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