Hydrostatics: Overview

When a body of fluid is near a massive object such as the Earth, a pressure gradient within the fluid is formed. In this section we will quantify these pressure gradients by finding an expression for pressure at some depth below the surface of an incompressible fluid. We will also explore applications of Pascal’s law which tells us how a change in pressure within a an incompressible fluid is transmitted to other locations within the fluid.

The Science Nuts explain hydrostatics with a few quick everday examples, enjoy!

Big Ideas

Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure.

Bid Idea 2: Fields existing in space can be used to explain interactions.

Big Idea 3: The interactions of an object with other objects can be described by forces.

Big Idea 4: Interactions between systems can result in changes in those systems.

Big Idea 5: Changes that occur as a result of interactions are constrained by conservation laws.

Big Idea 6: Waves can transfer energy and momentum from one location to another without the permanent transfer of mass and serve as a mathematical model for the description of other phenomena.

Big Idea 7: The mathematics of probability can be used to describe the behavior of complex systems and to interpret the behavior of quantum mechanical systems.

Learning Objectives

BoxSand Learning Objectives

Fluid-Mechanics.Hydrostatics.LO.BS.1: Apply pressure at a dpeth principles while solving problems.
Fluid-Mechanics.Hydrostatics.LO.BS.2: Relate Pascal's Law to hydraulic applications.
Fluid-Mechanics.Hydrostatics.LO.BS.3: Identify mechanical advantage in hydraulic systems.
Fluid-Mechanics.Hydrostatics.LO.BS.4: Construct FBDs and e-FBDs in parallel with a hydrostatics analysis to analyze systems.

College Board Learning Objectives

Fluid-Mechanics.Hydrostatics.LO.CB.3.B.2.1: The student is able to create and use free-body diagrams to analyze physical situations to solve problems with motion qualitatively and quantitatively. [SP1.1, 1.4, 2.2]
Fluid-Mechanics.Hydrostatics.LO.CB.3.C.4.1: The student is able to make claims about various contact forces between objects based on the microscopic cause of those forces.[SP 6.1]
Fluid-Mechanics.Hydrostatics.LO.CB.3.C.4.2: The student is able to explain contact forces (tension, friction, normal, buoyant, spring) as arising from interatomic electric forces and that they therefore have certain directions. [SP 6.2]

Enduring Understanding and Essential Knowledge

Enduring Understanding

Essential Knowledge

Fluid-Mechanics.Hydrostatics.EU.CB.3.B: Classically, the acceleration of an object interacting with other objects can be predicted by using $\vec{a} = \frac{\sum \vec{F}}{m}$.

Fluid-Mechanics.Hydrostatics.EK.CB.3.B.2: Free-body diagrams are useful tools for visualizing forces being exerted on a single object and writing the equations that represent a physical situation.

An object can be drawn as if it was extracted from its environment and the interactions with the environment identified.
A force exerted on an object can be represented as an arrow whose length represents the magnitude of the force and whose direction shows the direction of the force.
A coordinate system with one axis parallel to the direction of the acceleration simplifies the translation from the free-body diagram to the algebraic representation.

Fluid-Mechanics.Hydrostatics.EU.CB.3.C: At the macroscopic level, forces can be categorized as either long-range (action-at-a-distance) forces or contact forces.

Fluid-Mechanics.Hydrostatics.EK.CB.3.C.4: Contact forces result from the interaction of one object touching another object and they arise from interatomic electric forces. These forces include tension, friction, normal, spring, and buoyant.

Relevant Equation:
$F_{b}=\rho V g$
$P=\frac{F}{A}$

Assumptions

Describe what the assumptions are and why they're important

History

Physics Fun

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