A 1,000-gallon tank contains 200 gal of pure water. A brine solution containing .I lb of salt

Question:

A 1,000-gallon tank contains 200 gal of pure water. A brine solution containing .I lb of salt per gal is flowing into the tank at a rate of 4 gal / sec, and the well-stirred mixture is leaving the tank at the same rate. Let x denote the amount of salt in the tank at time t.
(a) Set u p (but d o not solve) the initial-value problem (both DE and initial condition).
A 1,000-gallon tank contains 200 gal of pure water. A

(b) Suppose that this situation continues for a very long time. What is the equilibrium solution xeq?
(c) After the solution has reached equilibrium, an additional faucet is turned on that supplies brine containing 2 lb/gal at a rate of 2 gal / sec. set up the new initial-value problem, assuming that the clock is restarted when the new faucet is turned on.

A 1,000-gallon tank contains 200 gal of pure water. A

(d) How long tf does it take for the tank to fill completely after the second faucet is turned on?
(e) How much salt is in the tank when t = tf?
(f) Set up the IVP for the amount of salt in the tank for t > tf, assuming that the tank overflows.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Differential Equations and Linear Algebra

ISBN: 978-0131860612

2nd edition

Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West

Question Posted: