Question

What did Daniel Bernoulli discover?
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Answer 1

Daniel Bernoulli (1700–1782) was a Swiss mathematician and physicist best known for major contributions in fluid mechanics, probability/utility theory, and early kinetic ideas for gases. The main things he discovered or introduced:

- Bernoulli’s principle / Bernoulli’s equation (Hydrodynamica, 1738): in steady incompressible flow, higher fluid speed corresponds to lower pressure; commonly written along a streamline as
p + ½ρv² + ρgh = constant.
This is a cornerstone of fluid dynamics and explains lift, flow in pipes, Venturi effects, etc.

- Early kinetic view of gases: he proposed that gas pressure arises from particle impacts and related pressure to particle motion — an important precursor to the kinetic theory of gases.

- Expected utility / solution to the St. Petersburg paradox (1738): he introduced the idea of diminishing marginal utility of wealth and proposed a logarithmic utility function to resolve the paradox, founding the expected-utility approach in decision theory and economics.

- Applications and contributions across mathematics and physics: work in hydrodynamics, elasticity, vibrations, and applied mathematics; important papers on mechanics and physiology.

(He is one of the famous Bernoulli family of mathematicians; some related concepts — e.g., Bernoulli numbers — were discovered by other family members.)

If you want, I can explain Bernoulli’s equation in more detail, show a derivation, or give examples of applications.