Balance Laws 2 Lecture 3 ME EN 412 Andrew Ning aning@byu.edu - PDF document

Balance Laws 2 Lecture 3 ME EN 412 Andrew Ning aning@byu.edu Outline Examples

Examples Far-field Forces Figure courtesy of Juan Alonso

No time dependence or other external forces: ✟✟✟✟✟✟✟✟ ∂ � � ρ� ρ� V ( � W · d � V dV – + A ) = ∂t V – S � � � � ✟ pd � τ · d � ✟✟✟✟✟ ↔ A + A + F other − S S Rewrite: � � � ρ� V ( � ↔ W · ˆ n ) + p ˆ τ · ˆ dA = 0 n − n S ✟ � � � ✟✟✟✟✟✟✟ ( − ) dA + ( − ) dA + ( − ) dA = 0 S inner S outer S cut

� � � ρ� ( � ✘ dA = � V ✘✘✘✘ ↔ W · ˆ n ) + p ˆ τ · ˆ n − n F b S inner � � � � ρ� V ( � F b = − W · ˆ n ) + p ˆ n dA S outer

Stator vanes on a jet engine • Infinite cascade of airfoils h • Incompressible • Velocity/pressure constant at stations Ry 1 and 2 Rx • Find reaction forces to keep a vane in place. Jet impinging on cart