2
Two constant flow rate of salty water streams are feeding to a tank, as shown in the
illustration below. Initially, the tank is filled with fresh water with no salt concentration CT = 0, at
t s 0. At time t =0 two constant equal volumetric flow rates of salty water influent, F, = F2 = Fi,
with concentrations C, and C2 start flowing into the tank. The constant liquid volume in the tank
is maintained at V by a constant effluent flow rate, Fe=2Fi, from the bottom of the tank. The
liquid in the tank is well mixed; therefore, a uniform (but not constant) concentration of salt is
maintained throughout the volume of the tank, CT = Ce.
a) Develop a mathematical model to predict the concentration of salt in the stream leaving the
tank as a function of time. Using your mathematical model, predict the final concentration in
the tank when it reaches a constant final value.
b) Make a Graph [ C. vs. time t ] - assume practical and realistic values for C1, C2, Fi, and V-
which will show Ce as a function of time.
c) Develop an algebraic expression that would allow you to calculate how long it would take
for salt concentration in the tank to reach 50% of the final concentration -using assumed
values for C1, C2, Fi, and V in part b.
Illustration
At t = 0 CT= 0
C1 , F1
C2, F2
CT, V
Ce, Fe
List of Variables:
F1
Volumetric flow rate of water entering the tank from pipe 1 [m3/s]
F2
Fe
Volumetric flow rate of water entering the tank from pipe 2 [m3/s]
Volumetric flow rate of the effluent water
[m /s]
time
V
[s]
volume of liquid in the tank
[m ]
C1
C2
salt concentration entering the tank from pipe 1
[kg/m3]
[kg/m3]
CT
salt concentration entering the tank from pipe 2
Ce
salt concentration in the tank at any time t
[kg/m3]
salt concentration in the effluent
[kg/m']
Assumptions
Mathematical Model
Solution of the Model
Discussion