"incompressible" - 1 õppematerjal

Hüdro- ja aeromehaanika

25) Grouping this equation from 1.25: v u v u v u v u v u u v - + u - + v - + - - - = t x y x x y y x y x x y y x y 1 2 p 2 p v u = - - + v 2 - xy yx x y (1.26) Commutative property of partial differentiation 2 p 2 p = xy yx 2 p 2 p - =0 xy yx Continuity equation for incompressible flow: u v u = + =0 x y Substituting to 1.26 v u v u v u v u - + u - + v - = v 2 - t x y x x y y x y x y (1.27) On the x-y plane the vector field for velocity is defined: u = ( u , v ,0 ) ( e ) ( e ) = (i , j , k ) When we calculate this curl, we get: i j k v u v u