RE: Required pipeline water velocity to flush air from line

From: <Steve>
Date: Mon Feb 25 2008 - 04:52:00 EST

Hi Erik

I have looked at the force balance previously, but it leaves me with the problem of how to estimate the effective bubble size (or volume of submerged object). This would them let me calculate the velocity at which the forces balance, and from that the required flushing flow rate. A couple of minor corrections:

Resolving in the direction of flow, in the turbulent range:

Fb=-Rho.V.g.sin alpha

Fd= Cf.S.0.5 Rho. V^2

or equating: V = sqrt (4g/3*D/Cf)

I might be worrying about the bubble size unncessarily - especially so for smaller pipes, but would be happier with a sound basis for deciding the bubble size rather than, say,centage of the pipe diameter. However we do have a limiting case of the bubble diameter equalling the pipe diameter. For example in a 150 ID vertical pipe, the buoyancy force will be roughly pi/6*(0.15)^3* 1000*9.81=17.3N
Assuming your drag coefficient of 0.45 (we can get the exact value from any number of charts), the corresponding velocity will be 2.09m/s A back check on Fd gived me 17.3N.
While this is a gross oversimplification is does tell me that a water velocity of 2.09m/s should keep bubbles moving in a 150 diameter pipe, regardless of inclination.

You can shoot me down now.

Thanks again

Cheers

Steve

To: PipingDesign@yahoogroups.comFrom: erik.scheir@pandora.beDate: Sun, 24 Feb 2008 11:48:57 +0100Subject: RE: [PipingDesign] Required pipeline water velocity to flush air from line

Hi Steve, The buoyant force (Archimede's Principle) says: Fb=Rho.V.g where: (verticalpipe)Rho = density of the fluidV = Volume of submerged objectg= gravitational acceleration.If the inclination of the pipe is alpha, then FB = Rho.V.g.tg alphaThe drag force is: Fd = Cf.S.v , where:Cf= coefficient : = 0.45 for a sphereS= section of the object V: velocity of the fluid.To sweep the air along with the fluid Fd should be greater then FbI hope this helps,ErikVan: PipingDesign@yahoogroups.com [mailto:PipingDesign@yahoogroups.com]Namens Steve McKenzieVerzonden: Friday, February 22, 2008 9:54 PMAan: PipingDesign@yahoogroups.comOnderwerp: [PipingDesign] Required pipeline water velocity to flush air fromlineGentsWith a water pipeline containing air, it is common practice to install air eliminators at the high points. However it should be possible to use the water to sweep the air along with it if the water velocity is sufficiently high. I could have a shot at calculating the velocity, but the assumptions would have to be on the simplistic side. The essential problem is to find the water velocity in a pipe of given downwards inclination, where the buoyancy force of the air bubbles equals the downwards drag force of the water on the air. The major independent variables would appear to be; pipe diameter, roughness, inclination, effective water depth in the pipe, air viscosity and density/pressure.Any help of referrals would be appreciated.CheersSteve
Mckenzie<http://1232432.sigclick.mailinfo.com/sigclick/05030104/0505034D/054D001\ 4126161.jpg> [Non-text portions of this message have been removed]

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[Non-text portions of this message have been removed] Received on Mon Feb 25 04:52:00 2008