Physics 152: Lectures on Fluids
Michael Fowler, UVa.
Beginning with Archimedes jumping out of a bath and running down the street shouting "Eureka" because he'd realized how to prove an expensive crown wasn't all it seemed, going on to his Principle of buoyancy and the concept of pressure, then to the much later realization that we live in an ocean of air with its own pressure, finally to Jefferson measuring the altitude of Monticello with a barometer bought in Philadelphia in 1776.
How Boyle established his famous Law PV = constant at constant temperature, and how we can use it to discover just how the atmospheric pressure decreases with altitude.
Contrary to most peoples' intuition, when fluid flowing through a pipe encounters a narrower section, the pressure in the fluid goes down. We show how this must follow from Newton's Laws, and demonstrate the effect.
After briefly reviewing friction between solids, we examine viscosity in liquids and gases, building up some understanding of what's going on at the molecular level. This makes it possible to understand some surprising results: for example, the viscosity of a gas does not change if the gas is compressed to greater density.
We present the calculus derivation of the smooth flow patterns for a wide river and for fluid in a circular cross-section pipe, and find the total flow for given slope or pressure drop.
M, L and T: all physics equations must have the same dimensions on both sides.This can be exploited to arrive at some interesting predictions without doing much math—for example, that the smooth flow rate through a circular pipe goes as the fourth power of the radius.
Dropping a small ball through a very viscous fluid: a dimensional prediction of the dependence of speed on radius, and an experiment with glycerin.
Another experiment, this time dropping coffee filters through air, with a very different result: but also predicted dimensionally! The Reynolds number: the dimensionless ratio of inertial drag to viscous drag.