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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

The Bernoulli's Principle was a physics principle formulated by Daniel Bernoulli that an increase in the speed of a fluid produces a decrease in pressure and that a decrease in the speed of a fluid produces an increase in pressure. The principle states that the total energy of a moving fluid remains constant at all times. Therefore fluid pressure is inversely proportional to fluid velocity. 

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

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

Step 2: Practical Application : Airplane and Helicopter Wings

An airplane is designed in such a way so that it can be lifted easily while take off. The wings of the plane are designed in a streamlined shape. While taking off, air travels with a greater velocity over the wings than under the wings. The greater velocity creates a lower pressure area over the wings. A lower velocity creates a higher pressure under the wings. This pressure difference, makes the airplane climb higher and higher. The Pictures explain the same principle. Therefore Airplanes and helicopters use Bernoulli's Principle to climb. 

Step 3: Demonstrations : Paper Airplane

Materials Needed: Paper, Scissors

Everyday, someone designs a new paper airplane but not every plane is able to fly properly and go higher using Bernoulli's Principle. After bending a piece of paper into the respective folds, we are supposed to get a plane that it thicker from the front and thinner from the end. This helps to give the paper plane better lift. 

Another Way of demonstrating this experiment is to make two paper airplanes of the same paper and structure and then cutting one from the ends as shown in the pictures. 

Airplane 1 : No cutting.
Airplane 2 : Cutting

We notice that Airplane 2 actually lifts and then lands showing a parabolic curve. Airplane 1 just shows a downward movement.

Step 4: Demonstrations : Blowing Over Paper

Materials Needed : Paper, Scissors

A stream of air over the paper creates a low pressure zone which lifts the paper due to the pressure difference: higher pressure under the paper and lower pressure over the paper. This levitates the paper in the air.

Step 5: Demonstrations : Tissue Paper Hair Dryer or Leaf Blower

Materials Needed: Tissue Paper Roll, Blow Dryer, Metal Rod

Slip a thin rod through the hole in a toilet tissue paper role. Have one person hold the rod by placing a hand on each side of the toilet paper roll. Then switch on the blow dryer and watch the magic. This is Bernoulli's Principle which lets the tissue paper fly high up in the air without falling. 

Step 6: Demonstrations : Ping Pong Ball Experiment 1

Materials Needed: Ping Pong Ball, Blow Dryer

A ping pong ball can be "floated" on a stream of air. The air rushing around the ball creates a pressure low enough to lift and support the ball. Even when the ball is not exactly over the air source! As long as the low pressure spot is under the center of mass of the ball, it will stay "afloat". And the high pressure regions around the ball push the ball in if it tries to escape the low pressure zone. 

We can repeat the same experiment using a balloon using a lower blow dryer power.

Step 7: Demonstrations : Ping Pong Ball Experiment 2

Materials Needed : Ping Pong ball, Paper, Tape

In this experiment, we need to create two types of funnels. One will be a cylinder of the exact same radius of the ping pong ball itself and the other will be made in a cone shape. We now need to place the ping pong ball in both funnels and blow out from one end. The ping pong ball shoots out from the cylinder but not the cone shaped funnel. 

When the ping pong ball is placed in the cone shaped funnel with the air blowing out, the ball won't fall out of the funnel. The rushing air creates an area of low pressure that holds the ball in place. 

Step 8: Demonstrations : Boomerang!

Most boomerangs are designed in a shape which helps them to stay in the air without falling and come back to the place from where thrown.  A boomerang has “arms” shaped like airplane wings which create lift. The boomerang is moving forward and the boomerang is spinning thus creating an uneven lift. The uneven lift created by the spinning boomerang makes it turn (like leaning on a bicycle)—and keep turning until it makes a circle and comes back to you.

Step 9: Demonstrations : Envelope

Blowing air over the open end of an envelope causes the two sides to separate due to the lower pressure of the flowing air. This happens because air from the high pressure regions surrounding the envelope rushes towards the lower pressure area thus opening the envelope and temporarily inflating it. 

Step 10: Practical Applications : Race Car

A Race Car, in fact almost all cars are designed in a way to avoid lift and stick to the ground at all times. We wouldn't want cars just suddenly rising up due to high velocity. So keeping in mind the Bernoulli Principle scientists designed cars in a way completely opposite to that of an airplane. A race car employs Bernoulli's principle to keep its rear wheels on the ground at all times while travelling at high speeds. A race car's spoiler—shaped like an upside-down wing, with the curved surface at the bottom—produces a net downward force, thus keeping the car to the ground. 

Step 11: Practical Applications : Insecticide Spray

When the plunger is pushed in, the air flows at a high velocity through a nozzle. The flow of air at high velocity creates a region of low pressure above the metal tube. The higher pressure of the atmospheric air acts on the surface of the liquid insecticide causing it to rise up the metal tube. The insecticide leaves the top of the metal tube through the nozzle as a fine spray.

Step 12: Practical Applications : Bunsen Burner

When the Bunsen Burner is connected to a gas supply, the gas flows at high velocity through a narrow passage in the burner, creating a region of low pressure. The outside air, which is at atmospheric pressure, is drawn in and mixes with the gas.
The mixture of gas and air enables the gas to burn completely to produce a clean, hot, and smokeless flame.

Step 13: Ending

So, there we have it; Bernoulli's Principle. It is quite surprising that such a small and simple physics principle is used almost every second in our daily lives. I hope the videos helped. :)

Thank You. :) Please rate this article and leave a comment. 

Manish Kumar
Sahr Jalil
<p>Hi, my name is Integza and i have a education channel on youtube.</p><p>I have a video explaining the Bernoulli's principle, is very graphical and easy to understand because doesn't use much technical terminology:</p><p>https://www.youtube.com/channel/UC2avWDLN1EI3r1RZ_dlSxCw?sub_confirmation=1&amp;feature=iv&amp;src_vid=t7MsYZgtXXo&amp;annotation_id=annotation_4127173749 </p>
<p>As I commented under your Bernoulli video, you work too hard to justify Bernoulli. The pressure is higher in the large section because there is a constriction where the diameter reduces. The pressure in the smaller section is lower because it is free to flow away from the higher pressure region. If you view the smaller section as simply a hole in the pressurized large section (view it as a pressurized tank), the fluid easily escapes out this &quot;hole&quot; to the lower pressure region. It is pressure differences that cause accelerations in a fluid. A higher pressure region represents a force (F) that pushes (accelerates A) the mass (M) of air toward a lower pressure region. F=MA.If you have a gradual change in diameter, the momentum description is not valid.</p><p>-- </p><p>Cheers</p>
<p>The majority of these demos are classical misinterpretations of the applicable science as well as Bernoulli's actual Principle. Some of the other comments bring-in many things including math which DOES NOT explain the physics/science.</p><p>The true physics is not difficult to understand if you can get all these misconceptions out of your mind.</p><p>Speed of a fluid DOES NOT create a lower pressure. </p><p>Speed past a surface (or visa versa) does not create a lower pressure. </p><p>Bernoulli mentions neither of these. </p><p>If a stream of fast air did have a lower pressure than surrounding air, then, the fast stream would be squeezed narrower and narrower by the higher pressure around it as long as it moved and this simply does not happen.</p><p> Pressure at a point in a fluid acts in all directions; can't violate that. Therefore, the pressure in the stream (at its outer boundary) pushes out with the same pressure as the atmospheric pressure outside it pushes inward.</p><p>Paper airplanes (flat balsa wings and Wright Bros wings) have no curved, 'LONGER' upper surface, so this well known bad explanation has a serious problem.</p><p>The lifting paper and tissue paper/leaf blower are a curved airflow followed by entrainment (from viscosity).</p><p>This floating ball explanation is messed up. If the pressure was lower UNDER the ball it would not be held up. Then, It is centered by curved airflow.</p><p>The atomizer (insectide spray) is due to a curved airflow (commonly called &quot;turning&quot; of the air) over the vertical tube's end.</p><p>The Bunsen burner is due to entrainment (viscosity).</p><p>The envelope opens because you blow air into it, thus increasing the internal pressure.</p><p>Air has mass and a force is required to accelerate mass (even air). That force is pressure (difference) and pressure alone. </p><p>A CURVED AIRFLOW requires a force because this is an acceleration. This force can only be a pressure difference. That pressure difference is from the relative motion of fluid and object.</p><p>Pressure differences are created DIRECTLY by the relative motion between fluid and object. [no Bernoulli &quot;fast&quot; air, no half venturi pinching, no other false science]. Walk through water and feel how you must push some water around! You create a higher pressure in front of you by pushing on the water (and lower pressure behind by moving away from water). THAT'S WHAT CREATES THE PRESSURE CHANGES.</p><p>That pressure difference (cause) accelerates water (effect) around you. A higher pressure region accelerates (pushes) air toward any (and all) lower pressure regions. The same thing applies to wings and air: except, to our advantage, the higher pressure is under the wing; lower above. </p><p>These very same pressure differences then cause all of the the fluid accelerations we see around a wing. Anything else is bad science and violates Newton.</p><p>This simple concept explains all the air flows around the wing (including the up-wash and down-wash). </p><p>The air above and below a wing are unrelated and Bernoulli can not be used to compare velocities and pressures. Therefore, saying the upper air is lower pressure because of the difference in speed to the lower air is completely false science and terrible math. Bernoulli deals with accelerations and pressures that occur along a single path (streamline).</p><p>Again: A higher pressure region accelerates (pushes) air toward any (and all) near-by lower pressure regions. </p><p>Also, it is the path the air is forced to take by the wing that is what you should focus in, not simply the wing's shape. </p><p>Finally, (once you fully understand it, it'll be no surprise that) from the siationary air's frame of reference, the fastest moving air around a wing is UNDER it ! This is easily shown on real wings. This blows the &quot;fast-air-has-lower-pressure-than-some-nearby-slower-air&quot; out of the water. That is a serious and long standing misunderstanding by amateurs, but not those in the field.</p><p>Don't believe me. </p><p>For a better understanding of the true physics, see these authoritative references:</p><p>Krzysztof Fidkowski How Planes Fly</p><p>https://m.youtube.com/watch?v=aa2kBZAoXg0 </p><p>David Anderson:</p><p>https://m.youtube.com/watch?v=hQ99JkaOwEk </p><p>Babinsky;</p><p>https://m.youtube.com/watch?v=XWdNEGr53Gw </p><p>McLean (though he gets rather heavy later in the video):</p><p>https://m.youtube.com/watch?v=QKCK4lJLQHU</p><p>Regards, Steve Noskowicz</p><p>Science &amp; Technical Advisor</p><p>challengerillinois.org</p>
The discussion between valhals_end and lemonie/eplunket was AWESOME!!! way to go Valhalas_end.
<p>Thank you, this really helped with my homework. 8/8!</p>
<p>Very Informative! (y)</p>
The curves :)
If&nbsp; airplanes relied upon Bernoulli's Principle, they wouldn't be able to fly upside-down would they?<br> <br> L
If they only flew in an incompressible (and ideal) flow regime, then technically yes, depending on the airfoil shape - there are symmetric wing designs that allow low-speed airfoils to fly upside down (but you can't neglect the fuselage and tail influences on aerodynamics when you extend from infinite-wing studies - see Prandtl Lifting Line theorems on airfoils - to fully 3D flow over airplanes). Most wings see compressible flow, though (if not fully spread across the wing, like in high transonic or supersonic flow, then in pockets of influence, which can be forced to occur on special airfoil designs down to Mach 0.3), where Bernouilli's Principle is superseded by compressible gas dynamics.<br><br>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.
It isn't right.<br> If you watch aeroplanes taking-off; they run along the ground then <u>lift the nose</u>, Bernouilli's Principle doesn't slowly get 'em higher the faster they go.<br> <br> L
Ahh, but you are missing a crucial point there - the aircraft's weight and center of gravity / centroid / center of inertia. Howtowithmanish is correct that during take-off, Bernouill's Principle does apply (the aircraft is moving at a low enough speed / Reynold's number for compressibility to not be an issue). The bottom of the wing is developing increasing pressure while the air above the top drops in pressure, developing a pressure and suction surface on the bottom and top, respectively. This generates lift (upward force normal to the wing's span). That's all Bernouilli's Principle is for - creating lifting force.<br><br>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.
It's not best explained by Bernouill's Principle; if you look at landing-flaps and how hydrofoils work in exactly the same way, then you realise that it's an old explanation that still kicks-around in text-books and word-of-mouth...<br> <br> L
Is sad that Bernoulli's principle is still being used to explain flight. Especially when the explanation is even easier. The sum of the forces equal zero. That's it. If the air is holding the plane up, then the plane must be pushing the air down. The figures that show airfoils with the air coming straight off the back are misleading. The air has to come off pointed down.
Oi, sorry, but that is painful to read. First off, look at the image below - you can clearly see smoke streaming around the airfoil and coming off in straight lines. This is a <a href="http://www.dept.aoe.vt.edu/~devenpor/aoe3054/manual/expt1/index.html" rel="nofollow">standard flow visualization</a> that is completely definable by the Bernoulli's Principle <em>when the proper simplifications have been made</em>.&nbsp; I will explain in a moment, but I must point out that Bernoulli's Principle is <strong><em>not </em></strong>used to explain flight, as I had explained several comments ago, but is <em>useful as a simplification</em>, because (and here's the kicker) it's equations are valid in low-speed regimes (with minor correction factors).&nbsp; 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.&nbsp; That includes all forms of the <strong>Navier-Stokes Equations </strong>(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.&nbsp; Bernoulli's Principle is conservative with respect to conservation of energy, thereby making it a <em>direct reduction of a fundamental law</em> (i.e. irrefutable within it's limits of applications).<br> <br> 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).&nbsp; Bernouilli's Principle states this: in an inviscid (frictionless), incompressible (no density variation), irrotational (non-vortical) flow, total pressure is conserved along a streamline.&nbsp; 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.&nbsp; 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.&nbsp; As I mentioned in my last comment, this is what generates the forces that eplunkett mentioned.&nbsp; 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.&nbsp; 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.&nbsp; 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.<br> <br> Finally, drag, which is not and can not be explained by Bernoulli's Principle, because it applies to frictionless flow.&nbsp; 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.&nbsp; 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).&nbsp; Lift balances gravity - straight up and down - and drag balances thrust - straight forward and backward.&nbsp; 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.<br> <br> Voila, you have elementary aerodynamics.&nbsp; Bernoulli's Equation in the potential regime + boundary layer solutions along the wing skin + wake models.&nbsp; This explains 95% of flows that occur below Mach 0.3, and with correction factors, can be extended to nearing Mach 0.85.&nbsp; Since the grand majority of commercial aircraft operate below Mach 0.85, this method is applicable.&nbsp; 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.<br> <br> 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.&nbsp; 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.&nbsp; 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.&nbsp; If you can apply the simplifications to your model and you manage to violate Bernoulli, you have messed up your simulation.&nbsp; Simple as that.<br> <br> Lemonie, as a fellow experimentalist, I would advise you watch some of <a href="http://www.youtube.com/watch?v=Xg6L-dnUZ8c&lr=1" rel="nofollow">Lumley's classic instruction videos</a> and early flow visualization videos on Youtube.&nbsp; Some of the <a href="http://www.youtube.com/watch?v=_LXW3pHNn_U&feature=related" rel="nofollow">old FAA videos</a> are also quite enlightening.&nbsp; 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.
They also say to never argue with an engineer. I tend to agree with that - that entire argument took me only 5 minutes to formulate, and I never even had to reference the 30 or so aerodynamics, fluid mechanics/dynamics, and CFD texts I have sitting on my shelves next to my computer. Believe me, I argued many of the points you and eplunkett raised way back in intro classes - my professor's must have enjoyed my naturally competitive and argumentative nature - and was always shot down by simple explanations drawn in minutes.
Its been almost 7 year since I graduated with my aero degree. Since then I've been exclusively working on aircraft structures. So knowledge as to whether or not the N-S equations ultimately boil down into some form of bernoulli's principle was dumped from my brain years ago. What I do know if that if the air imparts a force on the plane (lift), the plane has to impart a force on the air (downward motion). I realize the photo you included shows the streamlines (or pathlines... not sure of the difference in terminology) at the start and finish at approximately the same angle. That figure was not accompanied by the lift data, so it could be at zero lift. NASA has <a href="http://http://www.grc.nasa.gov/WWW/k-12/airplane/right2.html" rel="nofollow">a website and applet</a> that give a simplified explanation for why airplanes fly. I haven't ready the whole site, but the applet is a nice visual. I was also not saying that some form of bernoulli's was not at play at all. Sure, the upper surface does measure a lower pressure. My problem is that the principle is often misrepresented, for example, the idea of equal transit time over the upper and lower surface, or a venturi effect, both of which can be easily disproved.&nbsp;
I agree fully with your last point - the transit time is not the same, and can not be, as velocity of the air stream over the top has to increase to create a suction surface. But the argument that flow turning is what generates lift is not entirely valid for commercial aviation for one main reason (by the way, the image shows a cambered airfoil at zero angle of attack, which by definition of not being symmetric generates lift - I do not know the relative magnitude, but a NACA 2412 has positive lift at zero angle of attack...if I remember the charts right, I believe the CL value to be around 0.1 to 0.3 for low Re flow). If you study turbomachinery (aircraft compressors, fans, or propellers), you will often see very large air turning angles (sometimes reaching 90 degrees in impulse turbines, or between 30 and 50 degrees for lower power axial turbines), but these are achieved by inputting (compressor) or extracting (turbine) massive amounts of power from high-speed (in a rotating frame) flows, regardless of the flow type. For external aerodynamics, there is no large energy change - gravitational forces are minute compared to high-speed turbine shafts - so the relative amount of turning compared to the airfoil camber is necessarily small. This is also partially due to two phenomena: <br>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).<br>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 &quot;freestream&quot; 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 &quot;patching&quot; 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.<br><br>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.<br><br>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.
Yes! thanks for the contribution.<br> <br> L
Back in the late 80's there was a computer storage solution that relied on Bernoulli's Principle.<br><br>http://en.wikipedia.org/wiki/Iomega_Bernoulli_Box

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Bio: I am an A-Levels Student at Karachi Grammar School, Pakistan. My passion is physics and mechanics and I want to be a Mechanical Engineer in ... More »
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