Bernoulli

Bernoulli knew of the law of consistent energy. He figured that when air was sped up without energy dissipation to the outside there would be more energy in that air.
He figured that this energy rise was compensated by a lower pressure energy.

In Other words: if there is no friction the energy along a streamline is constant.
Energy in a streamline exists of pressure energy and motion energy.

Example: Air through a frictionless pipe:

This is the often heard "the faster the air the lower the pressure" is coming from.

4 examples of how to apply "the faster the air the lower the pressure" wrong:

1 A car goes 180 km/hr at the motorway, the air inside the car also moves with 180 km/hr.
The pressure inside the car must be very low.

2 Air inside a closed barrel. Inside the barrel a stir apparatus is placed, what rotates the air very fast when switched on. The barrel should implode because of the low pressure inside it.

3 A closed hull must have a small aerator hole drilled somewhere. Else the hull would implode at high speeds.
(A hole is indeed needed, but that is more for temperature expansion reasons.
4 If one blows over a sheet of paper the sheet goes up because pressure inside the high-speed air is lower.

An extra explanation why No. 4 is wrong:
The friction may not be forgotten!

Blow below the sheet of paper and you know for sure it is not true, because then the paper goes up.

Bernoulli's law applied to a sail: Because the direction of air is changed there must be a force, this force is being transmitted to the sail by a pressure, A lower pressure at leeward side, and a higher pressure at windward side.
Higher pressure means a lower speed, lower pressure means a higher speed.
The air will move faster on the leeward than on the windward side.

What do you gain by knowing air speeds up at leeward:
Not much, only that one should have as least as possible objects on the leeward because they will have a higher air resistance.
Flags etc should be placed on the windward side.

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