Pressure Gain in Pipe Expansions?

[GHartmann]

I have always assumed the K friction values and equations utilized for sudden or gradual expansions was a true friction loss in pressure. However, just the other day someone suggested that there would actually be a gain in pressure as the velocity head lost was converted back to pressure.

In all my years of experience I never analyzed a system this way, I wonder (with cobwebs in my brain) what is correct?

I am familiar with Crane, Moody's equations, and the equivalent methods but am stumped at this basic part of the theory.

 

[zdas04]

I've looked for this phenomenon several times and for concentric reducers if there is a dP (in either direction) it is too small to see with the instruments I used. I always figured that if there was any gain for an expansion, the clunky way that the reducers were configured (i.e., abrupt changes instead of smooth) lost the gain to boundary layer effects.

On the other hand I have seen measurable pressure increase through a reducing elbow. It is Reynolds Number dependent, but for Reynolds numbers in the low millions you can see a couple of psi increase through a reducing elbow in gas.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[bimr]

What you have been doing is correct.

At the start and end of your pipe run, the total energy in the fluid is equal to the pressure. Velocity is zero and contributes no energy. As you traverse the pipe, pipe losses occur and are subtracted from the energy grade line. The energy grade line can be represented by the Bernouli equation.

http://en.wikipedia.org/wiki/Bernoulli's_principle

Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Thus an increase in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic energy, and a decrease in its static pressure and potential energy. If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ρ g h) is the same everywhere.

As you traverse the pipe run, the total energy may be converted to velocity and then back to pressure, but you are only concerned with the energy grade line. As long as you have positive energy, the flow continues down the pipe run. Pipe velocity is generally controlled within a economical flow range in a pipe so that you do not experience extreme variations of kinetic energy due to velocity.

If you were working with open channel flow such as a flume or river, then the velocity is more important. The water level in a flowing flume is the hydraulic grade line (HGL is
obtained as EGL minus the velocity head V2/2g.

http://css.engineering.uiowa.edu/~cfd/pdfs/53-071/lab2.pdf

 

[katmar]

My take on it is that the Crane etc equations model the pressure losses due to friction and boundary layer separations, but on top of this there is the Bernoulli increase in pressure because of the decrease in velocity. To get the net change you have to offset the two. Depending on your system pressure, the change may be too small to see on a pressure gauge - as zdas04 has observed.

There was a discussion on this in thread378-207481

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"An undefined problem has an infinite number of solutions"

 

[bimr]

Regarding "However, just the other day someone suggested that there would actually be a gain in pressure as the velocity head lost was converted back to pressure."

In the same manner, as a conduit's (pipe) elevation changes in a pipe system, the internal pressure in the pipe correspondingly changes according to Newton's 2nd Law Conservation of Energy. Unless these energy changes are significant, they are neglected.

http://www.pipeflow.com/pipe-pressure-drop-calculations/pipe-elevation-changes

The take is this is basic hydraulics. Energy, Head, and Grade Lines.

The Energy Grade Line, also called the Energy Line (EL), is a plot of the Bernoulli equation or the sum of three terms in the work-energy equation. The EL is equal to the sum of the fluid's velocity head, the pressure, and the elevation head.

EL = (V²/2g) + (p/γ) + h

where
V = velocity
g = acceleration due to gravity
p =static pressure (relative to the moving fluid)
γ = specific weight
h = elevation height

A pitot tube can be inserted into a pipe such that the fluid initially flows into the tip of the tube, until the height of fluid in the tube balances the energy coming in, at which point the flow in to the tube stops and the fluid velocity at the very tip of the pitot tube becomes zero. The pressure and the velocity head of the fluid are in effect converted to the equivalent head in height of fluid (i.e. the fluid will rise to the elevation of the EL for that specific point in the flow).

http://www.pipeflow.com/pipe-pressure-drop-calculations/pipe-elevation-changes

http://www.youtube.com/watch?v=DJUZvYNVQ0g

 

[BigInch]

In piping work we're usually only concerned with the unrecoverable pressure losses and prefer to work on the conservative lower end, which is the HGL, not EGL, that being HGL + velocity head, although you can consider it if you like. In pressure flow, it is typically a very small component of the total. The pressure changes due to velocity change are for the most part entirely recoverable. That is an entirely different story in open channel or partially filled pipe flow where only changes in elevation contribute to the energy to drive the velocity component between one section to another.

If it ain't broke, don't fix it. If it's not safe ... make it that way.