Fluid Mechanics

Bernoulli's Principle

Bernoulli's equation employing the work-energy theorem and energy conservation.

The total energy in a steadily flowing fluid system is a CONSTANT along the flow path/throughout the displacement. (Fluid pressure is inversely proportional to its velocity.)

The total energy of the system is equal to the sum of the PE + KE + and Pressure Energy.

Bernoulli's Principle, when the heights are equal (y1 = y2, cancel):

- Fast flowing fluids have LOW pressure

- Slow flowing fluids have HIGH pressure

Continuity Equation: Q = A1v1 = A2v2

(Area & velocity are INVERSELY PROPORTIONAL!!!)

- If the tube narrows; speed will INCREASE

- If the tube widens, speed will DECREASE

http://www.youtube.com/watch?v=bC8v6hlXnSk

"10 kits blown and scattered about" hahaha

- Water always flows from high to low pressure

Intro to Bern Lec 1: http://www.youtube.com/watch?v=dH7Y0EVPvSo

Intro to Bern Lec 2: http://www.youtube.com/watch?v=tYFubWV31go

Corner kick example :) http://www.youtube.com/watch?v=83IAaasj4ac&feature=related

Yanni's Blue Video: http://www.youtube.com/watch?v=kXBXtaf2TTg&feature=related

Density of Water (expressions):

Pressure = Pa (pascals!!!)

- 1 Pa = 1 N/m²

^{- atmospheric pressure = 100,000 Pa}

^{- trick: 10m of water depth adds about 1 atm of pressure}

- pressure is produced by the collisions of fluid molecules with the surfaces with which the fluid is in contact

Poiseuille's Principle
An equation which describes laminar flow in a straight tube. V=P¹r4/8nl, where V= flow P= driving pressure r= radius of tube n= fluid viscosity l= length of tube.
"Thus, when one describes a patient as having "high blood pressure", it means that their heart is generating a very large P1 in order to produce the necessary Q to get blood to the tissue in a timely fashion."
http://www.youtube.com/watch?v=-jyBY726np4&feature=results_video&playnext=1&list=PL05679B8070040C79

The Hydraulic Press
http://www.youtube.com/watch?v=TjzKpke0nSU