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# Chapter 12: Fluid Mechanics

Difficulty Level: At Grade Created by: CK-12

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.

Chapter Outline

### Chapter Summary

1. Pressure is defined as P=FA\begin{align*}P = \frac{F}{A}\end{align*}
2. Density is defined as the ratio of mass to volume ρ=mV\begin{align*}\rho = \frac{m}{V}\end{align*}
3. Pascal’s Principle: A confined incompressible fluid under pressure will transmit that pressure equally throughout the system. P1=P2AoutAin=FoutFin\begin{align*}P_1 = P_2 \rightarrow \frac{A_{out}}{A_{in}} = \frac{F_{out}}{F_{in}}\end{align*}. 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.
4. Archimedes' Principle: The buoyant force on a submerged or partially submerged object is equal to the weight of fluid it displaces.
5. 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\begin{align*}P_1 + \frac{1}{2} \rho v{_1}^2 + \rho gh_1 = P_2 + \frac{1}{2} \rho v{_2}^2 + \rho gh_2 = \text{constant}\end{align*}

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Date Created:
Jun 27, 2013