Yet another Flow rate question

[MEdesigner]

I am trying to better understand conceptually flow through a long pipeline. in this case the pipeline is 60miles long with a diameter of 13feet. the outlet is located lower than the inlet by about 600 feet and the pipe has several elevation increases and decreases over the length of the run. The entire system is gravity fed.

I have seen measured pressure data over the length of the pipeline and observed rises and falls in the pressure which appear dependent on elevation gain, or pressure drop due to friction. The pipe maintains a constant diameter over it's entire length.

Does Bernoulli's equation hold true for this case? What I am really trying to understand is whether or not there are fluid velocity changes associated with the observed pressure changes.

 

[stewartcs]

Is it compressible or incompressible flow?

 

[MEdesigner]

incompressible

 

[stewartcs]

Sorry, I just saw in your post that it is gravity feed.

You can apply Bernoulli's equation so long as you allow for friction losses.

You will indeed see pressure changes at various points throughout where the elevation changes (and pipe diameter if it were to).

 

[stewartcs]

What I am really trying to understand is whether or not there are fluid velocity changes associated with the observed pressure changes.

It's safe to assume that the velocity won't change unless the diameter of the pipe changes at some point.

The elevation changes will result in a potential energy change (hydrostatic head change), but is not attributed to a velocity change.

 

[FredGarvin]

13'? Yowza. That's a big pipe. Are you certain that the pipe is completely filled during its operation? It most likely is but it's something to ask.

 

[MEdesigner]

it is more appropriate to call it a tunnel, rather than a pipe, and yes it is completely filled during use. My fluids experience is primarily with external flows so this type of internal flow problem is interesting and just outside of my comfort zone.

 

[MechanicalMan]

Bernoulli would have to be applied between two points, so if you're looking for data at the outlet, you will have to use that 600' difference as your overall delta z. You might be able to approximate the changes in elevation as minor losses in an elbow (assuming the changes in elevation are elbow-like).

 

[Q_Goest]

For incompressible flow, Crane recommends the use of the Darcey Weisbach equation for pressure drop. This equation provides the frictional pressure loss. Bernoulli's equation accounts for changes in pressure due to head and velocity only. Pick up a copy of the Crane paper here:
http://www.flowoffluids.com/

 

[stewartcs]

Crane TP410 also states that you can use the Darcy equation with reasonable accuracy for compressilbe fluids (such as air and steam) so long as the pressure drop isn't greater than 10% of the inlet pressure and the specific volume is based on either upstream or downstream conditions.

In either case you also need to use the Bernoulli equation to account for the elevation, velocity, and density changes.