Example Problem with Complete Solution

5D-1 : Charging a Water Tank 3 pts
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 :
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