# 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

- 12.1.
## Pressure in Fluids

- 12.2.
## Measuring Pressure

- 12.3.
## Pascal’s Law

- 12.4.
## Archimedes’ Law

- 12.5.
## Bernoulli's Law

### Chapter Summary

- Pressure is defined as \begin{align*}P = \frac{F}{A}\end{align*}
- Density is defined as the ratio of mass to volume \begin{align*}\rho = \frac{m}{V}\end{align*}
*Pascal’s Principle*: A confined incompressible fluid under pressure will transmit that pressure equally throughout the system. \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.*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: \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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Description

Covers pressure, density, Pascal’s Principle, Archimedes' Principle, and Bernoulli’s Principle.

Difficulty Level:

At Grade
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Date Created:

Jan 13, 2016
Last Modified:

Mar 31, 2016
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