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:
Jun 27, 2013
Last Modified:
Jan 14, 2016
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