# Bernoulli's Principle: Does it affect a non-flowing fluid in a moving container?

• woodfich
In summary: The pressure difference on the outside would cause the gas to flow in. The pressure difference would be highest in the rear of the aircraft for forward acceleration, due to the momentum of the air molecules and relative velocities of the molecules to the aircraft. Think of the molecules as birds flying around in the plane. As the plane accelerates to velocities close to those of the birds, they will start piling up at the back. From PV = nRT, assuming no change in temperature (T) or volume (V) (rigid airframe), more molecules (n) in the rear means higher pressure (P).
woodfich
Does Bernoulli's Principle affect a non-flowing fluid in a moving container?

As in, if I am in an air-sealed airplane at rest, and then the plane accelerates on the ground (but does not fly), does the gas pressure inside the plane change because the fluid (air inside the cabin) has a velocity with respect to the air outside?

Thanks.

woodfich said:
Does Bernoulli's Principle affect a non-flowing fluid in a moving container?
I believe you mean, "Does Bernoulli's Principle apply to a non-flowing fluid in a moving container?" The answer is no, but there is another effect. There will be a pressure on the walls of the container. From your perspective (sitting inside the plane), the air is not moving, and the walls of the plane are not moving, so the air inside the plane is stationary w.r.t. the walls of the plane. However, the air outside the plane is rushing past, so the pressure on the outside of the wall is less than the pressure on the inside. It is about the relative motion of the air w.r.t. the surface.

I thought Bernoulli's Principle only applied to flow along a streamline?

Anyway, my guess is that there would be a pressure gradient, highest in the rear of the plane for forward acceleration, due to the momentum of the air molecules and relative velocities of the molecules to the aircraft. Think of the molecules as birds flying around in the plane. As the plane accelerates to velocities close to those of the birds, they will start piling up at the back. From PV = nRT, assuming no change in temperature (T) or volume (V) (rigid airframe), more molecules (n) in the rear means higher pressure (P).

No. Bernoulli principle is a statement about conversation of energy, where the total energy of a fluid or gas is considered to be the sum of pressure, kinetic energy, and gravitational energy. Generally temperaure is ignored. In an idealized situation, the energy can be converted between pressure, kinetic, and gravitational without peforming any work, so the energy remains constant. If gravitational energy isn't changed, then pressure change of a mass of air is inversely proporpotional to the (velocity change)^2 (KE = 1/2 m v^2) of that air.

The key here is that it's how the speed of the air is changed, not the actual speed or relative motion. If the speed is changed with virtually no work involved, then Bernoulli applies.

turin said:
It is about the relative motion of the air w.r.t. the surface.
The relative motion doesn't matter, it's how the relative motion was created.

If part of the surface of a solid moving through the air doesn't disturb the flow of the air, then a "static port" (hole) can be placed at that surface and the pressure inside a chamber connected to the static port will be virtually the same as the static pressure of the still air, even though the surface is moving with respect to the air. The relative motion between solid and air doesn't affect the pressure.

http://en.wikipedia.org/wiki/Pitot-static_system

woodfich said:
Does Bernoulli's Principle affect a non-flowing fluid in a moving container?

As in, if I am in an air-sealed airplane at rest, and then the plane accelerates on the ground (but does not fly), does the gas pressure inside the plane change because the fluid (air inside the cabin) has a velocity with respect to the air outside?

Thanks.

The air inside is in motion w.r.t the air outside, but not w.r.t. the walls of the aircraft. What would drive the interior flow?

## 1. What is Bernoulli's Principle?

Bernoulli's Principle states that as the speed of a fluid increases, the pressure exerted by that fluid decreases.

## 2. How does Bernoulli's Principle apply to non-flowing fluids in moving containers?

Even though non-flowing fluids do not have a specific direction of movement, they can still experience changes in pressure due to the motion of the container they are in.

## 3. Can Bernoulli's Principle be observed in everyday life?

Yes, Bernoulli's Principle can be observed in many everyday situations such as when blowing air over a piece of paper to make it rise or when a fast-moving car creates a low pressure area that keeps a beach ball stuck to its open window.

## 4. Does the shape of the container affect Bernoulli's Principle in non-flowing fluids?

Yes, the shape of the container can affect how Bernoulli's Principle applies to non-flowing fluids. For example, a narrow container that narrows at one end will create a faster flow of air and a lower pressure at that end.

## 5. How is Bernoulli's Principle related to lift in airplanes?

Bernoulli's Principle plays a crucial role in the lift of airplanes. The shape of the wing causes the air to move faster over the top, creating a lower pressure area that lifts the wing and the plane. This is known as the Bernoulli Effect.

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