Solving Basic Thermo Questions: Calculating Velocity and Area in an Open System

[rjenkins]

I have question (probably figured that). I have an open system with mass flow rate going into one inlet and going through two outlets. I have all the terms for the two outlets (mass flow, velocity, area, temp, pressure). However for the inlet I'm missing the Velocity and Area.

In solving for the Velocity I figured I could you use the following equation

0 = h1 – h2 + (V1^2– V2^2)/2

But being I have two outlets in this case can I just plug in a 3rd term?

0 = h1 – h2 – h3 + (V1^2– V2^2 – V3^2)/3

 

[Nate810]

So for the inlet velocity I get:V3^2 = 3(h1 – h2 – h3) + (V1^2– V2^2) And then for the area:A3 = M3/(V3*ρ3) Where M3 is the mass flow rate of the inlet and ρ3 is the density of the inlet. Is this the correct approach? Yes, this is the correct approach. To calculate the velocity of the inlet, you can use the equation given above. And for the area, you can use the equation you provided.

 

[kyle8921]

Yes, you can definitely use a third term in the equation to account for the additional outlet. The equation you are using is known as the Bernoulli's equation, which is commonly used to calculate the velocity of a fluid in an open system. In this case, you are solving for the velocity at the inlet, so you will need to include all the relevant terms for the inlet and the two outlets.

However, it is important to note that this equation assumes that the fluid is incompressible and there is no energy loss in the system. So, it may not give you an accurate result if these assumptions do not hold true in your system. It is always a good practice to check the validity of the assumptions before using any equation.

Additionally, you will also need to consider the continuity equation, which states that the mass flow rate at the inlet must be equal to the sum of the mass flow rates at the outlets. This will help you in solving for the missing area at the inlet.

Overall, it is important to carefully consider all the relevant equations and assumptions before solving thermo questions in an open system. I would also recommend double-checking your calculations and units to ensure an accurate result.