"A tank initially contains 1000 kg of brine containing 10% salt by mass. An inlet stream of brine

containing 20% salt by mass flows into the tank at a rate of 20 kg/min. The mixture in the tank is

kept uniform by stirring. Brine is removed from the tank via an outlet pipe at a rate of 10 kg/min.

Find the amount of salt in the tank at any time t, and the elapsed time when the amount of salt in

the tank is 200 kg."

The solution to this equation is:

20 kg/min

Salt content

20% by mass

S =

-Tank, initial content 1000 kg

And by using the integral form of continuity equation for both brine and salt, and managed

to land on the following 1st order, non-homogeneous, linear differential equation for the

amount of salt (S, in kg) in the tank as a function of time (in minute):

ds S

+

dt

100 + t

(eq. 1)

4

Control volume

10 kg/min

C

2t (200 + t)

100 + t

(eq. 2)

100 + 100

And the constant of integration can be found as C = 10,000 if we use the initial condition

t = 0

(s = 100 kg

a) Beginning with eq. 1, and in a clear, step-by-step approach, show how we can achieve the

solution shown by eq. 2.

b) Plot both salt content (S) and brine content (B) as functions of time (t) on the same

diagram.