Find the quantity Q(t) of salt in the tank?

  • Thread starter Math10
  • Start date
  • #1
301
0

Homework Statement


A tank initially contains 40 gallons of pure water. A solution with 1 gram of salt per gallon of water is added to the tank at 3 gal/min, and the resulting solution dranes out at the same rate. Find the quantity Q(t) of salt in the tank at time t>0.

Homework Equations


None.

The Attempt at a Solution


I don't know how to set up the differential equation for this problem.
 

Answers and Replies

  • #2
20,844
4,543
Let V be the volume of liquid in the tank in gal, q be the rate at which liquid is entering (and leaving) the tank in gal/min, and C(t) be the concentration of salt within the tank in gm/gal at time t. Based on this, at time t, how much salt is in the tank? If the tank is well mixed, what is the rate that salt is leaving the tank? What is the rate that salt is entering the tank? Write a balance of input - output = rate of accumulation.

Chet
 

Related Threads on Find the quantity Q(t) of salt in the tank?

Replies
6
Views
3K
  • Last Post
Replies
0
Views
925
Replies
3
Views
2K
Replies
3
Views
152
  • Last Post
Replies
3
Views
12K
Replies
1
Views
443
  • Last Post
Replies
1
Views
7K
  • Last Post
Replies
3
Views
24K
Replies
3
Views
2K
Top