Daniel Bernoulli (1700 – 1782) was a Dutch-born scientist who studied
in Italy and eventually settled in Switzerland. Born into a family of
renowned mathematicians, his father, Johann Bernoulli, was one of
the early developers of calculus and his uncle Jacob Bernoulli, was the
first to discover the theory of probability. Although brilliant, Johann
Bernoulli was both ambitious for his son Daniel and jealous of his son’s
success. Johann insisted that Daniel study business and later medicine,
which Daniel did with distinction. It was mathematics, however, that
really captured Daniel’s interest and imagination. Despite Daniel’s best
efforts, Johann never acknowledged his son’s brilliance and even tried
to take credit for some of Daniel’s most important ideas.
After Daniel’s studies, he moved to Venice where he worked on mathematics and practical medicine. In 1724, he published Mathematical exercises, and in 1725 he designed an hourglass that won him the prize of the Paris Academy, his first of ten. As a result of his growing fame as a mathematician, Daniel was invited to St. Petersburg to continue his research. Although Daniel was not happy in St. Petersburg, it was there that he wrote “Hydrodynamica”, the work for which he is best known. Bernoulli built his work off of that of Newton.
In 1738, he published “Hydrodynamica”, his study in fluid dynamics, or the study of how fluids behave when they are in motion. Air, like water, is a fluid; however, unlike water, which is a liquid, air is a gaseous substance. Air is considered a fluid because it flows and can take on different shapes. Bernoulli asserted in “Hydrodynamica” that as a fluid moves faster, it produces less pressure, and conversely, slower moving fluids produce greater pressure.
We are able to explain how lift is generated for an airplane by gaining an understanding of the forces at work on an airplane and what principles guide those forces. First, it takes thrust to get the airplane moving - Newton’s first law at work. This law states that an object at rest remains at rest while an object in motion remains in motion, unless acted upon by an external force.
In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy and vice versa.
The formula for Bernoulli’s principle is given as:
p + 12 ρ v2 + ρgh =constant
Where,
p is the pressure exerted by the fluid
v is the velocity of the fluid
ρ is the density of the fluid
h is the height of the container