The Hole In The Wall Gang


Butch Cassidy and The Sundance Kid, move over! This not about you two.  It is a mystery, one that started taking shape in 1839.  Even today, not all agree on the solution.

I’ll try to keep this as non-technical as I can, but it may be somewhat daunting for the casual reader. If you don’t find it interesting, I won’t take offense.


This is about the flow of fluid through a hole in a wall, in other words, an orifice.


I was going to say, Since The Dawn of Man, but I don’t think we have to go back that far.

1839 — Adhémar Jean Claude Barré de Saint-Venant (now there’s a name for you) and Pierre Laurent Wantzel developed the first correct compressible flow equations for ideal flow in a nozzle.  Tests seemed to show that there is a limit to the flow that can get through the hole.  If you divide the upstream pressure into the downstream pressure, the resulting pressure ratio appeared to not produce higher flow once that ratio reached 0.4.

1885 — Osborne Reynolds independently derived the same equations and theorized (no test data as far as I know) that the flow is limited by the speed of sound through the orifice.

1916 — Lord Rayleigh (born John William Strutt) figured that things were not resolved and asked a guy named Hartshorn to dig into it.  Sorry to say that there are so many Hartshorns around, I’m not sure which one he is.  I’ll keep looking for him.  At any rate, his tests showed that there was no choke point at the sonic pressure ratio.  In fact he saw increased flow all the way down  to a pressure ratio of 0.2.

1926 — Stanton pointed out that the orifice vena contracta changes in size, depending on the pressure ratio, and he had photos to prove it.

[I know, you’re wondering what a “vena contracta” is.  Without too many words, the flow coming out of an orifice is “pinched” to a size that is smaller than the actual hole size, and the issue is that the amount of pinching is affected by the pressure ratio — the smaller the pressure ratio, the bigger the flow area of the vena contracta.]

1945 — Chester Smith published an article that set things back.  He claimed that the flow was limited by the actual hole size and the speed of sound, thus ignoring the change in the size of the vena contracta.  And you can’t even criticize his work because he says it wasn’t his!  He says he learned this from V. Petrovsky, but you can’t even question Mr. Petrovsky because he had died prior to the publishing of the article.

This is the so-called “choked flow” theory of orifice flow.  It shows up in some textbooks.  It’s what they taught me in college.  And, amazingly enough, it is still in use, even though it has been thoroughly disproved since 1926.  Check the Internet.  You’ll still find people who believe it.

1949 — Perry, and back to sanity.  His Masters Thesis shows test data for small diameter ratios (orifice diameter divided by pipe diameter).  Chester Smith missed the mark.

1951 — Grace and Lapple developed an equation covering flow for small diameter ratios.

1951 — Cunningham expanded the known data to a wide range of orifice diameter ratios.


Now you can sit around and argue over this, but the fact remains that there is a lot of good test data that shows the idea of “choked flow” in orifices is simply wrong.  No one is saying that the speed of sound is not involved, but what the data shows is that the size of the vena contracta varies with pressure ratio.  It’s no “CHOKE”!

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