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Unformatted text preview: Excerpt for Chapter II, Handout 4 from Dr. L. Sankar Modified by Dr. S.M. Ruffin Bernoulli Eqution : The u-, v- and w- momentum equations are nonlinear PDEs and are hard to solve. Fortunately, for inviscid flows without body forces, these equations yield a simple algebraic equation linking pressure and velocity. We derive this simple equation below. We start with the u- momentum equation. It has many forms. But the form that we use is: 1 = + + + x p z u w y u v x u u (3) This form is valid for steady, inviscid flows with no body forces. It is valid for compressible and incompressible flows. Multiplying this equation by dx we get: 1 = + + + dx x p dx z u w dx y u v dx x u u Recall that for a streamline, , = = = = = wdy vdz wdx udz vdx udy Or dz dy dx w v u k j i s d V r r r r r (1) Along a streamline, according to equation (1), udy=vdx, udz=wdx. The above momentum equation becomes: 1 = +...
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- Summer '07