16100lecture7_cg

16100lecture7_cg - Compressible Equations Conservation of...

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

View Full Document Right Arrow Icon
16.100 1 Compressible Equations Conservation of mass () 0 0 0 0, volume surface d dv u ndS dt u t D u Dt u incompressible ρρ ρ +• = +∇• = +∇ = ∇• = ∫∫∫ ∫∫ KK K K K Conservation of Momentum Net viscous force in : volume surface surface surface xx yx zx xy yy zy xz yz zz xx xx zx d udv uu ndS pn idS idS dt Note ds dx dy dz i dx dy dz j dx dy dz k u p uu tx x y z τ ττ τττ = + =+ + ++ + + ∂∂ + = +++ ∫∫∫ ∫∫ ∫∫ ∫∫ K K K K K K K x yx xx zx Du p Dt x x y z =− + + + ±²²²³ ² ² ²´ Recall: 2 , 3 j i ij ij ji u u u xx T τµ δ λ µµ µ  +   == K Incompressible Equations in Cartsian Coordinates 2 2 2 0, i.e. 0 1 1 1 uvw u xyz Du p u Dt x Dv p v Dt y Dw p w Dt z ν ∂∂∂ = = + ∇ K
Background image of page 1

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

View Full DocumentRight Arrow Icon
Compressible Equations 16.100 2002 2 Where 222 2 , kinematic viscosity D uvw Dt t x y z xyz µ ν ρ ∂∂∂ =+ + + ∇= + + Incompressible Equations for Cylindrical Coordinates () 22 2 2 11 0 2 12 1 rx rr r x x ru u u r x Du p u u uu Dt r r r r Du u u p u u u Dt r r r r Du p u Dt x θ θθ
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

Page1 / 2

16100lecture7_cg - Compressible Equations Conservation of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online