## This Bernoulli Stuff

*By Jeff Pardo*

*Published Date*

**speed up**! What's more -- unlike anything else you might try to cram into a smaller space (like intake air during the compression stroke of an internal combustion engine), when a

*fluid flow*is constricted, its pressure goes

**down**... not

**up**! I'm sure many of you have wondered just how it is that, as the air is moving faster, being squished (that's a technical term) it does so not at a higher pressure, but in fact a lower one! Why?

**THE MYTH OF LIFT**

For one thing, the statement that we've all read in ground school references, encyclopedias and physics texts, saying that air parcels traveling over and under a wing meet up again at the trailing edge is... just plain wrong! Actually, the truth is that with a high camber airfoil at near the maximum angle of attack, the air that travels over a wing can be accelerated to nearly twice the free-stream velocity! (Consider *that* the next time you wonder why bizjet manufacturers make such a big deal about top speeds that approach Mach 0.9.)

*Example*: If you inject pulses of dye in a wind tunnel, synchronized in a vertical line in front of an airfoil (see image below), you will see that the columns of dyed pulses traveling above the wing arrive at the trailing edge much *sooner* than their companion columns underneath.

It looks something like this:

**THE TRUTH OF LIFT**

That said, it is also true that a wing doesn't need to have any camber at all to develop lift. So, there's another factor involved in generating lift and this is Newton's Third Law of motion: Every action is accompanied by an equal and opposite reaction. The proverbial flying barn door will produce 'lift' by virtue of angle of incidence -- and enough power to tug it through the air -- as the molecules of air hitting it from below would cause 'impact pressure' and an upward 'lift vector.' After all, a rubber band powered balsa wood airplane flies, doesn't it? The truth on that one, dear reader, is mostly that it's basically Bernoulli, and not Newton. Here's a picture of a flying barn door airfoil:

Air is a continuous fluid, not a fusillade of molecule sized bullets hitting the wing. Although there IS impact pressure, it is not the main reason for our barn door slipping the surly bonds.

**FLUID CHARACTERISTICS**

Why IS it that a fluid which is obviously squished, rather than having a higher pressure (which is what you would intuitively expect) instead has a *lower* pressure?! Part of it is that air -- or any fluid -- has something we know as potential energy, and another thing we know as kinetic energy.

**LIFT -- BY THE NUMBERS... Hang On Tight**

Let's start out with pressure. It's a force per unit area (equation 1). If we multiply both numerator and denominator (the 'F' divided by the 'A') by a length dimension (call it 'D', for distance, in equation 2), we get work (or energy) divided by volume.

**POTENTIAL ENERGY*

P = F / A (1) P = (F . D) / (A . D) (2) P = Work / Volume*

*KINETIC ENERGY*

It turns out that 1/2 times mass times velocity squared is the kinetic energy of a physical object in motion. It looks like this:

KE = 1/2 . m . v2 (3)Well since density (usually represented by a lower case Greek letter, rho) equals mass per unit volume (4), if we solve for mass we get density times volume (5), or going one step further,

**density times area times length**(6).

ρ = m / V (4) m = ρ . V (5) m = ρ . (A . D) (6)If we consider everything we now have, instead of one half x mass x velocity squared, we get 1/2 times density times area times length times velocity squared (7).

KE = 1/2 . ρ . (A . D) . v2 (7) KE = 1/2 . ρ . v2 (8)And per unit of volume, it's just 1/2 x density x V-squared (8). There's the kinetic part. The sum total -- let's call it 'E' -- must never change. So if the sum of 'potential' (pressure) energy and motion-induced kinetic energy is constant (9), when one goes up, the other must go down. (Yes, even this is a bit over-simplified.)

E = P + (1/2 . ρ . v2) (9)

**NOT HAPPY WITH THE MATH-WEENIE VERSION?**

Well, think of it this way: When you turn on a faucet and a sink (or tub) starts filling up, what happens? Well a lot of things, but one is that water near the stream flowing in gets 'entrained' (OK sucked in) due to the viscosity -- cohesive forces -- of water. The same thing happens with air zooming over a wing. More air gets sucked in when a mass of high-pressure air moves towards an area of lower pressure. Another even simpler way to look at it, is that, since the air molecules above the wing have to travel a greater distance than the ones below it (in

*less*time, let alone the

*same*amount of time), they must be “stretched out”, kind of like a spring, and therefore the density is less there (and from that, the pressure, as well).

So, the next time you wonder why wings fly... well, that's why.