Example 1 A 1500 gallon tank initially contains 600 gallons of water with 5 lbs of salt dissolved in it. Waterenters the tank at a rate of 9 gal/hr and the water entering the tank has a salt concentration of (1+cos (t))lbs/gal. If a well mixed solution leaves the tank at a rate of 6 gal/hr, how much salt is in the tank when itoverflows?

Answered: Image /qna-images/answer/c801be5d-9582-42aa-9db1-2964fa18c5ff.jpg

Answered: Example 1 A 1500 gallon tank initially…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: The vat contains 230 gallons of liquid, which never changes. Sugar water with a concentration of 7 tablespoons/gallon flows through pipe A into the vat at the rate of 5 gallons/minute. • Sugar water with a concentration of 3 tablespoons/gallon flows through pipe B into the vat at the rate of 25 gallons/minute. The liquid in the vat is kept well-mixed. • Sugar water leaves the vat through pipe C at the rate of 30 gallons/minute. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (A) Write the DE model for the time rate of change of sugar in the vat: dS dt (B) Solve the differential equation to find the amount of sugar in the vat as a function of time. Your function will have an arbitrary constant K in it. Assume that K > 0. S(t) = (C) Suppose that there are 22 tablespoons of sugar in the vat at t = 0. How many tablespoons…
Please help me answer the first three questions. Thank you!
A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1/2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 35 minutes. (Round your answer to two decimal places.)
2. A large tank initially contains 100 gallons of brine in which 10 lb of salt is dissolved. Starting at t = 0, pure water flows into the tank at the rate of 5 gal/min. The mixture is kept uniform by stirring, and the well-stirred mixture simultaneously flows out at the slower rate of 2 gal/min. a) How much salt is in that tank at the end of 15 min and what is the concentration at that time? b) If the capacity of the tank is 250 gallons, what is the concentration at the instant the tank overflows?

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