# Bernoulli, Daniel

### wing ball gases theory

[ber noo yee] (1700–82) Swiss mathematician: pioneer of hydrodynamics and kinetic theory of gases.

Bernoulli’s principle. 1.–Liquid flow through a narrowed tube. 2.–Air flow supporting a wing: air has a longer path above the wing than below it, so it moves faster, and its pressure is lower, above the wing; hence there is an uplift acting on the wing. 3.–Trajectory of a golf shot: the dimpled, spinning ball counteracts gravity for much of its flight. 4–Diagram from Bernoulli’s *Hydrodynamics* , in which kinetic theory is used to show that *pV* is constant for a gas (Boyle’s Law). In reality, the average distance between gas molecules is about 300 times the molecular diameter at STP (ie much more than in the diagram in relation to the apparent size of the ‘atoms’).

This extraordinary family, in the century before and the century after this Daniel’s birth, produced 11 substantial mathematicians in four generations. Most of them worked mainly in applied mathematics and analysis, had talents in some other areas, from astronomy to zoology, and quarrelled vigorously with their relatives.

Daniel studied medicine in Switzerland and Germany and qualified in 1724, and published some major work in mathematics in the same year. In 1725 he was appointed professor of mathematics in St Petersburg, but found conditions in Russia primitive and returned to Basle in 1733 as professor of anatomy and botany and, later, of physics. He worked on trigonometry, calculus and probability. His work on hydrodynamics used ideas on force applied to fluids, and advanced both theory and a range of applications. One of his results (Bernoulli’s principle) deals with fluid flow through pipes of changing diameter and shows that pressure in a narrow section is lower than in the wider part, contrary to expectation. A closely related effect leads to the uplift of an aircraft wing; since the distance from leading edge to rear edge is greater over the top of the wing than below it, the air velocity over the top must be higher and therefore its pressure is lower; the result is uplift. Again, when a golf ball is driven off, the loft of the club causes the ball to spin, and the resulting airflow gives it lift so that it has an asymmetric flight, rising in nearly a straight line. As the spin decreases, the lift diminishes and the ball moves into a path like that of a thrown ball.

Bernoulli also proposed a mental model for gases, showing that if gases consist of small atoms in ceaseless rapid motion colliding elastically with each other and the walls of their container, experimental law should result. This was both a very early application of the idea of atoms and the origin of the kinetic theory of gases.

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