Bernoulli's and aerodynamic lift

Cecil's Columns/Staff Reports
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http://www.straightdope.com/mailbag/mairplanesfly.html

I think we all agree that lift is due to a pressure differential between two sides of a surface. It’s also true that any surface in an air flow has a boundary layer which is stationary with respect to the surface. One of the requirements for Bernoulli’s equation to hold is that the flow in the region of interest be “steady,” that is, that it be non-interactive (either with itself or a surface) and that the flow velocity be constant across a “Bernoulli tube” constructed in the region of interest. There must be no shear in the flow.

The flow in the boundary layer is not steady and so Bernoulli’s equation can’t be expected to hold there.

A common mistake in fluid dynamics is to say that in regions where the flow rate is high, the pressure is low; the higher the fluid velocity, the lower the pressure. To disprove this notion it is sufficient to examine closely a Pitot tube airspeed device. In this device, the ram pressure developed when the airflow is stopped is compared to another pressure, the free stream pressure. This is accomplished by connecting a differential pressure gauge between the tip of the tube and chamber opened to the flow by small holes whose areas are carefully placed to be parallel to the flow. The pressure in that chamber is the same no matter what the air speed is, even zero. As the aircraft changes speed, the pressure in this chamber stays the same.

A Venturi tube (see Venturi effect - Wikipedia ), approximates a Bernoulli tube and so the pressure in the constricted throat is lower than that at either flared end; Bernoulli’s equation holds approximately. The boundary layer’s effect can be ignored to first order.

In order for Bernoulli’s equation to be valid, there must be no entry or exit of fluid through the walls of the Bernoulli tube. This requirement is never met for an airfoil. As the air flows over the convex surface on the top, that flow entrains air from the main flow and a Bernoulli tube cannot be drawn.

  Charlie Crummer 
     charlie.crummer@gmail.com  :)
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Welcome to the Straight Dope Message Boards, ccrummer. Interesting comments, although I confess that as soon as “Bernoulli” is mentioned, my mind closes down.

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We have also agreed (at least not lately debated) that fluid pressure differential by lifting wing is reaction to fluid mass inertia, and not reaction to faster airflow.

Bernoulli holds for any fluid velocity differential. Yes it is possible to confine fluid velocity so that both velocity and pressure increases, but that does not negate Bernoulli’s principle.

A velocity differential is defined by boundary; no matter by solid or fluid. A vortex is fluid mass inertia balanced by pressure differential.

Peace
rwj