A 30-gallon tank initially contains 15 gallons of salt water containing 3 pounds of salt. Suppose salt water containing 1 pound of salt per gallon is pumped into the top of the tank at the rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. How much salt is in the tank when the tank is full?
A 30-gallon tank initially contains 15 gallons of salt water containing 3 pounds of salt. Suppose salt water containing 1 pound of salt per gallon is pumped into the top of the tank at the rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. How much salt is in the tank when the tank is full?
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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Transcribed Image Text:A 30-gallon tank initially contains 15 gallons of salt water containing 3 pounds of salt. Suppose salt water
containing 1 pound of salt per gallon is pumped into the top of the tank at the rate of 2 gallons per minute,
while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. How much salt
is in the tank when the tank is full?
Expert Solution
Step 1
Given that
The salt flux into the tank is always C_in * f_in, where C_in is the concentration of salt in the stream entering the tank, and f_in is the solution's flow rate. In this case:
The flux of salt in
The flux of salt out of the tank is given by
Where C(t) = N(t)/V(t) is the concentration of salt in the tank at time t.
V(t) is the volume of solution in the tank, and f_out is the flow rate of solution exiting the tank.
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