Consider the two interconnected tanks shown in the following figure. 2 gal/min 0.5 gal/min 1 oz/gal 3 oz/gal 4 gal/min Q,(1) oz salt Q,4) oz salt 40 gal water 20 gal water 2 gal/min Tank 1 Tank 2 2.5 gal/min Tank 1 initially contains 40 gal of water and 25 oz of salt, and Tank 2 initially contains 20 gal of water and 15 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 2 gal/min. The mixture flows from Tank 1 to Tank 2 at a rate of 4 gal/min. Water containing 3 oz/gal of salt also flows into Tank 2 at a rate of 0.5 gal/min (from the outside). The mixture drains from Tank 2 at a rate of 4.5 gal/min, of which some flows back into Tank 1 at a rate of 2 gal/min, while the remainder leaves the system. (a) Let Q,(t) and Q,(t), respectively, be the amount of salt in each tank at time t. Write down differential equations and initial conditions that model the flow process. Observe that the system of differential equations is nonhomogeneous. (Use Q1 and Q2 for Q1(t) and Q2(t), respectively.) oz/min, Q1(0) = oz of salt dt dQ oz/min, Q2(0) = oz of salt dt (b) Find the values of Q, and Q, for which the system is in equilibrium, that is, does not change with time. Let Q,E and Q,E be the equilibrium values. oz of salt oz of salt Q2E = (c) Let x1 = Q1(t) – Q,5 and x2 = Q2(t) – Q25. Determine an initial value problem for x1 and x2. Observe that the system of equations for x1 and x2 is homogeneous. (Enter you answer in terms of x1 and x2.) dx1 X1(0) = dt dx2 X2(0) = dt

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....