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che132a-hw-3 - m/min for 2 minutes and then the pouring...

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ChE132a: Analytical Methods of Chemical Engineering Professor Mike Gordon, Fall 2011 Homework #3: Due Wed., 26 Oct. 2011 (1) PGA p. 160-161 #2, 4 (work the integrals by hand); 15, 17, 22, 24, 27, 31, 45, 48 (2) Solve the following ODEs using Laplace transforms by finding Y(s) by hand. Use Mathematica to split Y(s) into partial fractions using the Apart[] command (or do it by hand to practice for the Midterm). Invert your result using the Laplace transform table on p. 198-199. Attach your code. (i) ) 2 cos( 2 4 t y y = with 0 ) 0 ( = y and 0 ) 0 ( ' = y (ii) 12 6 5 = y y y with 0 ) 0 ( = y and 10 ) 0 ( ' = y 3) [Counts double] Two tanks are connected by pipes as shown below: Tank #1 initially contains 11 lb m of salt dissolved in 60 gal of water; tank #2 initially contains 7 lb m of salt dissolved in 18 gal of water. The 2 gpm (gallons per minute) feed stream to tank #1 has a salt concentration of (1/6th) lb m /gal. At time t=0, the whole system is energized with the flowrates specified; four minutes later, salt is poured into tank #2 at a rate of 10 lb
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Unformatted text preview: m /min for 2 minutes and then the pouring stops. Assume that each tank is perfectly mixed. OVER a) How can you express the salt pouring process as a function of time? Think about the “pulse” function we used in class. b) Set up mass balances for each tank and find the salt concentration in each tank for all times using Laplace transforms and Mathematica. Define the amount of salt in tank #1 as x(t) and tank #2 as y(t). Attach your Mathematica work and highlight x(t) and y(t) on your printout. c) Plot x(t) and y(t) for the time domain [0, 200] minutes. d) How long does it take for the tanks to reach steady-state (just estimate it from your plots)? e) What is the salt concentration at steady state in each tank? f) Comment on how Laplace transforms might be useful in a chemical plant....
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