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BME Cheat Sheet Cheat Sheet (DRAFT) by [deleted]

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Assump­tions

1. The fluid is Newtonian
2. Fluid is isotropic
3. Fluid is incomp­res­sible
4. Fluid flow is steady state
5. Fluid flow is laminar
6. Fluid flow is fully developed
7. No slip condition
 

Units and Conver­sions

Pressure
1 Pa = 1 N/m2 = 1 kg/(m·s2)
 
1 atm = 101325 Pa = 2116.22 lbf/ft2

Microp­ipette Aspiration

where n is the surface tension of the cell [N/m]
if given thickness then n = σt

Buoyancy

Equal volumes feel equal buoyant forces.
Why? Identical pressure enviro­nments and equal water displa­cement.

Submerged Object: Archim­edes' Principle
Mass of Object - Submerged Mass = Density of Fluid x Volume of Object

Submerge object water level increases
Remove object from boat water level decreases

Terms and Facts

Viscosity
A material property, gives propor­tio­nality of shear stress and shear rate [g/cm·s]
Absolu­te/­Dynamic Viscosity
μ
Kinematic Viscosity
ν=μ/ρ
Non-Ne­wtown Fluids: τ = μγη
Shear Thinning (η < 1)
Faster you shear it, thinner it becomes; resistance decreases, becomes more uniform.
Shear Thickening (η > 1)
Faster you shear it, thicker it becomes; resistance increases.
Bingham Plastic (τ=μγ+τ_y)
Acts like a solid until the sheet stress reaches a critical value

Centri­oidal Moments of Inertia

xcp = -γ·Ixy·s­inθ·Ixy/Pcg·A = -Ixy·sinθ/hcg·A

ycp = -γ·Ixx·s­inθ·Ixy/Pcg·A = -Ixx·sinθ/hcg·A

F = γ·hcg·A = P·A

The center of gravity and center of pressure are different locations.
The force on the object occurs at the center of gravity.
The pressure on the object occurs at the center of pressure (use Ixx, and Ixy)

When calcul­ating the moment: remember the reaction forces

Manometer

Pressure = densitygravityheight = ρgh
If given N/m3 or lbf/ft3 then do not add gravity
Change in elevation change in pressure
Within a single fluid, pressure is constant along a height
Specific Gravy = [density of X] / [density of water]
move down (+), move up (-)