Ae311_fall_2011_governing_equations

Ae311_fall_2011_governing_equations - Prof. Daniel J....

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Prof. Daniel J. Bodony AE311, Fall 2011 Governing Equations Integral equations d dt ρ dV + V(t) d dt V(t) V(t) (1) S(t) ρu dV + ρu[(u − v) · n] dS = − S(t) p n dS + S(t) 1 ρ e + u · u [(u − v) · n] dS = − 2 1 ρ e + u · u dV + 2 d dt ρ[(u − v) · n] dS = 0 S(t) f visc dS + f visc · u dS S(t) ρ g · u dV − + V(t) (2) V(t) S(t) pu · n dS + S(t) ρ g dV q · n dS ˙ (3) S(t) Differential equations ∂ρ + ∇ · (ρu) = 0 ∂t ∂p ∂(ρu) + ∇ · (ρuu) = − + ∇ · τx + ρ g · ex ˆ ∂t ∂x ∂p ∂(ρv) + ∇ · (ρvu) = − + ∇ · τ y + ρ g · ey ˆ ∂t ∂y ∂(ρw) ∂p + ∇ · (ρwu) = − + ∇ · τ z + ρ g · ez ˆ ∂t ∂z 1 1 ∂ ρ e + ρu · u + ∇ · ρ e + ρu · u u = −∇ · ( pu) + ∇ · τ x u + τy v + τz w + ρ g · u − ∇ · q ˙ ∂t 2 2 1 (4) (5) (6) (7) (8) ...
View Full Document

This note was uploaded on 01/26/2012 for the course MUS 130 taught by Professor Lee during the Fall '08 term at University of Illinois, Urbana Champaign.

Ask a homework question - tutors are online