Ch09_3_MI - MAE130B Ch 09 (3) Momentum Integral Equation...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
MAE130B – Ch 09 (3) Momentum Integral Equation Changzheng Huang
Background image of page 1

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

View Full DocumentRight Arrow Icon
Ch 09 (3) Changzheng Huang 2 Momentum Integral Equation 1. Control volume analysis 2. A simple example 3. General velocity profile
Background image of page 2
Ch 09 (3) Changzheng Huang 3 1. Control volume analysis x (1) Plate width: b U U () w x τ 0 0 p U U xx p y ρ = −= ∂∂ = y (2) h δ (x) u=u(y) Boundary layer edge Streamline The control volume is shown in dashed area. From earlier analysis, Therefore we can assume pressure is constant in the flow field.
Background image of page 3

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

View Full DocumentRight Arrow Icon
Ch 09 (3) Changzheng Huang 4 1. Control volume analysis x (1) Plate width: b U U () w x τ 0 x dS ud S F ρ •= Vn v v y (2) h δ (x) u=u(y) Boundary layer edge Streamline Conservation of mass and x-momentum for steady flow, (1) (2) 0 0 x w dS dS u dS u dS x bdx δ ρρ •+ ∫∫ Here n is the unit normal pointing outward of the control surface.
Background image of page 4
Ch 09 (3) Changzheng Huang 5 1. Control volume analysis x (1) U U () w x τ y (2) h δ (x) u=u(y) Boundary layer edge Streamline (1) (2) 0 0 x w dS dS u dS u dS x bdx δ ρρ •+ •= ∫∫ Vn 0 0 10 1 U bh ubdy UU bh uubdy D −+ = +=
Background image of page 5

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

View Full DocumentRight Arrow Icon
Ch 09 (3) Changzheng Huang 6 1. Control volume analysis x (1) U U () w x τ y (2) h δ (x) u=u(y) Boundary layer edge Streamline 0 0 10 1 U bh ubdy UU bh uubdy D δ ρρ −+ = += 000 22 0 1 D UUbh uubdy Uubdy uubdy uu DU b d yU b UU δδ ρ =− = ⎛⎞ = Θ ⎜⎟ ⎝⎠
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 19

Ch09_3_MI - MAE130B Ch 09 (3) Momentum Integral Equation...

This preview shows document pages 1 - 7. Sign up to view the full document.

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