As shown in Figure Q5, a chilled water loop employs two separate pump loops for chiller and building system. Constant speed pumps are used for primary loop and variable speed pumps for the secondary chilled water loops. The regulating valve is used in commissioning to balance the chilled water loop. The modulating valves are used to control the loads of individual coils. The speed of the secondary loop is controlled to maintain the differential pressure at a proper level. The design chilled water flow rate of three zones is 25 L/s each. The pressure drop on each coil at design flow is 50 kPa. Same modulating valve is to be used for all zones. The flow coefficient of valve is 80. (Assuming the flow resistance of each pieces of pipelines is the same: X=0.001875kPaxs1-). Coil Coil Coil Differential Pressure Modulating valve Regulating valve Flow resistance of pipeline Chiller Zone 3 Zone 2 Zone 1 Figure Q5 Controller 5-a) Derive the optimal pressure set-point if fixed set-point will be used in operation. 5-b) Derive the pressure drop on the regulating valves at design condition the system is properly commissioned. 5-c) If the regulation valves are commissioned to allow both zone 1 and 2 have design water flow rate when regulating valves are fully open, check if the regulating valves are well sized.