US gpm and steady-state has been achieved?