3. A large tank with the capacity of 500 gallons is fully filled with pure water. Brine containing 2 pounds of salt per gallons is pumped into the tank at a rate of 5 gal/min. Find the amount A(t) pounds of salt in the tank at timer minutes, if the well-mixed solution is pumped out (a) with the same rate as the entering one; and (b) with the rate of 10 gal/min. In case (a), how much salt is in the tank after a long time? In case (b), what is the concentration of the solution in the tank by the time it is empty? (c) Let everything be the same except that, initially, the tank is filled with 250 gallons of pure water, while the well-stirred solution is pumped out with the flow rate of 2.5 gal/min. Find (t). What is the concentration of the solution in the tank by the time it is fully filled? Hint: minutes is V(t)=500 gallons (a) The volume of the solution in the tank at time (b) The volume of the solution in the tank at time minutes is V(t) = 500-5r gallons (c) The volume of the solution in the tank at time ſ minutes is V(t) = 250+ gallons Answer: (a) A(z)-1000-1000e after a long time it is 1000 lbs. (b) 4()-1000-10-- (c) A(r) = 5(100+) (100-): the concentration by the time it is empty is 2 lb/gal. the concentration by the time it is fully filled is 1.5 lb/gal. 10 5x10¹ 100+7
3. A large tank with the capacity of 500 gallons is fully filled with pure water. Brine containing 2 pounds of salt per gallons is pumped into the tank at a rate of 5 gal/min. Find the amount A(t) pounds of salt in the tank at timer minutes, if the well-mixed solution is pumped out (a) with the same rate as the entering one; and (b) with the rate of 10 gal/min. In case (a), how much salt is in the tank after a long time? In case (b), what is the concentration of the solution in the tank by the time it is empty? (c) Let everything be the same except that, initially, the tank is filled with 250 gallons of pure water, while the well-stirred solution is pumped out with the flow rate of 2.5 gal/min. Find (t). What is the concentration of the solution in the tank by the time it is fully filled? Hint: minutes is V(t)=500 gallons (a) The volume of the solution in the tank at time (b) The volume of the solution in the tank at time minutes is V(t) = 500-5r gallons (c) The volume of the solution in the tank at time ſ minutes is V(t) = 250+ gallons Answer: (a) A(z)-1000-1000e after a long time it is 1000 lbs. (b) 4()-1000-10-- (c) A(r) = 5(100+) (100-): the concentration by the time it is empty is 2 lb/gal. the concentration by the time it is fully filled is 1.5 lb/gal. 10 5x10¹ 100+7
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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Question
Transcribed Image Text:3. A large tank with the capacity of 500 gallons is fully filled with pure water. Brine containing 2
pounds of salt per gallons is pumped into the tank at a rate of 5 gal/min. Find the amount
A(t) pounds of salt in the tank at timer minutes, if the well-mixed solution is pumped out
(a) with the same rate as the entering one; and
(b) with the rate of 10 gal/min.
In case (a), how much salt is in the tank after a long time? In case (b), what is the
concentration of the solution in the tank by the time it is empty?
(c) Let everything be the same except that, initially, the tank is filled with 250 gallons of pure
water, while the well-stirred solution is pumped out with the flow rate of 2.5 gal/min. Find
(t). What is the concentration of the solution in the tank by the time it is fully filled?
Hint:
(a) The volume of the solution in the tank at time
(b) The volume of the solution in the tank at time
minutes is V(t)= 500 gallons
minutes is V(t)=500-5r gallons
(c) The volume of the solution in the tank at time
1
minutes is V(t) = 250+ gallons
Answer:
(a) A(z)-1000-1000e after a long time it is 1000 lbs.
(b) 4()-1000-10-
(c) A(r) = 5(100+)
(100-): the concentration by the time it is empty is 2 lb/gal.
the concentration by the time it is fully filled is 1.5 lb/gal.
10
5x10
100+7
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