Fluid dynamics is the study of how liquids act. Instead of working with distinct objects, we must look at how the fluid behaves as a unit - including pressure, density, and motion.
- Pressure is defined as P=FA
- Density is defined as the ratio of mass to volume ρ=mV
- Pascal’s Principle: A confined incompressible fluid under pressure will transmit that pressure equally throughout the system. P1=P2→AoutAin=FoutFin. The mathematical relationship that follows from Pascal’s principle shows how the application of a force in one part of the system can be multiplied in another part of the system.
- Archimedes' Principle: The buoyant force on a submerged or partially submerged object is equal to the weight of fluid it displaces.
- Bernoulli’s Principle: At those points in space where the velocity of a fluid is high, the pressure is low, and at those points in space where the velocity of a fluid is low, the pressure is high.
The mathematical equation that Bernoulli derived based on this principle is stated below.
Bernoulli’s Equation: P1+12ρv12+ρgh1=P2+12ρv22+ρgh2=constant