### Re: How does a funnel affect the force of wind?

Date: Fri Jun 8 17:13:11 2001
Posted By: Stephen Murray, Physicist
Area of science: Physics
ID: 990808282.Ph
Message:

Hi Jim,

A 60 mph wind is highly subsonic, which means that we can pretty much ignore any effects of compressibility, and use the (simpler) results for compressible fluids.

If all you were interested in was a tube of 1 m2 cross section that narrowed down to 0.25 m2, then it would be quite easy, and the solution could be found in the fluid dynamics chapter of a text such as Halliday, Resnick and Walker. For an inviscid, incompressible fluid in steady state flow (nothing changing with time), conservation of mass requires that Av=constant, where v is the fluid velocity and A is the cross- sectional area of the tube. Bernoulli's equation (essentially conservation of energy) gives us P + 0.5rv2+rgy=constant, where P is the pressure, r is the fluid density, g is the acceleration of gravity, and y is the height above some reference point. These two equations would tell you how the fluid accelerates and the pressure decreases in the constricted tube.

The problem which you're posing sounds more like a funnel embedded in what would otherwise be an infinite, uniform wind. That's a problem of the ilk encountered by aeronautical engineers. One of my colleagues with such a background suggested a couple of classic texts which may be of help to you. One is "Mechanics of Fluids," by Irving Shames, and the other is "Boundary Layer Theory," by Schlichting. The results will depend heavily upon the viscosity of the air and the length of the pipe, which will determine whether or not the boundary layers grow sufficiently to overlap and dominate the problem.

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