Designing a closed loop fluid system

[hydronicengr]

Homework Statement

I'm doing a project right now which deals with designing a closed loop recirculating system using water to cool multiple components. However, this post will only deal with the fluids portion.

Below is the diagram of a very simplified system. Note that the areas marked red are 90 degree fittings with a given k (loss coefficient) value. I am only given a supply pressure (P_supply) of 100 psi, the lengths of each of the sections (the lengths from dot to dot), the diameter of the pipes, the pipe material, and the temperature of the incoming fluid (water). The diameter of the pipes are all the same, so it's constant diameter. Also, assume that the system is on the same plane, so there is no height or elevation.

I am required to find:
- The pressure at P_return
- The volume flow rate (Q or V_dot)
- The k_component

Homework Equations

Bernoulli's Equation
Darcy Weisbach

The Attempt at a Solution

When I was given this project, it seemed somewhat confusing, so I asked for help from the project advisor. Unfortunately, he didn't give me a clear answer and he's unavailable for the next few days so I cannot ask him any questions for the time being. He just said that the volume flow rate does not have to be given and that there's a relation between pressure, flow, and headloss, and told me to read up on Hydraulic Grade Lines.

Also, he said to split the system up into sections, which are the areas between the red dots. This made me a bit confused because I was wondering how I would account for the 90degree bends so that I can add the loss coefficients, K, into the total head loss.

I have done many problems regarding finding pressure difference, total headloss, etc., but I am totally lost when it comes to finding these many unknowns. I am doing this analysis in Excel as well.

If any of you can give me some tips on how to find or solve this, please let me know.

Thanks!

 

[rude man]

The Bernoulli equation, based in part on conservation of energy, doen't allow for losses. You need to look at viscous flow (Reynolds number, etc.). This goes somewhat beyond the introductory physics level.

 

[hydronicengr]

Correct, I will add some more formulas to the original post.

 

[rude man]

I didn't see that you had mentioned Darcy-Weisbach. Sorry. That is one way to account for losses.

 

[DeeNos]

I would first recommend reviewing the fundamental principles of fluid mechanics, including Bernoulli's equation and Darcy Weisbach equation. These equations can provide valuable insights into the behavior of fluids in closed loop systems.

Next, I would suggest breaking down the system into smaller sections and analyzing each section separately. This will help you better understand the effects of each component, including the 90 degree fittings, on the overall system. Additionally, it may be helpful to create a diagram or flowchart to visualize the system and the flow of water through it.

In order to account for the 90 degree bends, you can use the loss coefficient (K) values provided. These values represent the additional head loss caused by the bends and can be added to the total head loss in each section.

Furthermore, understanding the relationship between pressure, flow, and head loss is crucial in solving this problem. As your project advisor mentioned, hydraulic grade lines can be helpful in understanding this relationship. They represent the total head at any point in the system and can help you determine the pressure at P_return.

Lastly, I would recommend utilizing available resources, such as textbooks or online resources, to further your understanding of fluid mechanics and closed loop systems. With a solid understanding of the fundamental principles and a thorough analysis of the system, you should be able to find a solution to your problem.