Quick question regarding bernoullis principle

In summary, Bernoulli's principle states that as the velocity of air or fluid increases, the pressure decreases. This can be seen in applications such as Venturi tubes, atomizers, and engine carburetors. For an aircraft wing, the upper surface is convex while the lower surface is flat, creating an airfoil shape. This shape causes air to accelerate over the upper surface, resulting in lower pressure and a net upward force, or lift, on the wing. However, Bernoulli's Law is commonly misunderstood and derived from the concept of conservation of energy, rather than the principles of pressure gradients and deflection of air.
  • #1
HelloMotto
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Ok I've just started learning about Bernoulli's principle so I don't have that much knowledge of it..
so anyways I know that as the velocity of air or fluid increases, the pressure decreases. In order for the velocity of the fluid to increase, there has to be like a constriction thingy.. I've searched google and all the examples i got was a narrow tube.

so my question is where is the constriction on a wing of an airplane?
 
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  • #2
HelloMotto said:
So my question is, where is the constriction on a wing of an airplane?

The examples you found with the constriction are things like Venturi tubes. This particular application of B's Principle, BTW, is the central gimmick for devices like atomizers (such as spray can nozzles) and engine carburetors (which were in fact inspired by perfume atomizers).

Anything that forces an acceleration of the fluid will work this way. For an aircraft wing, the upper surface is convex, while the lower surface is (nearly) flat. Air flowing over the upper surface, as the wing is pulled through the atmosphere, is caused to speed up relative to the air flow on the underside, thereby lowering the air pressure on the upper surface. The result is a net upward force on the wing, called the "lift".

Such a cross-sectional design for a wing is referred to as an airfoil [try googling that for more info]. BTW, humans didn't invent that -- the cross-sections of birds' wings are shaped that way (da Vinci noted that over 500 years ago); it's just one more example of inspired human copying...
 
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  • #3
Teachers and textbook writers have long misunderstood Bernoulli's law resulting in generations of confused students, some of whom have become teachers and textbook writers and continued the misunderstanding.

For a comprehensive explanation of the misunderstanding see http://user.uni-frankfurt.de/~weltner/Mis6/mis6.html (thanks and acknowledgments to Weltner and Ingelman-Sundberg).

Misunderstanding arises because two key concepts are commonly overlooked. They are both expressions of Newton's Second Law of Motion [itex]\textbf{F} = m\textbf{a}[/itex], applied to a fluid:
  • Acceleration of air is caused by pressure gradients. Air is accelerated in direction of the velocity if the pressure goes down. Thus the decrease of pressure is the cause of a higher velocity.
  • Pressure gradients perpendicular to the streamlines are caused by the deflection of streaming air. The deflection of air generates regions of lower and higher pressure according to the curvature of the streamlines
Text books commonly derive Bernoulli's Law from “conservation of energy”. This is not wrong but, by ignoring the first key concept, allows Bernoulli's Law to be misinterpreted as saying that lower pressure is caused by a higher velocity. The next step in bamboozling the student is to give examples of the second key concept as examples of Bernoulli's Law in action, such as spin, levitating balls, lifting pages and how aeroplane wings work.
 
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Related to Quick question regarding bernoullis principle

1. What is Bernoulli's principle?

Bernoulli's principle is a fundamental concept in fluid dynamics, which states that as the speed of a fluid increases, its pressure decreases. This principle is based on the conservation of energy and is used to explain various phenomena such as lift in airplane wings and the flow of water through pipes.

2. How is Bernoulli's principle applied in everyday life?

Bernoulli's principle is applied in many everyday situations, such as in the design of airplane wings, which are curved on the top and flat on the bottom to create a difference in air pressure, resulting in lift. It is also used in the design of carburetors in cars, where the faster flow of air over the top of a narrow tube creates low pressure, drawing fuel up from the bottom.

3. What are the limitations of Bernoulli's principle?

Bernoulli's principle is based on certain assumptions, such as the fluid being incompressible and the flow being steady and frictionless. In real-life situations, these assumptions may not hold, leading to deviations from the predicted results. Also, Bernoulli's principle only applies to fluids in motion, and cannot be used for stationary fluids.

4. How is Bernoulli's principle related to the continuity equation?

The continuity equation states that the mass of a fluid in a closed system remains constant, and is related to Bernoulli's principle through the conservation of energy. As the velocity of a fluid increases, its pressure decreases, but the mass flow rate must remain constant for a closed system. This relationship is expressed mathematically in the continuity equation.

5. Can Bernoulli's principle be applied to gases?

Bernoulli's principle can be applied to both liquids and gases, as long as the assumptions hold true. However, in gases, the change in pressure is not solely due to a change in velocity, but also due to a change in density. This is known as the compressibility factor, and it must be taken into account when applying Bernoulli's principle to gases.

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