Annular Flow calculator?

[sprintcar]

I'm looking for a quick spreadsheet or formulas to calculate annular flow. I've tried converting area to nozzle diameter (ie Cameron Hyd Data) but results were much too high.
Someone has "borrowed" the copy of Crane Tech Paper 410 which is supposed to have the info I need - Purchasing will probably take a decade to get the replacement.
The variables will be the 2 diameters, pressure differential and the length of the annular restriction. Fluid is water about 80F.
THANKS!!

"If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut."
-- by Albert Einstein

 

[TangoCleveland]

Crane 410 sayeth:

"Occasionally a conduit of non-circular cross section is encountered. In calculating the Reynolds number for this condition, the equivalent diameter (four times the hydraulic radius) is substituted for the circular diameter. Use friction factors given on pages A-24 and A-25 (Crane uses Moody friction factors).
R_H = cross sectional flow area / wetted perimeter
This applies to any ordinary conduit (circular conduit not flowing full, oval, square or rectangular) but not to extremely narrow shapes such as annular or elongated openings, where width is small relative to length. In such cases, the hydraulic radius is approximately equal to one-half the width of the passage.

To determine the quahtity of flow in following formula:
q = 0.0438 d^2 sqrt(h_l D / f L
the value of d^2 is based upon an equivalent diameter of actual flow area, and 4R_H is substituted for D."

Larry

 

[Zoobie]

I like the 'sayeth'. The best references are the ones that 'sayeth'. Crane is one of them. Unfortunately my undergrad fluids text didn't say very much to me...it made a good firestarter though.

 

[tlee123]

If the ratio of the diameters is .95 or higher, then you can do the analysis as flow between parallel plates, which should be fairly easy. The circumference is used as the width of the plate.

 

[sprintcar]

The annular gap is small.
The different size units range from [4.12" OD - 3.937" ID] to [14.119"OD - 14.063ID].
The width of the "orifice plate" section ranges from 1/2" to 1"

What I'm trying now is converting to a Hydraulic Diameter by using Hd(eff) = [(d1+d2)^2*(d1-d2)^3]^0.2
Then calculating flow by Q=19.636*C*Hd^2*h^.5
C is the orifice coefficient and I'm moving that around (based on Cameron pg 2-8)trying to get a curve fit to agree with 2 test points (I know, straight line!) and some old maintenance information.





"If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut."
-- by Albert Einstein

 

[tlee123]

I just ran some numbers as parallel plate flow. I don't know what pressure differentials you're dealing with but unless there are very low (<0.05 psid), we're dealing with turbulent flow and the parallel plate flow idea is no good. Oh well.

 

[sprintcar]

Pressure diff is on the order of 25 to 50 psi in one case, upwards to 100 psi in the other.
Thanks!

"If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut."
-- by Albert Einstein