Hi there,

This more of a general fluid mechanics question, which I've had no luck in finding the answer, but here goes anyway:

For long pipes of uniform diameter with constant flow rate, are there equations to calulate the velocity decrease due to friction in long pipes? I mean that the roughness of a pipe causes a frictional pressure drop, but how does this effect the velocity as function of length?

Any response will be appreciated.

J

As a direct solution to the steady Navier Stokes shows you, there shouldn't be a velocity drop in a steady solution from one end of the uniform pipe to the other. This makes sense intuitively, since if there were, you would be saying that you are putting more liquid into the pipe than you are getting out of it. In a nonsteady solution there can be all kinds of jumps and whatnot in the velocity profile, but the end effect will still need to be that as much comes out one end as is being put in the other, so a overall drop in the velocity can't happen,

Bob

Thanks for the response, Bob. I suspected this was the case!

J

This is only true for a fully developped flow (and so an incompressible one).

If the flow is not fully developped and incompresible, the velocity profile will evolve along the pipe and the maximum of the velocity will increase until developped flow is achieved.

For a compressible flow, the velocity profile is always evolving (until the sonic blockage is reached for a sufficiently long pipe, the so-called Fanno problem).

JF

This is really just to re-iterate what Bob said but you don't even need to look as far as the Navier-Stokes equation.

Go back to probably the first Fluid Mechanics lecture during your degree and you'll certainly remember the continuity equations which states that the product of area x velocity = V remains constant, i.e. dV=0. Therfore, for a straight pipe where the area does not change the velcoity hs to remain the same.

Thanks for all the input guys.

The real reason I'm asking this is that I have developed (with the help of previous models) a mechanistic/phenomenological model which predicts two phase flow patterns and associated pressure drop in pipes (I've also done some CFD simulations to compare this with). This prediction is primarily based on gas and liquid flow rates, conduit geometries and fluid properties. This is a steady state model, which is not changing with length, i.e. flow patterns will change with different hydraulic diameters or flow rates, but not with length.

My initial question arose from two-phase experimental observations where flow patterns are seen to evolve and change with length, even though the flow rates and geometry, etc. is unchanging. I thought that if there was a change in velocity, I could use this change to recalculate the flow pattern/pressure etc.

I was wondering if anyone knows if there is a way to model the flow pattern with length. All the model calculates with length is the frictional pressure drop. Is there a way I can use this to recalculate the flow pattern?

J

The change in velocity patterns in your experiment is not a consequence of the flow through the pipe but a consequence of the interactions of the two phases with each other. I would suggest you carefully check your (thermal) boundary conditions along the pipe as I reckon that your two phases are interacting with each other in your experiment, ie. the raio of e.g. wet steam to dry steam is constantly changing in your experiment. Also, take a closer look at the way phase changes and therelike are modeled in your code.