Unformatted text preview: flow, necessarily their cross product is zero. Therefore, f vortex = for Beltrami flow (b) For steady Beltrami flow, ∂ u / ∂ t = 0 , and the vortex force is zero, so that the Euler equation simplifies to ρ ∇ w 1 2 u · u W = −∇ p − ρ ∇ V If the flow is also incompressible, ρ is constant so that all terms can be grouped together in parentheses as follows. ∇ w p + 1 2 ρ u · u + ρ V W = Therefore, the quantity in parentheses must be constant, viz., p + 1 2 ρ u · u + ρ V = constant...
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 Spring '06
 Phares
 Fluid Dynamics, Derivative, Force, Lift, Beltrami flow

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