Fluids in motion
When a fluid is in motion the pressure within the fluid varies with the velocity of the fluid if the flow is streamlined. This pressure variation is a consequence of Bernoulli’s theorem proposed in 1740. This states that:
A proof of this theorem is shown below.
The forces generated by this pressure difference were first explained in 1852 by the German physicist Gustav Magnus, who solved the problem of why projectiles spinning about an axis other than their direction of motion will veer off course.
Applications and effects of the Bernoulli effect
One of the simplest demonstrations of the Bernoulli effect can be seen by blowing down between two sheets of paper. The air stream between the paper creates an area of low pressure here and so the sheets are drawn together. This effect can also be seen when two tall heavy lorries travel along rapidly side by side and are drawn together. The same effect has also been experienced at sea between two ships. This also explains the vibration of the reed in an oboe, the fast moving air steam between the two reeds causes lower pressure between them an so forces them together. Changes in this pressure cause the reeds to vibrate.
The shape of the cross-section of an aircraft wing is designed so that the velocity of the air above the wing is greater than that below it. A region of low pressure is therefore created above the wing and so the aircraft experiences an upward force known as lift (Figure 1).
Racing cars have inverted aerofoils so that the force is downwards, thus increasing the force between the car and the road (Figure 2).
Another striking example is the movement in the air of a smooth, spinning ball such as a table tennis ball (see Figure 3).
As the ball moves through the air it will drag some of the air round with its spin. This will increase the velocity of the air on one side of the ball and decrease it on the other, creating areas of low and high pressure. The ball therefore moves into the region of low pressure.
Giving the ball "top spin" will make it dip while "back spin" will make it rise (Figure 4).
(This explanation does not apply to a spinning cricket ball, however, where the smoothness of different faces and the seam will all affect its motion.)
The scent spray, the carburetor and the bunsen burner work because of the Bernoulli effect. For example, in the bunsen burner the high velocity of a jet of gas draws air into the burner (Figure 5).
One final fascinating application of the principle is the rotor-driven ship designed by the German naval engineer Anton Flettner and built in 1925. The ship, the Buckau, had its masts and sails replaced by two vertical cylindrical rotors 12 m tall and with a diameter of 2.7 m.
They were rotated about a vertical axis by two 11 kW electric motors below decks to a maximum speed of 125 r.p.m. (Figure 6). Just like the spinning ball, the combination of wind speed and rotor speed produced a force that propelled the ship through the water.
It was found that the Buckau could sail a full 20o closer to the wind than a traditional sailing ship, and that she could reach a speed of 14.3 km hr-1 when driven by rotors alone compared with 14.5 km hr-1 when using a traditional propellor.
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