Water
flows into a tank from two different pipes, A
and B, and leaves the tank through pipe C. The volumetric flow rates in the pipes are 7.4,
3.9 and 8.1 L/min, respectively. |
|
|
|
|
|
|
|
|
|
|
|
If the tank is initially empty, how much time is required for 1500 kg of water
to accumulate in the tank? Assume the density of water is 985
kg/m3. |
|
|
|
|
|
|
|
|
Read : |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Diagram: |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Given: |
VA |
7.4 |
L/min |
|
|
|
minit |
0 |
kg |
|
|
|
VB |
3.9 |
L/min |
|
|
|
mfinal |
1500 |
kg |
|
|
|
VC |
8.1 |
L/min |
|
|
|
r |
985 |
kg/m3 |
|
|
|
|
|
|
|
|
|
|
0.985 |
kg/L |
|
|
Find: |
Δt |
??? |
hr |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Assumptions: |
1 - |
The density of the water is uniform and constant. |
|
|
|
|
2 - |
All of the volumetric flow rates are constant: uniform-flow process. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Equations
/ Data / Solve: |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
The key equation in the solution of
this problem is the Differential or Rate Mass Balance Equation., with constant inlet
and outlet mass flow rates. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Eqn 1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Applying Eqn 1 to this problem yields : |
|
Eqn 2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Eqn 2 is useful because we can determine the time required to accumulate mass, m, in the tank using the following equation. |
|
|
|
|
|
|
|
|
|
Eqn 3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Next, we need to
determine the mass flow rates
from the volumetric flow rates of the three streams. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Eqn 4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Now we can plug
numbers into Eqns 4, 2 and 3, in that order to solve the problem. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
mA |
7.289 |
|
|
|
|
Δmsys |
3.152 |
kg/min |
|
|
|
mB |
3.8415 |
|
|
|
|
|
|
|
|
|
|
mC |
7.9785 |
|
|
|
|
Δt |
475.9 |
min |
|
|
|
|
|
|
|
|
|
|
7.931 |
hr |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Verify: |
The assumptions made
in this solution cannot be verified with the given information. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Answers : |
Δt |
7.93 |
hr |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|