This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 crosssectional 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 steadystate 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 ...
View Full
Document
 Spring '10
 HENSON

Click to edit the document details