Pressure and Lift

When we consider the forces acting on a wing,

for example, the lift force is proportional to the average pressure difference acting over

the lower and upper surface of the wing. This pressure difference is caused by the fact

that the average velocity over the upper surface of the airfoil is somewhat greater than

the average velocity over the lower surface (remember that a higher velocity corresponds

to a lower pressure). The pressure differences are usually small, but wings

have a large surface area so that the total lift force can be very large (a fully loaded 747

can weigh as much as 500,000 lbf). For low Mach number flow, the pressure difference

and the lift force are proportional to the difference in the dynamic pressures between the upper and lower surfaces of the airfoil.

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which depend on intermolecular cohesion, are usually extremely small.....

Because fluids cannot support shearing stresses, it does not follow that such

stresses are nonexistent in fluids. During the flow of real fluids, the shearing

stresses assume an important role, and their prediction is a vital part of engineering

work. Without flow, however, shearing stresses cannot exist, and compression stress or

pressure is the only stress to be considered (Elementary Fluid

Mechanics, 7th edition, by R.L. Street, G.Z. Watters and J.K. Vennard, John Wiley \&

Sons, 1996).

So we see that the most obvious property of fluids, their ability to flow and

change their shape, is precisely a result of their inability to support shearing stresses.

Flow is possible without a shear stress, since differences in pressure will cause a fluid

lump to experience a resultant force and produce an acceleration, but when a fluid is

deforming its shape, shearing stresses must be present.

With this definition of a fluid, we can recognize that certain materials that look like

solids are actually fluids. Tar, for example, is sold in barrel-sized chunks which

appear at first sight to be the solid phase of the liquid which forms when the tar is

heated. However, cold tar is also a fluid. If a brick is placed on top of an open barrel

of tar, we will see it very slowly settle into the tar. It will continue to settle as time

goes by --- the tar continues to deform under the applied load --- and eventually the brick

will be engulfed by the tar. Even then it will continue to move downwards until it reaches

the bottom of the barrel. Glass is another substance that appears to be solid, but is

actually a fluid. The glass flows under the

action of its own weight. If you measure the thickness of a very old glass pane you would

find it to be larger at the bottom than at the top of the pane.

This deformation happens very slowly because the glass has a very high viscosity,

and the results can take centuries to become obvious.

Another example: silly putty behaves like an elastic body when subject to rapid stress (it bounces like a ball) but it has fluid behavior under a slowly acting stress (it flows like a fluid under its own weight).