_______________________ Last Name, First CHE426: Problem set #81. Determine the open loop response of three ideal CSTRs in series when the inletconcentration of A, CA0, changes from 0.8 to 1.8 kmol/m3. The reaction is first order withreaction rate constant k = 0.5 s-1. The tank volume V is 0.10 m3 and the liquid flow rate F is0.05 m3/s. F F F F V V V CA0 CA1 CA2 CA3 Use Laplace transform to solve for the deviation concentration in each tank as a function oftime. Plot the deviation concentrations for three tanks for 0  t  4 s and use the Titlecommand to label the graph with your name.2. A liquid (SG = 1) is pumped through a heat exchanger and a control valve at a design rateof 200 gpm. The exchanger pressure drop is 30 psi at 200 gpm. Use Matlab to plot flow rateversus valve position x for linear and equal-percentage ( = 50) control valves. Both valvesare set at f(x) = 0.5 at design rate. The total pressure drop over the entire system (heatexchanger and control valve) is constant. Plot the results for 3 designed pressure drop overthe valve: 10 psi, 30, psi, and 120 psi. Plot all six curves in one graph and label the curvesproperly with the legend command. Use the title statement to label the graph with yourname.3.1 The overhead vapor from a depropanizer distillation column is totally condensed in awater-cooled condenser at 120oF and 227 psig. The vapor is 95 mol % propane and 5 mol %isobutene. The vapor design flow rate is 25,500 lb/h and average latent heat of vaporization is125 is 125 Btu/lb.Cooling water inlet and outlet temperatures are 80 and 105oF, respectively. Thecondenser heat transfer area is 1000 ft2. The cooling water pressure drop through thecondenser at design rate is 5 psi. A linear-trim control valve is installed in the cooling waterline. The pressure drop over the valve is 30 psi at design with the valve half open.The process pressure is measured by an electronic (4-20 mA) pressure transmitterwhose range is 100-300 psig. An analog electronic proportional controller with a gain of 3 isused to control process pressure by manipulating cooling water flow. The electronic signalfrom the controller (CO) is converted into a pneumatic signal in the I/P transducer.a) Calculate the cooling water flow rate (gpm) at design conditions. Water density is62.3 lb/ft3 and 1 ft3 = 7.48 gal.b) Calculate the size coefficient (Cv) of the control valve.c) Calculate the values of the signals PM, CO, SP, and PV at design conditions.d) Suppose the process pressure jumps 10 psi. How much will the cooling water flowrate increase? Determine values for PM, CO, SP, and PV at this higher pressure.Assume that the total pressure drop over the condenser and control valve is constantat 35 psi.FFH e a t i n p u t qTiTR e f l u x d r u mP TP CI / PP MS PC OP VC o n t r o l v a l v eC o o l i n gw a t e rC o n d e n s e rV a p o r4. Consider a well-mixed tank with a water steady flow rate F of 200 L/min. The volume ofwater in the tank is 1,000 L. The inlet water temperature is 60oC. The system is at steady statewith heat input sufficient to heat the outlet water temperature to 80oC. Suddenly the inlettemperature experiences a step change from 60oC to 70oC. The thermocouple measuring thetank temperature has a first order transfer function relating the measured temperature dmTtothe actual temperature Td(s) in the tank according to( )( )dmdT sT s = 10.33 1s +Determine the closed loop response of the tank temperature if the tank has a negative feed-back system with proportional gain KC = 20.a) Obtain an expression for Td(t) and plot the response from 0 to 20 minutes using Matlab with your name printed on the graph.b) Use simulink to obtain the response and compare with the results in part (a).5.2 Consider a manometer as illustrated below. The manometer is being used to determine thepressure difference between two instrument taps on an air line. The working fluid in themanometer is water. Determine the response of the manometer to a step change in pressureacross the legs of the manometer for the cases when the inside tube diameter are 0.10 cm,0.20 cm, and 0.35 cm. Data: manometer fluid length, L = 250 cm; g = 981 cm2/s;  = 0.0097 g/cms,  = 1.2 g/cm3.0 for < 010 cm for 0tPtgr�D=���a) Obtain the equation in time domain and plot the response using Matlab. Label thegraph with your name using the title command.b) Use simulink to obtain the response. Label the pressure step forcing function on thesimulink model with your name. Turn in the simulink model and the graph fromsimulink. Label the graph with your name. Reference levelhP1P2P = 01 P = 02 Initial Final6.2 A pneumatic PI temperature controller has an output pressure of 10 psig when the setpoint and process temperature coincide. The set point is suddenly increased by 10oF (i.e. astep change in error is introduced), and the following data are obtained:Time, s 0- 0+ 20 60 90psig 10 8 7 5 3.5Determine the actual gain (psig/oF) and the integral time.7.1 A circulating chilled-water system is used to cool an oil stream from 90 to 70oF in a tube-in-shell heat exchanger shown. The temperature of the chilled water entering the process heatexchanger is maintained constant at 50oF by pumping the chilled water through a cooler located upstream of the process heat exchanger. The design chilled-water for normal conditions is 600 gpm, with chilled water leaving the process heat exchanger at 65oF. Chilled-water pressure drop through the process heat exchanger is 15 psi at 800 gpm.Chilled-water pressure drop through the refrigerated cooler is 15 psi at 800 gpm. The temperature transmitter on the process oil stream leaving the heat exchanger has a range of 40-180oF. The range of the orifice-differential pressure flow transmitter on the chilled water is 0-1500 gpm. All instrumentation is electronic (4 to 20 mA). Assume the chilled-water pump is centrifugal with a flat pump curve (total pressure drop across the system is constant).The control valve has a linear trim with Cv = 128.81 gpm/psi0.5. The valve is 40 percent open at the 800 gpm design