Water flow system - Design and Optimization

[Mechanic77]

Hello all,

I'm a Mechanical engineer with no prior experience in designing flow systems.

I'm struggling with a hydraulic system that I have to design.

the number of unknowns is large. but maybe by dividing the system to small sections, a solution can be found.

I attached a schematic drawing to the thread,as well as some pages from a fluid mechanics book I have, and on which I rely in my calculations.

Basically, I need to design and optimize a system that will circulate water in 2 pipes.
first, I need the water to flow out of a reservoir, through a ∅50mm pipe.
the water then enter a pump.
Volume flow through the pump is 160 [liter/min].
after the pump there is a junction.
Most of the water will continue to the rest of the system (lower right section in the drawing) and return to the reservoir,
but a small percentage of the water will have to flow through a narrower pipe (with an unknown diameter ∅Z)

This pipe will eventually converge at its end, in order to increase the speed of the water, flowing into the box shown on the top. at this convergence the pipe diameter should be ∅X (∅X<∅Z).

the box is actually a rectangular prism, not open to atmosphere.
its cross-section size is about 20x20mm, and the height is about 80mm.

Conditions in the prism should be:

1. Water flow - between 0.5 [liter/min] to 5 [liter/min][/li]
2. Formation of air bubbles should be as low as possible (clear flow).[/li]
3. Water should fill the entire box, without dead regions (would love to hear what you think about that possibility considering the current design - is it possible to achieve? do I need turbulent or laminar flow for that?)

Then, the water needs to come out slower from that box, so the pipe diameter at the box outlet should be
∅Y and then diverge back to the same pipe diameter before the box (e.g. ∅Z). this means ∅X<∅Y<∅Z.

After the water flows out of the box it has to flow towards the main line (∅50mm) and back into the pump,
and vise versa.

I know that I should probably use the Bernoulli equation and take into account losses (using Darcy-Weisbach friction factor)
I find it very confusing to understand where to use [ΔP] and where to use [ΔP loss] (these 2 terms show in the pages I attached)

the givens are:
Total flow rate: 160 [liter/min]
Pressure before the pump: (-0.1)[bar]
pressure after the pump: 0.7[bar]
main line diameter: ∅50mm

especially I would like to know the volume flows, pressures, water speed at all the points I marked in the smaller pipe. and of course the required diameters, including the ones in the convergence and divergence inside the box.

There is also 1 more question I wrote on the drawing itself.

I can't seem to understand where to start solving this problem and will appreciate any help you can offer.

Thanks a lot in advance!

 

[Compositepro]

It would help for you to explain why we should be interested in this problem as it appears to be very much like homework. And to answer one of your questions the pressure after the pump cannot be the same as the pressure before the pump if there is any flow. Your main issue in solving this problem, is that there must be adequate delta P across the pump to create flow in the bypass loop through the closed tank, and this depends on a flow restriction in the main loop, which you do not show. Assume an adjustable valve that will give you say 10 psi across the pump, so now you have enough information to solve the problem

 

[Mechanic77]

Hi,

First, thanks for your reply.

Second, I can assure you that this is not a homework problem, but a real system which is part of a product we are trying to design.
I am just trying to understand how to apply the rules and use the equations I learned long time ago.

Third, Of course the pressure before and after the pump can't be the same when there is flow. I know that.
In the drawing I attached I asked specifically about P1 and P2 which are both after the pump. please have a look at the drawing.

And fourth,

Assume an adjustable valve that will give you say 10 psi across the pump, so now you have enough information to solve the problem

Couldn't understand what you mean. in the drawing the pressure across the pump is given. and it is not 10 psi.

Thanks in advance.

 

[Compositepro]

Okay, sorry the bottom of your picture was covered by a tool bar on my laptop screen. Well, you show three points in the pipe after the pump and ask what the pressure difference is between the three point while showing essentially nothing between the points. No wonder you can't figure it out.

 

[Mechanic77]

you show three points in the pipe after the pump and ask what the pressure difference is between the three point while showing essentially nothing between the points.

Essentially nothing between the points?

what about the junction in between them?

3 points:
1st - right after the pump
2nd - right at the junction
3rd - after the junction

The volume flow after the junction decreases. This means the velocity decreases as well. from Bernoulli's conservation energy equation this must affect the pressure at each point.
Am I wrong here?

I'm mostly interested in understanding what is the pressure at the 2nd point.
Is it the same as the 1st or the 3rd point, or maybe something else?

 

[Compositepro]

Per your drawing these points may be inches apart or miles apart. There is no information to base any calculation upon.

"I'm mostly interested in understanding what is the pressure at the 2nd point.
Is it the same as the 1st or the 3rd point, or maybe something else?"

Answer: yes.

 

[Mechanic77]

Per your drawing these points may be inches apart or miles apart. There is no information to base any calculation upon.

The system is not yest designed, so I don't have the exact distances,
but let's assume the distance between the pump outlet and the junction is a few meters. about 2 to 3 meters (horizontal flow at the same height)

How does it affect the pressure right at the junction, with relation to the pressure right after the pump (P2), and the pressure in the main line after the junction (P1) (let's assume that P1 is 2 to 3 meters far into the main line after the junction).

Does this help to clarify?

Thanks.

 

[LittleInch]

Yes. All three will be the same within two decimal places.

For what you're trying to do, forget bernoulli and just look at pressure drop. You know the pressure drop, 0.8 bar, you know the flow rate, though 0.5 to 5 is a bit of a large range-what flow do you want?? You can estimate the lengths so work out the ID you need. Note that for what you're trying to do the ID X is likely to be very small and will probably generate 80%+of the frictional losses. You might end up at choked flow.

It will be am iterative process so start worth your flow, 80% of 0.8bar pressure loss, an estimate of length of your smallest pipe and see what I'D matches those conditions.

I don't understand your issue about dead regions. If the outlet is at the top then all air will get blown out and although it goes back to the pump inlet (back to the reservoir would be better) in time all the air will disappear. The velocity coming out of your small pipe will be enough to stir everything around.

Does that help?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.