Liquid static head vs. dynamic head?

[pushpole]

It's been a looooooong time since I delved into fluid properties.

I'm trying to predict flow based on a known static head. I have a water column which will result in 6 psig of static head. The height of the water column will not change during the flow. I know the downstream piping will flow at 51gpm with a 125 psig source throttled to 5 psig and 40 gpm when throttled to 3 psig.

I don't need very many significant digits!
Thanx for any help.

 

[Q_Goest]

Hi pushpole,
I posted a tech paper that applies here:
https://www.physicsforums.com/showthread.php?t=204473

Note equation 1 (Darcy-Weisbach) equation, shows that pressure drop in a pipe (dP) is proportional to the square of the fluid velocity. Note also it is proportional to friction factor f, which will also change with fluid velocity. Luckily in your case, the friction factor won't change too much if dP doesn't change much (ie: from 5 psi to 6 psi) so you might just ignore that. The result is that dP varies only as a square of the flow. So if you know the flow is 51 GPM with a dP of 5 psi, then the flow would be 56 GPM with a dP of 6 psi. Note also that using a pressure drop of 3 psi results in a calculated flow of 40 GPM, just as you've suggested, so the friction factor variation is seen to be too small to be significant.

 

[pushpole]

I understand your response. Great link for my future reference.

I'm having a little trouble with the concept of static head vs. dynamic head. If I start flowing water out of the head tank (static pressure of 6 psig). The pressure should drop at the tank outlet/pipe inlet as PE is converted to KE. How would I compare this to my measured stable dynamic readings?

Thanx again!

 

[Q_Goest]

Not too sure what you're asking here. I assume you have a tank at some pressure, say 6 psig, and a pipe coming out that dumps to atmosphere somewhere. You open the valve and get a flow out which you've measured when the tank is at 5 psi and 3 psi. I believe that's the scenario you have.

If that's the case, then the pressure you read on a pressure gage which is oriented perpendicular to the flow velocity will read the static pressure. If you had a bunch of these lined up along your pipe, you'd see the tank at 6 psi and as you went along, you'd see a drop in pressure in each of the gages until it finally read zero. The only caveat to this is if the pipe goes up or down in elevation or if the pipe diameter changes, in which case pressure will change according to Bernoulli's equation in addition to the irreversible pressure losses predicted by the Darcy Weisbach equation. See equation 16 in the paper.

If you're wondering how the pressure will vary if your gage is parallel to the flow, that's a different story, but I don't think you'll need to concern yourself with that.

Hope that helps.

 

[pushpole]

Thank you for the help. What I'm trying to reconcile in my limited brain is the difference I would see in flow based on the source.

You are correct in your assessment of the basic layout. The uncertainty I'm trying to reconcile is the demonstrated flow capability using the throttled external source, the 5 psig and 3 psig readings (taken perpendicular to flow downstream of the throttle valve) and the static head tank source.

head tank pressure = 6psig = all Potential Energy
observed flow= 5 psig @ 51 gpm = Kenetic Energy + Potential Energy
A conversion of 1 psig from PE to KE resulting in 50 gpm flow through a 1.5" pipe seems like a lot. However, if the numbers support the observations I will certainly accept it.

Bottomline,
Can I expect the head tank to perform like the throttled 125psig source?

Thanx again!