Mixing problem involving 3 inlets and 2 outlet pipes

[tin llenaresas]

help!
how do we solve a mixing problem involving 3 inlet pipes and 2 outlet pipes?is it okay to just add up the 3 rates of input as well as their respective concentrations?
all the sample problems i have encountered involves only 1 inlet and one outlet pipe..

 

[HallsofIvy]

You start by actually explaining the problem! You could have could have one pipe that goes back to the tank itself with two additional inlet pipes and one additional outlet or any variation on that.

Do you have a single tank with 3 pipes coming in and two pipes going out? If that is the case, then, yes, you can treat that as a single with the sum of the inputs. But be careful about how you sum that- you can't just add the concentrations. You have to sum the amount of "substance" that comes in every second. For example, if you have one pipe bringing in a solution at 3 L/s, with concentration 10 g/L of salt and a second pipe bringing in a solution at 5 L/s with concentration 5 g/L of salt, then the first pipe will bring in (3 L/m)(10 g/L)= 30 g/s and the second will bring in (5 L/s)(5 g/L)= 25 g/s. The two pipes will bring in a total of 30+25= 55 g/s. That's the information you need to set up your equation.

 

[tacman]

To solve a mixing problem involving 3 inlet pipes and 2 outlet pipes, you will need to use a system of equations to determine the flow rates and concentrations of each inlet and outlet. It is not sufficient to simply add up the rates and concentrations of the three inlets, as the flow rates and concentrations may vary at each inlet and outlet. You will need to take into account the flow rates and concentrations at each inlet and outlet, as well as the mixing that occurs within the system.

One approach to solving this type of problem is to set up a mass balance equation for each component (such as mass of water, salt, etc.) in the system. This will involve identifying the initial concentrations and flow rates at each inlet, as well as the concentrations and flow rates at the outlets. From there, you can use algebra to solve for the unknown concentrations and flow rates.

It is important to note that the number of inlets and outlets does not change the fundamental approach to solving the problem. You will still need to use a mass balance equation and consider the flow rates and concentrations at each inlet and outlet. The only difference is that you will have more variables to solve for in the system of equations.

If you are unsure of how to approach the problem or need further assistance, it may be helpful to consult a textbook or seek guidance from a teacher or tutor. Practice problems involving multiple inlets and outlets can also help you become more comfortable with solving these types of problems.