×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Pressure loss, Vena Contracta

Pressure loss, Vena Contracta

Pressure loss, Vena Contracta

(OP)
I need some help with finding the pressure loss in an annulus system. Very simplified:

It consists of a bar. Around it two pipes, such that it forms two annuluses. Think of this system blocked in one end, and there is drilled a hole in the inner pipe radially, such that the flow from the "outer" annulus can flow into the "inner" annulus. The flow media is water or hydraulic oil...

Dimensions outer annulus: D1 and d1
Dimensions inner annulus: D2 and d2
Dimensions drilled hole:  D
Flow: Q
Pressure outer annulus: p1
Pressure inner annulus: p2

What is the pressure loss through the "port"? OR:
What is the pressure difference between the two?

In advance, thanks...smile

RE: Pressure loss, Vena Contracta

Assuming Q1 = Q2, I think basically you're looking at the pressure difference being equal to the equivalent of the change in velocity heads between d1 and d2.

BigInchworm-born in the trenches.
http://virtualpipeline.spaces.msn.com

RE: Pressure loss, Vena Contracta

(OP)
BigInch...: This is a problem occuring quite often in tools designed in our company, and I've spoken with several experienced people on the field.

If I could measure parameters before the tool was produced, I would be very happy, however this is not the case...(!)

Litterature on this does not exist. If you search this problem, you most likely end up with bernoulli equation, conservation of mass etc. (modified) But in these cases, one or more parameters are missing. The orifice plate analogy is menat to measure flow (which I already know)....

One more thing: The Vena Contracta area parameter needed in these equation are missing...

More views on this matter, people??...winky smile

RE: Pressure loss, Vena Contracta

What is the velocity thru the hole? 0.1 ft/sec?  100 ft/sec?  A reasonable reply depends on this.

Good luck,
Latexman

RE: Pressure loss, Vena Contracta

(OP)
For now, the velocity on the incompressible hydraulic oil fluid is in the area between 7-14 m/s...

RE: Pressure loss, Vena Contracta

I have long been under the impression that a vena contracta exists only for a jet of liquid entering a half-universe of gas.  

A jet of liquid entering a chamber filled with initially quiescent liquid is quite a different thing; it eventually sets up a toroidal flow, and ...

Oh.  Back to the original question.

The drilled hole(s) can be modeled as orifice(s).  The problem you face is that the orifice coefficient is only accurate for a sharp-edged orifice; no chamfer, no radius, no burrs.  A laser-cut hole is a decent approximation of that ... unless somebody decides to break the edges, or radius them, "to make it flow better".  Yes, it does make the orifice flow better, but less predictably.


Mike Halloran
Pembroke Pines, FL, USA

RE: Pressure loss, Vena Contracta

Post this in the petroleum engining area, they do annulus flow all the time.  The set up will be based on a equivalent flowing area (D^2 - d^2)*3.14.  The friction factor will be a "wetted area function (D + d) * 3.14.

RE: Pressure loss, Vena Contracta

Let's see.  7-14 m/s is about 23-46 ft/sec.  Let's call it 35 ft/sec.

Let's assume Co = 0.6 and β = 0.3

K ≈ (1-β2)/(Co2 x β4) ≈ 120

ΔP = 0.0001078Kρv2

ΔP = 0.0001078(120)(62.4)(35)2 = 1000 psi

Okay, at the other end of the spectrum . . .

Let's assume Co = 0.7 and β = 0.7

K ≈ (1-β2)/(Co2 x β4) ≈ 4.33

ΔP = 0.0001078(4.33)(62.4)(35)2 = 35 psi

The true answer depends on the relative size of the hole to the size of the annuli.  I may have bracketed the answer, but you'll need to use your exact dimensions and sharpen the pencil on the calcs (I used a shortcut orifice method and the density and viscosity of water) to get the true answer.  And, don't forget the oil has to change directions 90o right before and after the hole.  I'd use K = 0.3 x 2 and the average velocity in the annuli for that.

Good luck,
Latexman

RE: Pressure loss, Vena Contracta

On second thought, I'd use K = 1.2 (a branch tee, not an elbow) x 2 and the average velocity in the annuli for the change in direction right before and after the hole.  

Good luck,
Latexman

RE: Pressure loss, Vena Contracta

(OP)
Hello, everyone...

Back to work again...smile

Thank's for all your good replies. Someone is referring to a wetted area, but the losses in the annulus area is very small.

Latexman: Where do you find the discharge coefficient? And what is the ? in your equation? Is this the modified Bernoulli?

Is there some litterature you could referr to?

RE: Pressure loss, Vena Contracta

blckwtr,

The discharge coefficient and equations came out of Crane's Technical Paper 410:

http://www.flowoffluids.com/tp410.htm

I see no ? in my equations.  Put a checkmark in the Process TGML option in Step 2 Options.  That may help.

Good luck,
Latexman

RE: Pressure loss, Vena Contracta

(OP)
Oh, that is ?... (Beta) I just took copy paste from character map...

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources