Fluid Mechanics


Archimedes Number

The significant formula for Archimedes number, analyzes fluidization as it relayes to a system of density differences (not to be confused with pi, the Archimedes constant):

  , where:

Ar = Archimedes Number

g = Gravity (m/s2)

L = Characteristic Length (m)

 = Fluid Density (kg/m3)

Bernoulli's Equation

Valid between any two points in an ideal fluid:

 , where:

p = Pressure of Fluid (Pa)

 = Specific Weight (N/m^3)

v = Velocity (m/s)

g = Gravity (m/s^2)

z = Height (m)

Buoyancy Force

 , where:

B = Buoyancy Force (N)

 = Density of Fluid (kg/m^3)

V = Volume of Fluid Displaced (m^3)

g = Gravity (m/s^2)

Capillary Height

 , where:

h = Height in capillary (m)

 = Surface Tension (N/m)

 = Contact Angle (material property)

Cauchy Momentum Equation

 , where:

 = Density (kg/m3)

D = Material Derivative

v = Velocity Field (m/s)

t = Time (s)

 = Del Operator