How do we model water flow problems?

[tp86]

Homework Statement: Sorry there is no homework statement with this problem
Relevant Equations: n/a

Hi guys. This is my first post here. I love physics but I am unsure how do model water flow type of problems. If anyone could please help us with how we can analyse this it would be much appreciated. It not homework but a problem we are having on our property with water flow.

Please see the diagram I made below for our current situation. There are 2 outlet pipes that go to 2 pumps and would like to know how much additional water flow and pressure the outlet that is connected to both tanks would have? I do not need a precise answer but would like to know physically how i would model this and if it would likely have much more flow (as in 10% more 20% more or 50% more etc) Note: I do not need to know the actual exact water flow value but more of a percentage likelyhood - that's all

2 large water tanks equally filled (notice coupling pipe between them) supplies water to 2 different outlets at the bottom. One received water from only 1 tank, and the other from both tanks at once.

Additionall info:
- Both water tanks are on flat ground and filled to the same level
- All pipes are of same diameter
- All outlets and coupling are at the same height from ground


Is anyone able to help me model this please? I have never done any water flow type of problems in physics and not too sure where too being.

Thank you in advance :)

 

[BvU]

!

How about reading a book on fluid flow to grasp the physical principles ? PF isn't into lengthy lecture series, I'm afraid.

But if you are determined enough, you could work through pressure drop calculations (e.g. here, with a useful equation here. Or find a calculator to do the work.

Your system is pressure driven; with a bernoulli equation and pressure drop calculations you should be able to get some results. Provide a lot more detail (drawings, pipe data) if you want an example.

If the pipe between the tanks is wide enough, both tanks should empty at the same rate.

$\$

 

[Gordianus]

I'd start with incompressible, inviscid líquids (Feynman 's "dry Walter").

 

[tp86]

Hi BvU. Thank you for the info and the references. I've had a quick read but not properly yet as Im beginning to see its quite involved to analyze properly!

Thank you for the suggestion also Gordianus.

This brought me to the idea of analyzing the water (lets pretend its inviscid) and instead of water atoms, could we model them as tiny steel ball bearings and use a basic Newtonian model.

All the ball bearings have a force on them due to gravity. The movement will be complex like fluid dynamics but it is not hard to see at the point with the T intersection there will be momentum from 2 directions joining together.

Please see this demonstration I made

And this resulting momentum should cause the ball bearings to bounce off the insides of the pipe and cause an additional flow of balls at the output (compared to the output that doesn't converge from 2 tanks)

Similarly, this system should produce very similar results to a situation where there is only 1 tank and one output has only 1 output from the tank and the other output has 2 outputs from the tank.

I'd love to know what you guys think of my simplified analysis

 

[BvU]

I don't think the steel balls are a good analogon for fluid flow.
Here's another link with more focus on flow analysis.

For your casus:

• What is a typical flow
• Wat is the pipe (internal) diameter
• What are the pipe lengths
• What is the tank diameter
• Height difference from fluid level to tank exit ?

$\$

 

[tp86]

Thanks mate. I'll have a read today. Just for a bit of further information the reason for the question is that we actually have a large water pump connected to each of the 2 outlets. One of the pumps is making a very loud rattle (I suspect it to be the pump connected to the pipe that is fed by only 1 tank)

And the one with much less rattle being the one being fed by both tanks.

So our theory is that one of the pumps is being staved of water flow / pressure

We were not looking for exact calculations so much, but from the more I read, it really depends on things like pipe diameters and lengths and for that you really need to use the proper equations

Part of the problem is the manufacture has raised the pumps (on a pump stand) about 1.5m from the ground. Of course at this height the pressure and flow will be less

 

[BvU]

we actually have a large water pump connected to each of the 2 outlets

How ?

Are you going to spoon feed this ? So the lot is not gravity driven but pumped. Anything else ? A 2 km pipe to a corn field ?

Rattling pumps ? Or cavitation ? How about a detailed drawing, isometrics, etc ?


Dug up some more goodies for pressure drop calculations:

https://www.engineeringtoolbox.com/darcy-weisbach-equation-d_646.html

https://www.engineeringtoolbox.com/colebrook-equation-d_1031.html

 

[tp86]

Hi mate. I did a quick sketch.

I've only shown 1 tank to simplify it a little. So the large water tank is a reservoir we use in case we run out of mains water pressure. The large tank feeds the pump you see on the right (this is actually for an automated carwash)

So the PVC pipe length in total I would say would be somewhere around 20m in total and I believe the pipe diameter is about 50mm (I might have to check on this tomorrow morning though when Im there)

You asked, cavitation or rattling. Personally I think the problem may have started off as cavitation and over a couple of years it's escalated to metal on metal rattling. I do not know if the lack of pressure has caused damaged or not

The actual pump specifications are on here https://arimitsupumps.com/wp-content/uploads/2022/12/model_TR709KV.pdf

It states on there inlet pressure should be -5 to 70psi.

If the pump is trying to feed in water fast and there is not enough pressure keep up, cavitation will defiantly occur near the inlet and will cause damage to pump for sure. I do not know for sure that's what happened but its a possibility

It is an interesting problem. You could almost make an experiment with a straw forking off to 2 pipes, going into the bottom of a water reservoir - like a plastic bottle. vs a normal straw going into a plastic bottle. Then try drink from each of the straws to see if there is much noticeable flow difference and how the height of the straw from the top of the reservoir effects the flow.

Just an idea I had