# Day 91 (part 2)

Daniel Bernoulli was born into a family of mathematicians. Daniel was sent to Basel University at the age of 13 to study philosophy and logic. His interests were quite varied and included music and frequencies, probability studies and the political economy.

Written earlier but not published until 1738 was his work Hydrodynamica. This was the first correct analysis of water flowing from a hole in a container. It contained an equation that relates pressure to fluid speed and elevations.

Bernoulli’s equation is a consequence of energy conservation as applied to an ideal fluid.

P + ½ v2 + gy = constant

The sum of the pressure (P), the kinetic energy per unit volume (½ v2), and the potential energy per unit volume (gy) has the same value at all points along a streamline.

This means (ultimately) that swiftly moving fluids exert less pressure than do slowly moving fluids You see 2 balloons floating near each other, separated by 1-2 cm. You blow between the balloons. What do they do?

Spray bottles (perfumes, etc.) operate using this principle. When you squeeze the bulb, a stream of air moves across the liquid in the bottle lowering the pressure there. Some of the fluid comes up in the tube because of the lower pressure.

In the carburetor of a gasoline engine, the low pressure region is produced by air drawn in by the piston through the air filter. The gasoline vaporizes, mixes with the air, and enters the cylinder of the engine for combustion.

When an artery has an aneurysm (weakened spot where the artery walls have ballooned outward), blood flows more slowly at the location. This results in an increase in pressure in the vicinity of the aneurysm relative to the pressure in other parts of the artery. This excess pressure can cause the artery to rupture.

Airplane wings are designed so that the air speed above the wing is greater than that below. Therefore, the air pressure above the wing is less than the pressure below, and there is a net upward force on the wing, called the ‘lift.’

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