_______________________ Last Name, First CHE426: Problem set #41. An engineer has designed a system in which a positive-displacement pump is used topump water from an atmosphere tank into a pressurized tank operating at 150 psig. A controlvalve is installed between the pump discharge and the pressurized tank.With the pump running at a constant speed and stroke length, 350 gpm of water ispumped when the control valve is wide open and the pump discharge pressure is 200 psig.If the control valve is pinched back to 60 percent open, determine(a) the water flow rate 350 gpm(b) If the pump reduces speed so that the water flow rate is 250 gpm at 60 percent valveopen, determine the pump discharge pressure220.9 psig2. A 2 L glass jar is half filled with water and half filled with air at a temperature of293oK. After 92 mg (=10-3 mol, mw = 92) of liquid toluene is added, the jar is sealed. At293oK, the Henry’s law constant for toluene is KH,g = 0.15 [Matm-1]. Note: M= mol/L,gas constant = 82.0510-3 Latm/molKC L i q u i d w a t e rtP tA i rDetermine the equilibrium partial pressure (atm) of toluene in the gas phase and theequilibrium concentration (M) of toluene in the water.SolutionPt = 5.2310-3 atmCt = 7.8610-4 M3.2 We want to design a control valve for admitting cooling water to a cooling coil in anexothermic chemical reactor. The normal flow rate is 60 gpm and the minimum flow rate is25 gpm. To prevent reactor runaways, the valve must be able to provide three times thedesign flow rate. The pressure drop through the cooling coil is 5 psi at the design flow rate of60 gpm. The cooling water is pumped from an atmospheric tank. The water leaving the coilrun into a pipe in which the pressure is constant at 2 psig. Size the control valve and thepump.SolutionCv = 26.12 gpm/psi0.5 and PT = 92.5 psig. The pump head is then PP = PT +2 = 94.5 psi.4.2 A process for transferring oil from a storage tank to a separation tower is shown in FigureP-5b. The tank is at atmospheric pressure, and the tower works at 12.7 psia. Nominal oil flowis 1000 gpm, its specific gravity is 0.90, and its vapor pressure at the flowing temperature of90oF is 14.85 psia. The pipe is 8-in. Schedule 40 commercial steel pipe, and the pumpefficiency is 80%. Size a valve to control the flow of oil if the frictional pressure drop in theline is found to be 6 psi. Use a pressure drop of 10 psi across the valve and estimate theannual cost if the electricity price is $0.20/kW-hr and the pump operates 8200 hr per year.N o m i n a l T r i m s i z e1 / 4 3 / 8 ½ 3 / 4 1 1 . 5 2 3 4 6 8 1 0O r i f i c e D i a . ( i n . ). 2 5 0 . 3 7 5. 5 0 0. 7 5 0 . 8 1 2 1 . 2 5 0 1 . 6 2 5 2 . 6 2 5 3 . 5 0 0 5 . 0 0 0 6 . 2 5 0 8 . 0 0 0V a l v e s i z e ( i n . )R e d u c e d T r i m F u l l C a p a c i t y T r i m3 / 411 ½234681 01 . 7 3 . 7 6 . 4 1 11 . 71 . 71 . 73 . 7 6 . 4 1 1 1 23 . 8 6 . 6 1 2 1 3 2 53 . 8 6 . 7 1 3 1 9 2 6 4 61 4 3 1 4 7 1 1 03 2 4 9 1 1 3 1 9 55 3 1 2 6 2 0 8 4 0 01 3 3 2 2 4 4 1 5 6 4 02 3 3 4 4 2 6 4 8 1 0 0 0Figure P-5a Flow coefficient for Masoneilan’s valve Schedule 40.C r u d e t a n kP = 1 a t m8 f t4 f t6 4 f tS e p a r a t i o n t o w e rP = 1 2 . 7 p s i aP u m pFigure P-5b An oil transferring systemSolution ------------------------------------------------------------------------------------------$ 8,918/year5.2 A 4-in Masoneilan valve with Cf = 0.9 and full trim has a capacity factor of 195 gpm/psi1/2when fully opened. The pressure drop across the valve is 10 psi.(a) Calculate the flow of a liquid solution with density 0.8 g/cm3.(b) Calculate the flow of gas with average molecular weight of 35 when the valve inletconditions are 100 psig and 100oF.(c) Calculate the flow of the gas from part (b) when the inlet pressure is 5 psig. Calculate theflow both in volumetric and in mass rate units, and compare the results for a 4-in. FisherControls valve (Cv = 183, Cg = 6650, C1 = 36.3).Solution(a) Calculate the flow of a liquid solution with density 0.8 g/cm 3 .˙m= (689.4 gpm)(60 min/hr)(8.330.8 lb/gal) = 275,660 lb/hr(b) Calculate the flow of gas with average molecular weight of 35 when the valve inletconditions are 100 psig and 100 o F.Qscfh = 836(195)(0.9)114. 7√(35 /29)(560 )(0.512) = 331,400 scfhThe mass flow rate is determined from˙m = 2.8(195)(0.9)(114.7)√(3529)520560(0.512) = 30,550 lb/hr(c) Calculate the flow of the gas from part (b) when the inlet pressure is 5 psig. Calculate theflow both in volumetric and in mass rate units, and compare the results for a 4-in. FisherControls valve (Cv = 183, Cg = 6650, C1 = 36.3).Qscfh = 836(195)(0.9)19 .7√(35 /29)(560 )(0.972) = 108,100 scfh˙m = 2.8(195)(0.9)(19.7)√(3529)520560(0.972) = 9,965 lb/hrUsing formulas from Fisher Controls we haveQscfh = 6650√520(35 /29)(560 )(19.7) sin59.64 1036.3 19.7rad� �� �� �= 105,800 scfh ˙m = 1.06(6650)√(0 .115)(19 . 7)sin59.64 1036.3 19.7rad� �� �� �= 9,761 lb/hr6. A control valve is to regulate the flow of steam into a heat exchanger with a design heattransfer rate of 10 million Btu/hr. The supply steam is saturated at 20 psig. Size the controlvalve for a pressure drop of 10 psi and 100% overcapacity. Assume a Masoneilan valve withCf = 0.8.Solution ------------------------------------------------------------------------------------------From Figure 3.5-3, a 8-in. Masoneilan valve, with a coefficient of 640, is the smallest valvethat can provide the service. 7. The temperature of a CSTR is controlled by an electronic (4 to 20 mA) feedback controlsystem containing (1) a 100 to 260oF temperature transmitter, (2) a PI controller with integraltime set at 2 minutes and proportional band at 25, and (3) a control valve with linear trim, air-to-open action, and Cv = 10 gpm/psi0.5 through which cooling water flows. The pressure dropacross the valve is a constant 25 psi. If the steady state controller output is 12 mA, how muchcooling water is going through the valve? If a sudden disturbance increases reactortemperature by 10oF, what will be the immediate effect on the controller output signal and thewater flow rate?Solution ------------------------------------------------------------------------------------------(a) If the steady state controller output