Markdown Syntax

• Markdown is a lightweight markup language with plain text formatting syntax.
• Markdown is used for documentation, blogs and notes.

Basic Syntax

Headers

• Headings from level 1 to 6 are supported, using # to ###### respectively.

Emphasis

• Italic text can be denoted using *italics* or _italics_.
• Bold text can be denoted using **bold** or __bold__.
• Bold and italic text denoted using ***bold italics*** or ___bold italics___.

Lists

• Unordered lists use * for each element with nested list support.
• Ordered lists use numbers followed by a period: 1.

Links

• Insert links with: [Link Text](URL).
• Add a title which is displayed on hover with: [Link Text](URL "Link Title").

Images

• Insert images with: ![Alt Text](URL).
• Add a title which is displayed on hover with: ![Alt Text](URL "Image Title").

Code

• Inline code is formatted using backticks: `inline code`.
• Code blocks are created using triple backticks:

``` Code block here ```

Quotes

• Blockquotes use the > symbol at the start of each line.

Tables

• Tables are created using pipes | and dashes - to define columns and headers.

Horizontal Rules

• Horizontal rules are created with --- or ***.

Escape Characters

• To display characters that Markdown interprets as syntax, use a backslash \ before the character.

Additional Features

• Markdown has different implementations that add extra features and one should consult the documentation.

Bernoulli's Principle

• Discovered by Daniel Bernoulli in the 18th century.
• Bernoulli's principle states that an increase in fluid's speed lowers pressure or decreases potential energy of the fluid.

Conservation of Energy

• Bernoulli's principle is a consequence of the conservation of energy.
• Follows the work-energy principle where work done equals change in kinetic and potential energy.

Bernoulli's Equation

• Mathematical expression of Bernoulli's principle where:
  • P represents fluid pressure
  • ρ represents fluid density
  • v represents fluid speed
  • g represents acceleration due to gravity
  • h represents fluid height
• Equation: $P + \frac{1}{2} \rho v^2 + \rho g h = \text{constant}$

Applications

• Used in aerodynamics.
• Used in fluid mechanics to design pipelines and pumps.
• Helps explain tornadoes and weather patterns in meteorology.

Limitations

• Only applies to inviscid flows (no viscosity).
• Needs to be applied to incompressible fluids (constant density).
• Only applicable to steady flows (constant velocity).

Examples

• Speed increases and pressure decreases in a narrower pipe.
• Air flows faster over the top of an airplane wing.
• Low pressure in the center of a tornado.