# Bourmoulli's principle

1. Apr 13, 2012

### ramly

Hypothetical question:

One day you were taking a ride from a friend. While on the highway, you noticed a crack on the passenger side of the window. You placed a piece of paper by the crack, and the paper was sucked out of the window.

How exactly did this happen? And what equations would I use in trying to explain this.

2. Apr 13, 2012

### Hobold

Because the air out of the car is at a higher velocity in reference to the window than the inner air, by Bernoulli's principle, the pressure outside must be lower, therefore you have a pressure force acting on the paper and thus it is "sucked" to ouside.

3. Apr 13, 2012

### ramly

oooh okay. what equations would I use to describe this? and what forces are included?

4. Apr 13, 2012

### Naty1

not so easy to model:

I would think aircraft wing designers would have the experience.....

5. Apr 13, 2012

### Staff: Mentor

Though this is a typical explanation of Bernoulli's equation/principle, I'm sorry, but I don't like it because "pressure" is too vague of a concept in this explanation. My explanation is this:

Bernoulli's principle is a conservation of energy statement. In a closed system, where air can move freely from one place to another, energy is conserved within that airstream. There are different types of energy for flowing air, but in the case of your car, you have static pressure energy and velocity pressure energy. In other words: there is more than one type of "pressure". Bernoulli's principle simply states that the sum of these energies is always constant along a streamline (along the flow of the air). Inside the car, the air is not moving, so all of the pressure (pressure energy) is in the form of static pressure. Outside the car, the air is moving, so some of the pressure is in the form of velocity pressure. So you have this:

SPin = SPout + VPout

Since SPin is greater than SPout, air is pulled out through the window.

6. Apr 13, 2012

### rcgldr

Because the shape of the car tends to separate the flow at the front, diverting the air outwards away from the car, and upwards over the roof, along with some turbulent flow, resulting in lower pressure just outside the window. There is ventilation to allow air from outside the car to flow inside the car, and depending on the location of the outside ventilation ports, there may be some ram air effect, increasing pressure inside the car by a tiny amount. When a window is partially or fully open, there's going to be a lot of circulation.

In the case of many aircraft, a small hole in the side of the fuselage is connected to a pipe which leads to a chamber, called a static port. The hole is placed at a part of the fuselage where the air's speed is not affected by the fuselage or prop wash. Despite the air flowing by the hole (there's a thin shear boundary layer between the hole and the flowing air), the chamber pressure is essentially the same as the ambient pressure outside regardless of the aircraft's speed (as long as the speed is reasonably sub-sonic).

Last edited: Apr 13, 2012
7. Apr 13, 2012

### tiny-tim

i don't like this argument

Bernoulli's equation only applies along a streamline, and there's no streamline going through the hole in the window

better to say that the pressure inside the car is atmospheric pressure,

and a streamline outside the car but very close to it starts and finishes (a long way in front and behind) at zero speed and atmospheric pressure, but in the middle must have a high speed and therefore a lower pressure

8. Apr 13, 2012

### ramly

Thank you so much!

9. Apr 14, 2012

### rcgldr

True if using the car as a frame of reference, but what if using the road (on a no wind day), or the air itself? Then it's the air inside the car that is moving.

For the air outside the car that is unaffected by the movement of the car it's static pressure is the same as ambient. For the air affected by the movment of the car, it's higher at the front of the car, and lower along the sides and roof due to diversion and turbulence, and lower at the rear due to the air filling in what would otherwise be a void at the rear of the car as the car moves through the air.

For the air inside the car, the static pressure depends on ventilation. If the ventilation involves some form of ram air effect, the pressure is higher. If the only ventilation was located towards the back of the car where pressure is reduced, then the pressure is lower. The ventilation could be setup to that pressure inside the car was ambient (if the vent ports were setup in the same way as static ports on an aircraft).

The slightly open window will result in turbulent circulation inside the car, so it's not clear if the paper flies out because of circulation or pressure differential.

Last edited: Apr 14, 2012
10. Apr 14, 2012

### 256bits

My sentiments entirely.