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Symmetric Groups

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Tangent and Normal Line

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The Essential Mathematics of Lie Groups

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The Integers Modulo n Under + and x

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The Limit Definition of the Exponential Function

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Vector Calculus

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Volume Integrals

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Spin 1 Eigenvectors

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Factor Analysis

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How this site works ...

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Quantum Field Theory

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Path Integral Formulation

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Relativistic Quantum Field Theory

Quantum Mechanics

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Basic Relationships

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Clebsch-Gordan Coefficients

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Electron Orbital Angular Momentum and Spin

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Entangled States

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Multi Electron Wavefunctions

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Pauli Exclusion Principle

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Pauli Spin Matrices

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Photoelectric Effect

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Position and Momentum States

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Probability Current

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Schrodinger Equation for Hydrogen Atom

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Schrodinger Wave Equation

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Schrodinger Wave Equation (continued)

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Spin 1/2 Eigenvectors

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The Differential Operator

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The Essential Mathematics of Quantum Mechanics

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The Observer Effect

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Time Dependent Perturbation Theory

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Time Evolution and Symmetry Operations

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Time Independent Perturbation Theory

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The Weibull Distribution

Solid State Electronics

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Band Theory of Solids

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The P-N Junction

Special Relativity

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Electromagnetic 4 - Potential

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Energy and Momentum, E = mc²

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Lorentz Invariance

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Lorentz Transform

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Lorentz Transformation of the EM Field

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Newton versus Einstein

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Spinors - Part 1

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Spinors - Part 2

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The Lorentz Group

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Velocity Addition

Statistical Mechanics

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Black Body Radiation

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Entropy and the Partition Function

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The Harmonic Oscillator

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String Theory

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Bosonic Strings

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Extra Dimensions

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Introduction to String Theory

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Kaluza-Klein Compactification of Closed Strings

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Strings in Curved Spacetime

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Toroidal Compactification

Superconductivity

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Introduction to Superconductors

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Superconductivity (Lectures 1 - 10)

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Superconductivity (Lectures 11 - 20)

Supersymmetry (SUSY) and Grand Unified Theory (GUT)

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Chiral Superfields

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Generators of a Supergroup

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Grassmann Numbers

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Introduction to Supersymmetry

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The Gauge Hierarchy Problem

test

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The Standard Model

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Electroweak Unification (Glashow-Weinberg-Salam)

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Gauge Theories (Yang-Mills)

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Gravitational Force and the Planck Scale

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Introduction to the Standard Model

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Isospin, Hypercharge, Weak Isospin and Weak Hypercharge

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Quantum Flavordynamics and Quantum Chromodynamics

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Special Unitary Groups and the Standard Model - Part 1

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Special Unitary Groups and the Standard Model - Part 2

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Special Unitary Groups and the Standard Model - Part 3

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Standard Model Lagrangian

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The Higgs Mechanism

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The Nature of the Weak Interaction

Topology

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Units, Constants and Useful Formulas

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Last modified: January 26, 2018


Pascal's Principle
------------------
Pressure is transmitted undiminished in an enclosed non-compressible fluid.

Consider a bottle:

    |  |
    |--| F₁ = A₁P₁
    |  |
   /    \
  |      |
  | |||| |
  | vvvv |
   ------  F₂ = A₂P₂
           P₂ = P₁ + hρg

Hydraulic Jack:

        P₁ = A₁F₁     P₂ = A₂F₂    
       |  |         |          |
       |--|    ^    |..........| P₂
    d₁ |  |    h    |          | d₂
    P₁ |..|    v    |----------|
       |  |_________|          |
       |                       |
        -----------------------

P₁ = P₂ + hρg

F₁/A₁ = F₂/A₂ + hρg

conservation of energy: F₁d₁ = F₂d₂

d₁ = (F₂/F₁)d₂

   = (A₂P₂/A₁P₁)d₂

   = (A₂P₂/A₁(P₂ + hρg))d₂

   = {A₂(F₂/A₂)d₂}/{A₁((F₂/A₂) + hρg)}

   = F₂d₂/{A₁((F₂/A₂) + hρg)}

If we negelect the weight of the fluid (ρ = 0) so that the pressure 
throughout the enclosed volume will be the same then:

d₁ = F₂d₂/{A₁(F₂/A₂)}

  = d₂/{A₁(1/A₂)}

  = d₂(A₂/A₁)