Pump head in pipe with changing diameter/area

[KevinH673]

I have concentric (annulus) pipes with water flowing through them. The inner pipe is solid, with water obviously flowing between the outside of the innner rod, and the inside diameter of the outer rod.

Currently, there is 10 mm diameter small rod, and a 15 mm inside diameter on the outer rod. The flow rate from our pump is 9 GPM.

We are changing the small rod to 6 mm. How can I solve for the head the pump must have? I haven't worked with head calculations, and I want to make sure the pump will work okay. The rods are completely horizontal (no vertical gradiant).

Possible equations I've dug up:

Bernoulli's Equation:
Head Loss=(Pressure (water fluid)/Spec. Weight) + (Veloc.^2/(2*g)) + Height

Shaft Head=Horsepower/(Specific Weight*Flow Rate)

Though I'm not sure either of these are right! I'm getting a solution for the head in the 600 ft range, and this is entirely too high!

Thanks for any help anyone can offer.

 

[katmar]

In equation 8.30 your author has
[Δ]P = h x [ρ]
instead of the formula in my earlier post. This is basic physics so I can only guess he has defined some strange units for h.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[cvg]

I think maybe there is some discrepancy between formulas in U.S. and metric units, especially as I see dimensions given in both feet and meters...

 

[Apakrat]

Amen to cvg!

Just remembered an old rule of thumb, “For every 1 hp of drive, the equivalent of 1 gpm @ 1500 psi can be produced.”

A little numbers playing insinuates that the pressure on the existing 98.17 mm² is about 250 psi as delivered by a 1.5 hp motor.

Question of KevinH673:
Is the 1.5 hp motor/pump used only for delivering solution through this concentric (annulus) pipe?


At 74th year working on IR-One PhD from UHK - - -

 

[KevinH673]

Apakrat, no the motor sends fluid through a system that includes some 10' of tube, as well as two or three elbows. The concentric tubes are the ones that are changing in the system though.

 

[Apakrat]

Evidently, from Your earlier statements above, You need to maintain near the same existing pressure passing thru this concentric tube section.

Without getting into theories, mathematics, etc, nor the worry of calculating possible motor/pump requirement, including cost, would it not be easier, simpler and more economical to just reduce the outer tube sizing and maintain near the same area around the proposed 6 mm inner size, thus maintaining near existing flow and pressure?

Believe You can find stock piping(tubing), fitting near this condition.​

At 74th year working on IR-One2 PhD from UHK - - -

 

[KevinH673]

Apakrat, this was precisely my first suggestion to this problem. It makes sense to do, knowing that pressure will be the same, so flow should be okay. However, I first started investigating this further to make sure the heat pulled from the YAG rod would be sufficient. I also don't believe anyone ever optimized the inside diameter of the flow tube, so I set out to do this (and then running into my problem!). Your suggestion does make sense though!

 

[Apakrat]

Please forgive me, but my interest in this posting is that I am trying to learn also.

Don’t actually know why the YAG rod diameter needs to be reduced. Will guess from prior statements, the present YAG rod is not performing a desired heat exchange, using the present flow rate volume. Exposure to a larger heated medium layer would possibly achieve a desired goal.

Perhaps You might want to look at installing an adjustable Needle Valve in the 15 mm line, down stream of the concentric YAG piping section.


At 74th year working on IR-One2 PhD from UHK - - -

 

[KevinH673]

The YAG rod's diameter is decreasing in order to give a better "mode" burn from the laser (basically, making a more uniform 'circle' from the laser beam for cutting). Doing this will affect the total power, though.