Mixing Salt in Water in One Tank
Mixing Salt in Water in One Tank
This example comes from [1], Section 2.2, Modeling with First Order Equations.
The equation is
dQ(t)
dt
rQ(t)
100
r
4
where is time in minutes, is the amount of salt in the tank at time , is the rate of flow in and out of tank in gallons per minute. At time the tank contains pounds of salt in a tank containing 100 gallons of water. Assume that the tank is well stirred. In this example the mixture flowing into the tank contains 1/4 pound of salt per gallon, so one would expect that the tank will eventually contain 25 pounds of salt.
t
Q(t)
t
r=3
t=0
Q
0
Dragging the locator on the right changes the initial amount of salt found in the tank.
More than 1/4 pound of salt per gallon is colored dark orange or brown while less than 1/4 pound per gallon is colored dark green.