Fluid Mechanics

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Compressibility

 , where:

 = Compressibility (m2/N)

V = Volume (m3)

p = Pressure (Pa)

Continuity Equation (Fluids)

 , where:

 = Density (kg/m3)

t = Time (s)

 = Del Operator

u = Velocity Field (m/s)

Darcy Friction Factor

For non-laminar flow, refer to Moody chart.  For laminar flow:

 , where:

f = Darcy Friction Factor

Re = Reynolds Number

Definition of Newtonian Fluid

A newtonian fluid must satisfy:

 , where:

 = Shear Stress (Pa)

 = Dynamic Viscosity (Pa*s)

u = Velocity in direction of shear (m/s)

y = Direction perpendicular to shear (m)

 

Deviatoric Stress Tensor

For isotropic fluids,

 , where:

 = Deviatoric Stress Tensor (Pa)

 = Dynamic Viscosity (Pa*s)

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