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Made by Manish Kumar.

Made by Manish Kumar.

"Look down at the veins tracing their way up your fingers. They are made of stardust. This is a truth rooted purely in science, one of the many that make the subject beautiful to me. However, it is a shame most science students will not realise this during the course of their studies. What could have been a passion for astrophysics becomes instead distaste for formulae of elliptical orbits students are unable to fully comprehend. Were I to change the way science is taught in institutes, I would encourage appreciation for the implicit over memorisation of the explicit, nurture understanding and curiosity for derivations over worship of formulae, and demonstrate practical applications to clarify ambiguous theory." - Sahr Jalil 2011

My friend Sahr, wrote this for our team's evaluation form to LUMS PSIFI 2012. The question was, "How would you change the way science is being taught in institutes?"

Science cannot be taught just based on theory, but it needs to be taught based on observation, something formula and rote-learning cannot teach. And this example, is perfect to reflect over this thesis.

## Step 1: Definition

Practical Applications:

An Aeroplane relies on Bernoulli's Principle to generate lift on its wings.

A Helicopter uses the same method to generate lift on its wings.

A Race-car uses Bernoulli's principle to stay on the ground (down force).

An Insecticide Spray also uses Bernoulli's Principle to spread out the spray over a larger area.

A Bunsen Burner

Simple Demonstrations:

Envelope Experiment

Ping Pong Ball Experiments

Balloon Experiment

Paper Experiment

Boomerang

Lets first look over one practical application and then demonstrations and then more practical applications. :)

**Signing Up**

Very Informative! (y)

L

Most of these practical examples would operate at high enough speeds so compressibility would be an issue, but for simple understanding, Bernouilli's Principle can be applied.

If you watch aeroplanes taking-off; they run along the ground then

lift the nose, Bernouilli's Principle doesn't slowly get 'em higher the faster they go.L

As the aircraft continues in it's ground roll, increasing in speed, the lifting force increases until it matches and then exceeds the weight of the airplane. If you have a long enough runway, you can take off without ever lifting the nose (flat takeoff) because you are generating enough positive lift. But to expedite this, the planes take advantage of both ground-effect (which generates an upwash of air that helps lift the plane) and use their flaps or tail to force a rotation, lifting the nose (although some planes are designed with a center of gravity (CG) such that upward lift will automatically force the nose up - planes with canards are great examples). When the nose lifts, you again rely on lift to continue off the ground and stay aloft.

L

when the proper simplifications have been made. I will explain in a moment, but I must point out that Bernoulli's Principle isused to explain flight, as I had explained several comments ago, but isnotuseful as a simplification, because (and here's the kicker) it's equations are valid in low-speed regimes (with minor correction factors). There's a very good reason every aerodynamics text worth it's salt begins with Bernoulli - all standard flow dynamics equations can be simplified down to the Bernouilli's Equation. That includes all forms of theNavier-Stokes Equations(which I would hope nobody would try to argue that they do not apply, as the N-S equations are the product of three centuries of advanced flow mechanics, visualiazation, and mathematics, are the basis of every commercial and research numerical simulations available, and can be proven in closed-form solution for several easily-tested flows) , RANS, all numerical CFD solutions, all averaged turbulence solutions, etc. Bernoulli's Principle is conservative with respect to conservation of energy, thereby making it adirect reduction of a fundamental law(i.e. irrefutable within it's limits of applications).Now, to the reason the smoke, which is carried by the air and can therefore be used to visualize the flow pathlines (not streamlines, not streaklines). Bernouilli's Principle states this: in an inviscid (frictionless), incompressible (no density variation), irrotational (non-vortical) flow, total pressure is conserved along a streamline. This is an Eulerian interpretation, which refers only to streams, but can be brought by following stream vectors to a Lagrangian (particle following) form, which brings in paths. Total pressure is defined as the summation of static pressure and flow potential energy; ergo, to be conserved, if potential energy (flow speed) increases, as it does over the top of an airfoil, static pressure must decrease, and vice versa. As I mentioned in my last comment, this is what generates the forces that eplunkett mentioned. Now this phenomena is a fine explanation of airfoil dynamics, lift generation, and flight (simplified) because the flow away from the airfoil cannot be disturbed by the wing, and as viewed by the moving airfoil is a potential flow. Close to the airfoil surface, yes, you have a boundary layer that starts as laminar at the leading edge, trips into turbulence at a separation point, and creates a wake after the trailing edge, but contrary to eplunkett's idea, the wake does not point down - if it did, it would have to disturb the air well below the wing, and as once the wing has passed there are no forces acting on that region to maintain the downward angle of the streamlines, they must never point down. Yes, in a real flow you will have some flow deflection, but as real flows have vorticity (they are not irrotational), corrections must be made to account for this - this deflection cannot be explained by Bernoulli's Principle in potential flow due to irrotational restrictions, but vorticity can be brought into the Bernoulli Equations to explain this.

Finally, drag, which is not and can not be explained by Bernoulli's Principle, because it applies to frictionless flow. This requires a correction, and as drag is based on skin friction that is inherently calculable in the boundary layer regime, we patch the boundary layer solution to the potential flow over the wing. Drag must be overcome by engine thrust - as eplunkett stated, the sum of the forces must be zero (this only applies to steady or static forces, but in aircraft cruise, we treat airflows as quasi-steady). Lift balances gravity - straight up and down - and drag balances thrust - straight forward and backward. If the streamlines pointed down after the wing, you'd have to have one more opposing force pointing upward and leaning back toward the tail, which does not exist.

Voila, you have elementary aerodynamics. Bernoulli's Equation in the potential regime + boundary layer solutions along the wing skin + wake models. This explains 95% of flows that occur below Mach 0.3, and with correction factors, can be extended to nearing Mach 0.85. Since the grand majority of commercial aircraft operate below Mach 0.85, this method is applicable. This is how aerodynamics was done in the 1950's, this is a cornerstone of Computational Fluid Dynamics (CFD) (since all CFD solvers must be able to solve potential flow models), and this is why Bernoulli's Principle is and will still be taught as a simple method to explain flight.

Now, feel free to pick all of that apart - as I have said, all of this analysis is done in simplistic terms subject to many restrictions. But as those restrictions can be removed only by applying empirical correction factors or utilizing numerical simulations, since there is no closed-form solution to the Navier-Stokes equations, this is how aerodynamics works from the bottom up. I can tell you that after 6 years in Mechanical and Aerospace programs of study at my university and 2 years of graduate research, everybody refers back to the Bernoulli Equations as a basis. If you can apply the simplifications to your model and you manage to violate Bernoulli, you have messed up your simulation. Simple as that.

Lemonie, as a fellow experimentalist, I would advise you watch some of Lumley's classic instruction videos and early flow visualization videos on Youtube. Some of the old FAA videos are also quite enlightening. Sorry if I sound angry or come on too strong in these posts, but as many of my professors and research team members have pointed out, anyone who scoffs at or ignores the basics and bases will forever cripple their understanding of the subject at hand.

1) For a cambered airfoil, the airfoil generates an upwash effect at the trailing edge for positive attack and a downwash for negative, due to vortices that grow over the suction surface being shed (outside of regimes of realizable vortex structures like Von Karman sheets).

2) One of the main principles of potential flow lies in the inability of particles to traverse across streamlines without an energy (force) input. As I mentioned before, if the air at the trailing edge deflects downward considerably, eventually it must meet the "freestream" air that is unaffected by the airfoil, which is modeled as a uniform potential flow (ignoring wind and wash). If you separate the streams of freestream and airfoil-traversing air, as is done in the "patching" methods of boundary layer + Bernouilli's + potential freestream, when the airfoil-traversing air reaches the freestream, it cannot cross the streamlines in the freestream, because no external force is acting upon the airfoil stream at that point to continue their downward deflection. Thus, as it reaches the freestream streamlines, the airfoil streams must turn to match the freestream.

Here's where both of our points meet halfway, though - my explanation refers to far-field effects, before and after the airfoil has passed, while your deflection phenomena is a near-field effect, directly at the trailing edge. In my regime, Bernoulli's Principle is applicable because of the potential flow assumption (which holds very well for uniform freestream flow), but in your regime, unless the aircraft is flying at a very low Reynolds number (or the airfoil is a of very special laminar design class), the trailing edge and wake are turbulent, and Bernoulli's Principle can not be applied without liberal corrections. So yes, directly at the trailing edge of the airfoil, you will see a downward deflection, but this region can not be considered in my argument - this would be implicit in the wake models and boundary layer models that need to be added to potential flow / Bernoulli's Principle equations for the far-field. Additionally, as air is never truly incompressible, the effects of any downward deflection can be naturally damped by compressibility effects, reducing the visibility of these deflections - similarly, the wake of the wing will damp out far behind the trailing edge (although the length scale there can be several airframe lengths) and collapse back into the freestream flow.

If you've been out of aerodynamics for a while, take a look back at the Lanchester-Prandtl Lifting Line theorem derivations and compare against thin-airfoil and thin-plate solutions. Most of these derivations include a boil-down to the methods I described above, since this chain can be used to predict many airfoil solutions to within 80% or so accuracy of numerical solutions, depending on the assumptions, flow structures, and how the solutions are patched - not a bad basis, especially since in the first half of the 1900's, these were the only tools available in closed-form. By the way, it's not that the N-S equations boil down to Bernoulli's Principle per se, but rather the N-S equations inherently hold Bernoulli's Equations in their analytical form. Yes, algebraically, you can reduce N-S to Bernoulli if you apply the right substitutions, boundary conditions, and assumptions, but it's more important that under these restrictions, N-S will always give the exact same solution as Bernoulli, because both are derived from fundamental equations.

L

http://en.wikipedia.org/wiki/Iomega_Bernoulli_Box