Pressure Drop of a Commercial Enlarger (recuder)

[Latexman]

Maybe I've gotten sloppy on this, but I usually ignore the pressure drop of a commercial enlarger. The reason being the small pressure drop is usually offset pretty much by the pressure increase due to velocity decrease (Bernouilli effect). Anyone else do this? If so, is there a situation where you do not ignore the pressure drop of a commercial enlarger? I think I picked this habit up from a fluid flow guru in the company many years back and I tend to do it all the time now.

Good luck,
Latexman

 

[BigInch]

Its not all Bernoulli. There are additional turbulent losses that can be caused by the rapid expansion, which can reach values almost 50% higher than flow in the other direction. Depends on the angle of expansion.

For a Reducer,

Head loss, Hf = (1/Cc - 1)^2 * V2^2 / 2 / g
where,

Cc = 0.582 + 0.0418/(1.1-D2/D1)
D1 = upstream inside diameter
D2 = downstream inside diameter
V2 = downstream fluid velocity
g = acceleration due to gravity

For an Expander, divide the above Hf by 0.7

Wish I could remember where I got that.

http://virtualpipeline.spaces.msn.com

 

[katmar]

Latexman, I agree with you that in all but the most extreme cases you can safely ignore the pressure drop through the expander. The reason for this is that the pressure drop for turbulent flow through a pipe is very sensitive to the diameter of the pipe. The pressure drop varies with approximately the fifth power of the diameter.

The result of this is that where you have a pipeline made up of two different sizes the overall pressure drop is usually determined by the section with the smaller diameter. The large diameter section, and the expander, are often negligible. Obviously, if you have a short section of small pipe followed by an expander and a long section of the larger pipe this may not hold.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[BarryEng]

For a water pipeline, the usual head loss for a reducer is about 0.04 v^2/2g. Squeezing the streamlines (in a reducer) does not result in as large a loss compared with the diffuser.

The usual head loss for a diffuser is about 0.24 v^2/2g. The higher head loss is caused by the streamlines being pulled apart causing instabilities (Karmen vortices). At large angles of diffuser, the surface flow on the diffuser, is actually the reverse of the general flow.

I do have an empirical formula (from Fluids by Davis) that I can post (if you require it) after I get home from work. Yes - I still go to work (trying to reduce the pile of VISA card bills).

Dougherty & Ingersol (Fuid mechanics) has a graph showing that the minimum loss is for an included angle of the diffuser of about 4 to 7 degrees. The loss increases to a max at about 60 degrees & then drops about 1/3 to a constant loss from 90 to 180 degrees (sudden expansion).

The reason for the max loss at about 60 degrees, is that this is the max interference between the pipe wall & the expanding streamline. The loss stabilises over 90 degrees due to a developed cone of water (at an angle of about 60 degrees) with a zone of 'dead water' back to the pipe wall.

If you want this info (from Dougherty & Ingersol), I can look up a set of values & post on this thread. I will check this thread later, for any requests.

If you want further info, try BHRA (British Hydraulic Research Assn) tables by Miller. This is a very thick book with a lot of text, graphs, tables etc.

If you have a specific problem, post the info on this thread & I will look up either Dougherty & Ingersol, or BHRA for their values.

 

[CJKruger]

Latexman, I agree. In most cases the error would be insignificant.

For various reason though, I have changed the way I do hydraulic calcs. I now do the pressure drop for the pipes and expanders/reducers/entrances separately.

The benefit is that it also works for compressible flow, I never have to worry about the "exit pressure loss", and I know the actual pressure at all important points in my circuit.

For info - For a sudden pipe expansion there is always a pressure increase (from momentum balance).

 

[BigInch]

Found where I got that formula, from "Piping Handbook", McGraw Hill 5th Edition p 3-132.

The equation is for "sudden" contractions or enlargements and reducers turned one way or another are not specifically discussed. My opinion is that a "sudden" change must describe the limiting condition and head losses for the smoother transition reducers, supposedly with less turbulence, must fall within the envelop of the sudden equation. With lack of any specific evidence, that would appear to describe a viable conservative method.

The text goes on to say,

In the case of a sudden enlargement, the loss cannot exceed the head required to produce the given change in velocity, while with a sudden contraction the loss usually is somehwat less owing to a lesser amount of turbulence. This is in keeping with the ^ NOT SO well-known fact that the energy losses accompanying a decrease in velocity generally are greater than those associated with an increase.

(the gray text is my own personnal notation)

http://virtualpipeline.spaces.msn.com

 

[Latexman]

Yeah, that was not intuitive to me either.

Good luck,
Latexman

 

[prodigal20]

please i want to know much about the Darcy equation & the Chezy equation.and also the differences between diffusers and nozzles