Venturi Expansion Factor and Discharge Coefficient

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davi johnes
Posts: 3
Joined: Mon Aug 02, 2010 1:47 pm

Venturi Expansion Factor and Discharge Coefficient

Post by davi johnes »

I have two questions that I would appreciate if any one help me to find their answers. let's start.

The discharge coefficient used for venturi in the calculator is:

Cd=a+b.(Ln Re)^2+c.(Ln Re)^3

and apparently the expansion factor used for it, is:

Buckingham Eq: Y=1-(0.41-0.35*beta^4).(p1-p2)/(k.p1)

Now first question is this, why we don't use the equation below?

Y= sqrt((r^2/k).(k/k-1).((1-r^(k-1)/k))/(1-r).(1-beta^4/1-beta^4.r^2/k))

Perry's Chemical Handbook, 8th Edition, ch.10, page 10.18, Eq. 10.26, for Venturis and Nozzles


I mean I can't understand why we should use Buckingham equation instead, while in page 10.17 of that Handbook the
Buckingham equation (Eq. 10.23) is introduced as orifice expansion factor.


And the second question is that why the discharge coefficient factor and Reynolds number given by the calculator does not
satisfy the applied formula (Cd= a+b.(Ln Re))^2+c.(Ln Re)^3)
for example consider the given data below:
p1=830 kpa, p2=550 kpa, rho= 9.6998 kg/m3, D1=tube diameter=55 mm, D2=Flowmeter Throat diameter=30 mm, ni=kinematic viscosity=15 mm2/s
the results for this existing data would be:
ReD=270435.38 , Red= 495798.22 , Cd=0.985

but after substituting the parameters a, b, c and ReD in the equation we got: Cd=0.989

Actually I'm working on a personal project to produce a program code for this, but I got some different answers for
Q (Volumetric flow rate). some differences are really unreasonable! for example with this given data I've got
Q=494.9869, but calculator says Q=630.8259 .Please help me figure out this problem.
admin
Site Admin
Posts: 375
Joined: Mon Feb 08, 2010 7:47 pm

Re: Venturi Expansion Factor and Discharge Coefficient

Post by admin »

Really like your comments, as it will bring better solutions (calculator) at the end...

I would like to point out that ISO 5167-4 is covering this "Measurement of fluid flow by means of pressure differential devices ... - Part 4 Venturi tubes" and I think it should be used as reference for this.

That first equation is for limited range of Reynolds number as for Re=2e5 to 2e6 -> Cd=0.985. For other Re numbers this equation is used.
Also this is the case if 200 mm < D < 1200 mm and 0.4 < beta < 0.7 which is not the case in your example.

For the second equation, you are right and once I get ISO 5167-4 I noticed it, but have to change it within the calculator. But in the same standard is stated that that equation is valid only for above mentioned ranges of Re, D and beta, so your Venturi sizes are not covered with that formula.
Pipe flow calculations - since 2000
davi johnes
Posts: 3
Joined: Mon Aug 02, 2010 1:47 pm

Re: Venturi Expansion Factor and Discharge Coefficient

Post by davi johnes »

I appreciate you for the info. that's very helpful.
Yes ,ISO 5165-4 has introduced the same equation (the second equation that I've mentioned from Perry) for venturi expansion factor and also you are right about the validity range (in fact, that was a real fatal mistake from me! and a real relevant point from you!). But let me ask something, is the Buckingham's formula valid for my venturi size or not anyway? i.e. do you mean that Buckingham equation is applicable for venturis? and also would you mind explaining more about this:
For the second equation, you are right and once I get ISO 5167-4 I noticed it, but have to change it within the calculator. But in the same standard is stated that that equation is valid only for above mentioned ranges of Re, D and beta, so your Venturi sizes are not covered with that formula.
admin
Site Admin
Posts: 375
Joined: Mon Feb 08, 2010 7:47 pm

Re: Venturi Expansion Factor and Discharge Coefficient

Post by admin »

No, Buckingham's formula is for orifice as you said.

Expansion factor formula
Y= sqrt((r^2/k).(k/k-1).((1-r^(k-1)/k))/(1-r).(1-beta^4/1-beta^4.r^2/k))
is used for values of D2/D1; D; ReD that are in the range that is stated in ISO 5167-4 for different types of Venturi tubes.

Diameters of your Venturi are just ok for "classical Venturi tube with a machined convergent section" and Cd for it is Cd=0.995.

And for that "type" the diameter should be D>50 mm in order to use above formula for expansion factor which is just ok for your problem and for it, expansion factor formula above can be used also for expansion factor calculation.
Pipe flow calculations - since 2000
admin
Site Admin
Posts: 375
Joined: Mon Feb 08, 2010 7:47 pm

Re: Venturi Expansion Factor and Discharge Coefficient

Post by admin »

And just to point out following:
davi johnes wrote:I have two questions that I would appreciate if any one help me to find their answers. let's start.

The discharge coefficient used for venturi in the calculator is:

Cd=a+b.(Ln Re)^2+c.(Ln Re)^3

and apparently the expansion factor used for it, is:

Buckingham Eq: Y=1-(0.41-0.35*beta^4).(p1-p2)/(k.p1)
Venturi tube calculator http://www.pipeflowcalculations.com/venturi/index.htm is for incompressible flow only, as stated on the page bellow calculator button.
It can be used for gases but only for small pressure drops that will not cause to big change in density.

Expansion factor is as explained in theory page
http://www.pipeflowcalculations.com/pip ... ifices.htm
for nozzles and orifices and not for Venturies.
Pipe flow calculations - since 2000
davi johnes
Posts: 3
Joined: Mon Aug 02, 2010 1:47 pm

Re: Venturi Expansion Factor and Discharge Coefficient

Post by davi johnes »

Its great, I got it. but let me ask one more question if you don't mind, Is the used expansion factor in this calculator also like perry's one? I mean if that is, why haven't you mention it in the theory page? (http://www.pipeflowcalculations.com/pip ... ifices.htm)
And also I think the users of calculator should not be allowed to enter data out of the validity range of the existing formulas because If they allowed, they wouldn't know anything about the invalidity of the results and then this could be a logical error.
Anyway thanks for your patience.
admin
Site Admin
Posts: 375
Joined: Mon Feb 08, 2010 7:47 pm

Re: Venturi Expansion Factor and Discharge Coefficient

Post by admin »

As fluid is considered as incompressible no expansion factor is included in calculator, for this time but will be soon.

For the second point you are right of course and it will be indicated more clearly. Thank you for your analysis.
Pipe flow calculations - since 2000
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