{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

3.4 - Excerpt for Chapter II Handout 4 from Dr L Sankar...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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: 0 1 = + + + x p z u w y u v x u u ρ (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: 0 1 = + + + dx x p dx z u w dx y u v dx x u u ρ Recall that for a streamline, 0 0 0 , 0 = = = = = × 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: 0 1 = + + + dx x p dz z u u dy y u u dx x u u ρ (4) Now,
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}