Fluid Mechanics

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Rayleigh Number

, where: 

Ra = Rayleigh Number

Gr = Grashof Number

Pr = Prandtl Number (evaluated at film temperature)

Reynolds Number

 , where:

Re = Reynolds Number

V = Velocity relative to fluid (m/s)

L = Characteristic Length (m) (ie. Hydraulic diameter for a pipe, Diamter of sphere in fluid, etc)

 = Kinematic Viscosity (m^2/s)

Shear Stress in Fluids

 , where:

 = Shear Stress (Pa)

 = Dynamic Viscosity (Pa*s)

u = Velocity of Fluid along Boundary (m/s)

y = Distance from bounday (m)

Simplified Continuity Equation

For incompressible, steady-state flow:

 , where:

u = Velocity in x-direction (m/s)

v = Velocity in y-direction (m/s)

w = Velocity in z-direction (m/s)

Simplified Navier-Stokes Equation

Assuming incompressible flow and constant viscosity:

 , where:

 = Density of Fluid (kg/m^3)

v = Velocity (m/s)

t = Time (s)

 = Del Operator

p = Pressure (Pa)

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