Bernoulli's Principle

Until now all of our consideration regarding fluids has been dedicated to stationary fluids. (hydrostatics and aerostatics). Strangfly enough, if one causes these fluids to move, the resulting phenomena (aerodynamics and hydrodynamics) become worthy of study. One of the earliest to study these phenomena was Daniel Bernoulli. His rule, called Bernoulli's equation, states


P = pressure within the fluid
(rho) - the mass density of the fluid
v = the speed of the fluid
g = the local acceleration due to gravity
y = a change in vertical displacement

Let us consider a non-compressable fluid flowing in a horizontal pipe of uniform diameter. In this example, all quantities are unchanging throughout the pipe. But what if we place a constriction in the pipe? Because the fluid is not compressable, it must speed up as is passes through the constriction. According to Bernoulli, if the velocity goes up, the pressure in the fluid must go down in the constricted area.

Consider an airplane wing, flat on the bottom, curved on the top. As the wing is pushed through the air by the propulsion system, simple relativity suggests that the wing is at rest and the air is moving over wing. The air, which must try to remain at rest with respect to the ground, passes over and under the wing simultaneously. Because it must travel further over the top of the wing compared to the bottom, Bernoulli suggests that the pressure below the wing is higher than the pressure above the wing. It is this pressure differention that accounts for flight.

A baseball thrown in an evacuated space (say the moon) travels through space in a simple parabolic path; the entire path can be contained in a single vertical plane; there is no side-to-side motion possible because there is no air to push it sideways.

All that changes if the ball is thrown on Earth in air. The path is still parabolic, but the pitcher will try make a hitable pitch (i.e., a strike) virtually un-hitable by putting large amounts of spin on a ball. Let us consider a right-handed pitcher attempting a curve ball. In throwing this pitch, the thrower will impart to the ball a very large anti-clockwise spin. The spinning ball drags air with it as it rotates. When this rotating air encoounters the tranlational flowfrom being thrown, the ball has high velocity air on one side; lower velocity on the other.The ball is pushed to the left, away from the right handed batter. Once in a grreat while, a right=handed pitcher throws a screwball. giving the ball a spin in the opposite direction to keep it away from left-hand battters