_______________________ Last Name, First CHE426: Problem set #101. Liquid (SG = 1) is pumped from a tank at atmosphere pressure through a heat exchangerand a control valve with linear trim into a process vessel held at 100 psig pressure. Thesystem is designed for a maximum flow rate of 400 gpm. At this maximum flow rate thepressure drop across the heat exchanger is 50 psi.A centrifugal pump is used with a performance curve that can be approximated by therelationship.Pp = 198.33  1.45810-4F2where Pp = pump head in psi and F = flow rate in gpm(a) Calculate the fraction that the control valve is open when the throughput is reduced to200 gpm by pinching down on the control valve.(b) An orifice-plate/differential pressure transmitter is used for flow measurement. If themaximum full-scale flow reading is 400 gpm, what will the output signal from theelectronic flow transmitter be when the flow rate is reduced to 150 gpm?2.1 A circulating chilled-water system is used to cool an oil stream from 90 to 70oF in a tube-in-shell heat exchanger shown in Figure 1. The temperature of the chilled water entering theprocess heat exchanger is maintained constant at 50oF by pumping the chilled water througha cooler located upstream of the process heat exchanger.The design chilled-water for normal conditions is 1000 gpm, with chilled waterleaving the process heat exchanger at 60oF. Chilled-water pressure drop through the processheat exchanger is 15 psi at 1000 gpm. Chilled-water pressure drop through the refrigeratedcooler is 15 psi at 1000 gpm.The temperature transmitter on the process oil stream leaving the heat exchanger hasa range of 40-200oF. The range of the orifice-differential pressure flow transmitter on thechilled water is 0-2000 gpm. All instrumentation is electronic (4 to 20 mA). Assume thechilled-water pump is centrifugal with a flat pump curve (total pressure drop across thesystem is constant).T TT CF TE l e v a t i o n 0 'E l e v a t i o n 1 5 'E l e v a t i o n 2 0 'T a n k a t a t m o s p h e r i cp r e s s u r eC i r c u l a t i n g c h i l l e d w a t e rH e a te x c h a n g e rC o o l e r9 0 FoH o t o i lC o o l e d o i l 7 0 FoR e f r i g e r a n t5 0 FoFigure 1 A circulating chilled-water systema) Assuming linear trim determine Cv for the chilled-water control valve that is 40percent open at the 1000 gpm design rate and has a maximum flow of 2000 gpm.b) If Cv = 200 gpm/psi0.5, determine the total pressure drop through the system.c) Determine the value of the signal from the temperature transmitter.d) Determine the value of the signal from the flow transmitter.e) If Cv = 200 gpm/psi0.5 and the total pressure drop through the system is 186.25 psi,determine the fraction open of the chilled-water control valve when the chilled-waterflow rate is reduced to 500 gpm.3. Consider the following control system with U(s) = 1/s, Kc = 2 and D = 1.a) Determine C(t = 1.25) b) Determine the offset.4. Determine the offset for the following control system with U(s) = 4/s, Kc = 25. Determine the ultimate gain and the ultimate frequency for the following control system6.R1R2A1A2h1h2Q2iQ1iFCFTSPLTLCQThe two tanks system shown above is initially at steady state with q1i = 8 cfm and q2i = 4cfm. The following data apply to the tanks: A1 = 1 ft2, A2 = 1.25 ft2, R1 = 2 ft/cfm, and R2 =0.8 ft/cfm. a) Determine open loop steady state gain for h1 when the flow q2i is increased from 4 to 6cfm.b) Determine closed loop steady state gain for h1 when the flow q2i is increased from 4 to 6cfm.References1. Process Modeling, Simulation, and Control for Chemical Engineers by Luyben2. D.R. Coughanowr and S. LeBlanc, Process Systems Analysis and Control, McGraw-Hill, 3nd edition,