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Unformatted text preview: Homework #4 ChE 361 Spring 2010 Problem 1. Consider a plug ﬂow reactor in which the following series reaction occurs: A → B → C. The reaction rates per unit volume of the ﬁrst and second reactions are r1 = k1 CA and r2 = k2 CB , respectively, where k1 = k2 . The reactor has constant volumetric ﬂow rate q and pure component A feed at concentration CAi . The cross-sectional area of the reactor is A. The variable z is the axial distance along the reactor, with z = 0 denoting the reactor entrance. 1. Derive the following model equations by writing the appropriate diﬀerential mass balances: q dCA (z ) + k1 CA (z ) = 0, A dz q dCB (z ) + k2 CB (z ) − k1 CA (z ) = 0, A dz 2. Solve the two diﬀerential equations to obtain CB (z ). 3. Use the initial condition to determine the constant of integration. 4. Determine the value z at which CB (z ) reaches a maximum. CA (0) = CAi CB (0) = 0 Problem 2. Consider a constant volume, continuous stirred tank in which two feed streams of diﬀerent binary compositions are mixed. The ﬁrst feed stream has mass ﬂow rate w1 and mass fraction x1 , and the second feed stream has mass ﬂow rate w2 and mass fraction x2 . The outlet stream has mass ﬂow rate w and mass fraction x. Assume that liquid density ρ and volume V are constant. The parameter values are: w1 = 1 kg/min, x1 = 0.8, w2 = 3 kg/min, x1 = 0.4, ρV = 2 kg. 1. Derive the following model equation by writing the necessary material balances: 1 dx = [w1 (x1 − x) + w2 (x2 − x)] dt ρV 2. Find the steady-state outlet mass fraction x. ¯ 3. Deﬁne a new variable x (t) = x(t) − x. Using the given parameters, show that the ODE in ¯ part 1 can be rewritten in terms of this new variable as: dx = −2x dt 1 4. Solve the diﬀerential equation in part 3 for x (t). Given the initial condition x(0) = 0.4, ﬁnd the solution x(t). Graph the solution in Matlab. Problem 3. Problem Set 1.3, Problem 26 Problem 4. Chapter 4 Review Questions, Problem 26 2 ...
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- Spring '10