Bernoulli effect

Two very nice demonstrations:

1. Hold two strips of paper, each about 5 - 10 cm long and 1 - 2 cm wide, in front of your mouth parallel to themselvs and to the floor. Blow between the sheets of paper. The far ends of the pieces of paper are forced together!

2. Hold your head back, blow straight up into the air, you can balance a ping pong ball on the column of air (for those of reduced lung capacity, a hair dryer will suffice but it looks much cooler if you are providing the air power manually)

In 1738, physicist and mathematician Daniel Bernoulli published Hydrodynamica, a work that contained the first correct analysis of water flowing from a hole in a container. This book considered the basic properties of fluid flow, pressure, density and velocity and gave their fundamental relationship through what is now known as Bernoulli's principle.

Bernoulli's principle essentially states that:

p + (½ * P * v^2) + (P * g * h) = constant

Where: p= pressure; P= density; v= velocity; h= elevation; g= gravitational acceleration

Provided that:
-Points 1 and 2 are on a streamline
-The fluid has constant density
-The flow is steady
-There is no friction

When a fluid moves, the pressure within the fluid is no longer only due to all of the weight above it. Instead, the fluid will begin to loose pressure according to Bernoulli's equation.

By relating Bernoulli's equation to the Continuity Equation you can prove this. It is known that when a fluid is in motion, it must move in such a way that mass is conserved. To see how mass conservation places restrictions on the velocity field consider the steady flow of fluid through an opening. The inflow and outflow are one-dimensional, so the velocity and density are constantover the area A.

Taking this into consideration, it can also be proven that:
-decreasing area = increasing velocity
-increasing velocity = decreasingpressure

These facts make the principle more variant because the rate that the water comes out is dependent on how much water is above the hole pressing down, and as this water drains the amount decreases and so the pressure decreases. Thus, the rate of drainage is exponential – the less water in the container the faster it will drain out.

The practical applications of Bernoulli's principle are far reaching. Bernoulli himself discovered one before he had even created the proper equation for it. Bernoulli discovered the first way to accurately measure blood pressure. He wanted to find a relationship between the speed at which blood flows and it's pressure. He experimented by puncturing the wall of a pipe with a small, open-ended straw and noted that the height that the fluid rose up the straw was related to the fluid's pressure in the pipe. Soon physicians all over Europe were measuring their patient's blood pressure by sticking point-ended glass tubes directly into their arteries.

Luckily, 170 years later another man discovered the less painful method still in use today. (The one they wrap around your arm.) Nevertheless, Bernoulli's original method of measuring pressure is still used today in other areas, such as to measure the air speed of an aircraft.

This principle states that if a fluid or air moves across a surface faster then the surrounding air, then the pressure for that area will be decreased.

Imagine a cross section of a wing:

   ---__

 /      ----___

-----------------

Notice how the top of the wing is more curved (excuse my bad illustration). The wind going below the wing goes normally, but the wind trailing over the top follows the curve and meets up with the wind beneath. Since the speed is different, it creates this cool mini-vortex that leads to a lower pressure. The result is the pressure is negative above the wing, and the wing moves up to fill the vacuum.

A common misperception is that the wind molecules above and below the wing are matched up at the end. Nope, fortunately, because then the difference in speed would not give rise to a sufficent pressure difference. In fact, because of the sharp trailing end of the wing, it leaves behind a starting vortex, and correspondingly there is circulation about the wing, ie the speed of the air below it minus that above it is negative.

Bernoulli's principle states that the faster traveling wind above the wing creates a low pressure area, pulling the wing up in the air.

Some cars, especially racecars use this principle. Most drag racers usee this upside-down, so that the horizontal fin on the back of the car actually pulls them downwards towards the road.

Many thanks to Krimson for the Physics lesson