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Taxonomy_of_fluid_mechanics - The Taxonomy of Fluid...

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The Navier-Stokes Equation The Taxonomy of Fluid Dynamics Valid for any fluid ( ) ( ) ij V VV g t ρ ρ ρ σ + ∇⋅ = + ∇⋅ r r r r r r The Cauchy Equation Inviscid Flow Nonlinear Viscous terms drop out Bernoulli equation valid along streamlines Euler equation DV P g Dt ρ ρ = −∇ + r r r Valid for Newtonian fluid only 2 DV P g V Dt ρ ρ µ = −∇ + + r r r r Irrotational Flow Linear Viscous terms drop out Bernoulli equation valid everywhere Superposition valid
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