ok here is a mixing problem that i tried to do, it seems pretty straight forward. Could someone take a look and let me know where i went wrong? thanks in advance...
Suppose that a large mixing tank initailly holds 500 liters of water, in which 20 kg of salt have been dissolved. another brine solution containing 1 kg/liter is pumped into the tank at a rate of 3 liters/min and the solution is well stirred. solution is then pumped out of the tank at a rate of 4 liters/min. I am supposed to write a differential equation for the amount of salt in the tank at a particular time.
so V(water in tank) = 500 liters
Initial mass(salt) = 20 kg
rate of brine in = 1 kg/liter @ 3 liters/min
rate of brine out = A kg/liters @ 4 liters/min
dA/dt = rate in - rate out
so dA/dt = [(1 kg/liters) (3 liters/min)] - [(A kg/500 liters) (4 liters/min)]
so dA/dt = (375-A)/125 ; A(0)= 20 kg.
it seemed really straight forward....