{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

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,

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}