Fluids design problem - piping layout

[dr3wsum1]

Homework Statement

The picture is what the prof. gave us. It isn't the most understandable but I will try my best to describe what's going on.
As the picture shows it is a top view of the layout. The big blob on the left is a large reservoir where elevation is not needed. v, v1, v2, v3 are all valves. The piping splits off into three houses (this is where the picture is confusing). At the end of the pipe near the valve, it bends 90° up to the top of the house where it empties and I'm going to assume the valves are at the top.

1) We are to design the pump power and D1, D2, and D3 while all valves are open.

2) For the designed system, what would be:
- Q1 if v2 and v3 are closed?
- Q2 if v1 and v3 are closed?
- Q3 if v1 and v2 are closed?

Givens:
Q=4.5 [m^3/hr] This is not the flow rate in the feed pipe
diameter of feed pipe is .2 [m]
I chose commercial steel as my material so ε=.046 [mm]
We are to make assumptions for minor losses.

Homework Equations

He gave us an equation to use for the pump power. Power=Q(p2-p1) where p2 is the pressure at the end of the pump and p1 is at the beginning.

The Attempt at a Solution

Honestly, I have no idea where to start. That's why I came here so that maybe if I could get a starting point, I could figure the rest out.
I'm thinking the first thing I would do is find the pressures at the pump to find the power, then I could find the flow rate in the feed pipe. But, I am running into a lot of unknown variables.

I appreciate any and all help. Thanks

 

[Q_Goest]

Hi dr3wsum1, welcome to the board. The problem you have is a tough one because it generally takes considerable iteration. Are you familiar with the Darcy-Weisbach (DW) equation and Bernoulli's equation? You should have them in your fluid mechanics book but if not, they can also be found in the manual I posted online here: https://www.physicsforums.com/showthread.php?t=179830
(See post #2)

The DW equation (1) is on page 2. Note the Bernoulli's equation (16) on page 14 has been modified to add the head loss due to irreversible pressure loss. You can calculate irreversible pressure loss from the DW equation.

Note also the flow restriction for a valve is given by equation (11) on page 6. Unfortunately, you don't have the valve's Cv, so you may want to just ignore the valve and assume it's the same as a length of pipe. That would be a good assumption for a full port ball valve but not a good one for most other valves. Unless you have that information though, you can't put a value in for it.

Your first question:

1) We are to design the pump power and D1, D2, and D3 while all valves are open.

requires that you have diameters for the verticle lengths of pipe and also some sort of information for the flow rate. Not sure what your flow rate is for this pump. You mention 4.5 cubic meters per hour but I'm not sure where that flow rate is intended to be. Is that for the pump? You'll need to break up the pipe into sections where the flow rate is the same through that section, then apply the DW equation to determine the irreversible pressure loss and if there's a change in elevation, add in any pressure changes per Bernoulli's. For instance, the first 25 meters after the pump has the flow for all three houses going through it. Use the DW equation to determine pressure drop through that section of pipe. All you need is a flow rate which I'm assuming you have. The first T then has some of the flow going vertically to the first house, and the remainder going horizontally to the second 2 houses. Is there supposed to be any pressure at the valve outlet? If not, you can use Bernoulli's to determine the head at the T and then calculate the flow rate from the DW equation. If there is pressure at the end of the T and you know what it is, just add that to the head and calculate flow from the DW equation. If you don't have anything, please explain what you do know about the system. There has to be something more to determine flow losses and head pressure in the system. Continue to determine flow through the verticles by breaking up the flow at each T and applying the DW equation and Bernoulli's. If you have to guess at flow rate, do that, then go back and itterate with the information you have for pressure or flow. Since it appears you haven't been given all the information needed to solve this problem, you will need to be more specific about what you do have.

Your second question:

2) For the designed system, what would be:
- Q1 if v2 and v3 are closed?
- Q2 if v1 and v3 are closed?
- Q3 if v1 and v2 are closed?

is similar to the first except you have only one pipe open in each of the 3 cases, so you don't have to break up the system into parts and itterate as much. You just have to apply the DW equation and Bernoulli's.

Hope that gives you a start. Please post what you know about the system if you can, including any assumptions you have to make. As it stands, there doesn't appear to be sufficient information to get an answer.

 

[mtech88]

dr3wsum1 did you ever figure it out?