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/m^{3}. 








Read : 















Diagram: 















Given: 
V_{A} 
7.4 
L/min 



m_{init} 
0 
kg 



V_{B} 
3.9 
L/min 



m_{final} 
1500 
kg 



V_{C} 
8.1 
L/min 



r 
985 
kg/m^{3} 










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: uniformflow 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. 















m_{A} 
7.289 




Δm_{sys} 
3.152 
kg/min 



m_{B} 
3.8415 










m_{C} 
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 



















































































































