Pressure loss pipe system: Conversion from known fluid1 to fluid2

[Brainface]

TL;DR Summary

Pipe system with unknown geometry. Given pressure drop at a specific flow rate with one fluid. What is the pressure drop using a different fluid?

Hello, everyone,

I am currently working on the following (real) problem, where I am not getting anywhere.
It would be super nice if you could have a look at this. Thank you very much :-).

I have a pipe system (Black Box) of which I only know the following things:
At a set flow rate with a given fluid at room temperature I have a pressure loss of x bar after flowing through the system. The exact geometry or internal structure of the pipe system is completely unknown.

Question: How big would the pressure loss be if I took another (different density/viscosity) fluid instead of the given fluid?
Using the formulas for wall friction losses and losses due to bends, valves etc., I have been able to construct the following ratio.

However, I can't get any further now, because I only know the total pressure loss with Fluid 1, but not the shares of the wall friction and the friction caused by bends, valves...
Furthermore: I have assumed a laminar flow in my equation. However, since I do not know the pipe diameter, this may not apply.

Is there a way to solve that problem? Can I use these equations in the first place or are my thoughts the wrong approach?

Thanks a lot.

Best wishes,
Ben

 

[BvU]

Hello strangeface, !

Given pressure drop at a specific flow rate with one fluid. What is the pressure drop using a different fluid?
Is there a way to solve that problem?

Pressure drop is mainly proportional to ${1\over 2}\rho v^2$ , same as with drag.
If you only have $\Delta p$, you can't determine both the poportinality coefficient and $v$. As you concluded correctly.

 

[Chestermiller]

Hello strangeface, !

Pressure drop is mainly proportional to ${1\over 2}\rho v^2$ , same as with drag.
If you only have $\Delta p$, you can't determine both the poportinality coefficient and $v$. As you concluded correctly.

This is not quite correct, because the friction factor is going to depend on the Reynolds number, which is inversely proportional to the fluid viscosity.

 

[Chestermiller]

Summary:: Pipe system with unknown geometry. Given pressure drop at a specific flow rate with one fluid. What is the pressure drop using a different fluid?

Hello, everyone,

I am currently working on the following (real) problem, where I am not getting anywhere.
It would be super nice if you could have a look at this. Thank you very much :-).

I have a pipe system (Black Box) of which I only know the following things:
At a set flow rate with a given fluid at room temperature I have a pressure loss of x bar after flowing through the system. The exact geometry or internal structure of the pipe system is completely unknown.

Question: How big would the pressure loss be if I took another (different density/viscosity) fluid instead of the given fluid?
Using the formulas for wall friction losses and losses due to bends, valves etc., I have been able to construct the following ratio.

View attachment 263464

However, I can't get any further now, because I only know the total pressure loss with Fluid 1, but not the shares of the wall friction and the friction caused by bends, valves...
Furthermore: I have assumed a laminar flow in my equation. However, since I do not know the pipe diameter, this may not apply.

Is there a way to solve that problem? Can I use these equations in the first place or are my thoughts the wrong approach?

Thanks a lot.

Best wishes,
Ben

If the flow truly is laminar, and there are no changes in elevation (so the density doesn't matter, assuming constant volume flow rate), the pressure drop is going to be proportional to the viscosity. But, aside from polymer melts and solutions, I highly doubt that the flow will be laminar. If the Reynolds number is above 2100, the flow will be turbulent, and you are just going to have to bite the bullet and use the actual system details to calculate the pressure drop.

 

[Lnewqban]

Welcome!

...
I have a pipe system (Black Box) of which I only know the following things:
At a set flow rate with a given fluid at room temperature I have a pressure loss of x bar after flowing through the system. The exact geometry or internal structure of the pipe system is completely unknown.

Question: How big would the pressure loss be if I took another (different density/viscosity) fluid instead of the given fluid?...

Welcome, Ben!
Your problem is very difficult, since you don't know many key facts.
A good guess is the best you can do.

What type of pump pushes the fluid through the mysterious pipe system may introduce an additional variable: the volumetric flow rate delivered by that pump corresponding to the new dynamic or absolute viscosity.

Please, see:
https://www.engineeringtoolbox.com/centrifugal-pumps-viscosity-d_670.html

https://www.mcnallyinstitute.com/14-html/14-04.htm

https://en.wikipedia.org/wiki/Darcy–Weisbach_equation

 

[jrmichler]

You cannot assume laminar or turbulent flow. You need to find that out. If you can measure the pressure drop over a range of flow rates, you can find if the flow is fully turbulent, fully laminar, or somewhere in between. Be careful because the flow could be laminar at low flow, and turbulent at high flow.

If fully laminar, the pressure drop at a given flow will be proportional to the viscosity. If fully turbulent, the pressure drop at a given flow will be proportional to the specific gravity. Unless the viscosity of the next fluid is enough higher to drive the flow toward laminar. If partially laminar / partially turbulent, the pressure drop at a given flow will be proportional so some function of viscosity and specific gravity.

Without pressure drop tests over a wide range of flows, and fluids with the highest and lowest viscosity to be used, you are just guessing in the dark.

 

[Chestermiller]

What are the densities and viscosities of the two fluids? Are you comparing them on the basis of the same mass flow rate or the same volume flow rate?

 

[Brainface]

Thanks a lot for all your answers. They are very helpful.
Originally I wanted to compare at the same volume flow rate (I don‘t have the numbers for densities/viscosities right now unfortunately)
As this is not as straightforward as I hoped, I may just bite the bullet and see if I can get some information on the geometries as suggested.

But one thing should be possible, right?
In the manual there is a pressure drop test listet to see if the pipe system is fully working (no clogging or deposits). For that I tune the demanded flow rate and check if the pressure drop equals the number as printed in the manual.

Let‘s say I only want to conduct this pressure drop test with the new fluid.
As long as I maintain the same Reynolds number as with the original fluid (adapt flow rate accordingly), I should be able to use my equations to convert the allowed pressure drop number of the manual to the new one, right?

 

[Chestermiller]

Thanks a lot for all your answers. They are very helpful.
Originally I wanted to compare at the same volume flow rate (I don‘t have the numbers for densities/viscosities right now unfortunately)
As this is not as straightforward as I hoped, I may just bite the bullet and see if I can get some information on the geometries as suggested.

But one thing should be possible, right?
In the manual there is a pressure drop test listet to see if the pipe system is fully working (no clogging or deposits). For that I tune the demanded flow rate and check if the pressure drop equals the number as printed in the manual.

Let‘s say I only want to conduct this pressure drop test with the new fluid.
As long as I maintain the same Reynolds number as with the original fluid (adapt flow rate accordingly), I should be able to use my equations to convert the allowed pressure drop number of the manual to the new one, right?

That would take the viscosity out of the picture, but not the density.