Determing Pressure in Cracked Pipe

[amiket]

Hi,

I'm trying to find an equation that relates the size of a crack (or slit) in a pipe to the pressure drop. Basically I'm trying to find an equation similar to an orifice plate, but for a crack in the pipe instead. The end of the pipe would be capped so that all flow is directed out of the crack. Also, there may be multiple cracks at the end of the pipe on different sides of it. If anyone has any ideas it would be much appreciated. I've attached a rough sketch of the system.

Thanks

 

[dhengr]

Amiket:
It seems unlikely, to me, that you will find any nice clean formula for random size, shape, location cracks for the situation you are suggesting. The idea that there is a formula or a std. calc. approach for a well defined orifice plate, seems reasonable. There is a well defined set of conditions, well defined geometry, plate orientation, shape, size, edge shape, etc. of the orifice; this is something you can start to define in a closed form math solution. Then there has also been a considerable amount of testing to verify the mathematical derivations. The cracked condition that you are looking at is highly dependant upon the stress level immediately before the start of the failure, and that we have a pretty good ability to define/calc. But, as the crack starts, likely at some small defect in the pipe, the crack growth and shape become very indeterminate and are highly dependant upon the micro-structure of the pipe in the region of the crack starter. Also, the start of a crack would be highly dependant upon any secondary stresses, secondary effects of any sort from things like end caps, fitting joinery, etc.

 

[IRstuff]

Perhaps treat the cracks as slots and start with:

http://www.mathworks.com/help/physmod/hydro/ref/orificewithvariableareaslot.html?refresh=true

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=394381

http://cedb.asce.org/cgi/

http://WWWdisplay.cgi?108457

TTFN
faq731-376

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[racookpe1978]

IRStuff. Good idea. But only if the crack does not grow and split the pipe in half.

Seems far more likely to have a pit erosion or corrosion area - which is somewhat more like a circular orifice hole.

Leaking above ground or into loose soil (no resistance); or into rock or concrete? Flow resistance?

 

[LittleInch]

amiket,

There is a huge difference between a machined or cut rectangular slot and a "crack". Which is it?

Slots see above the excellent references by IR stuff, Cracks see dhengr - basically no chance as the shape and size is not regular enough for anyone to bother working it out.

Is this for a real life situation or just wondering? Any data to go with it?

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[amiket]

Thanks for all the suggestions. Treating it like a slot seems to be the best approach. We are trying to find a different method to estimate the area of underground cracks based on pressure and leakage rate.

 

[BigInch]

Normally it's the reverse; calculating a lost volume with a known hole diameter and an estimated pressure drop across the hole.