What is the Bernoulli Equation?

In summary, the Bernoulli principle, discovered by Swiss mathematician and physicist Daniel Bernoulli, states that as the speed of a fluid increases, the pressure within the fluid decreases. This principle is commonly observed in the lift force of airplane wings and the flow of water through pipes. It explains how airplane wings generate lift and has various practical applications in fields such as aviation, hydraulics, and medicine. However, it does have limitations, as it does not take into account factors like viscosity and turbulence.
  • #1
PhysicsGnome
8
0

Homework Statement


I recently was given an interesting problem I thought I'd share with the community here. It's a fun exercise in mathematics. Given the equation:

Po/P = [1+((k-1)/2)*Ma^2]^(k/(k-1))

From this stagnation ratio, derive the Bernoulli Equation:

Po = P + 1/2 * rho * V^2

Anyway, it's not for homework, so no real need to solve it. Hope you enjoy deriving equations as much as I do. Have fun!
 
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  • #2
what are k, M, a?
 
  • #3
k in this case is 1.4 (for air)

Ma is the mach number.
 

FAQ: What is the Bernoulli Equation?

What is the Bernoulli principle?

The Bernoulli principle states that as the speed of a fluid (such as air or water) increases, the pressure within the fluid decreases. This principle is often observed in the lift force of airplane wings and the flow of water through pipes.

Who is Bernoulli and what did he discover?

Daniel Bernoulli was a Swiss mathematician and physicist who discovered the principle that bears his name. In 1738, he published a paper on the relationship between fluid speed and pressure, which has since become known as the Bernoulli principle.

How does the Bernoulli principle apply to flight?

The Bernoulli principle explains how airplane wings generate lift. As air moves over the curved shape of the wing, its speed increases, causing the pressure on the top of the wing to decrease. This creates a pressure difference between the top and bottom of the wing, resulting in lift.

Are there any limitations to the Bernoulli principle?

While the Bernoulli principle is a useful concept in understanding fluid dynamics, it does have its limitations. For example, it does not take into account factors such as viscosity and turbulence, which can have a significant impact on fluid behavior.

How is the Bernoulli principle used in real-world applications?

The Bernoulli principle has a wide range of practical applications, such as in aviation, hydraulics, and ventilation systems. It is also used in medical devices like nebulizers and inhalers, which utilize the principle to create a fine mist for inhalation.

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