16100lectre27_cg

16100lectre27_cg - Poiseuille Flow Through a Duct in 2-D y...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Poiseuille Flow Through a Duct in 2-D Assumptions: Velocity is independent of 0 , = = x v x u x Incompressible flow Constant viscosity, µ Steady Pressure gradient along length of pipe is non-zero, i.e. 0 x p Boundary conditions: No slip: () 0 walls are not moving 0 uy h vy h = = To be clear, we now will take the compressible, unsteady form of the N-S equations and carefully derive the solution: Conservation of mass: 0 ) ( = + V t K ρ But 0 = t because flow is steady and incompressible. Also, since = constant, then V V K K = ) ( 0 = + = y v x u V K Finally, 0 = x u because of assumption #1 long pipe. 0 = y v h y + = h y = y x
Background image of page 1

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

View Full DocumentRight Arrow Icon
Poiseuille Flow Through a Duct in 2-D 16.100 2002 2 Now, integrate this: C v = = constant Apply boundary conditions: ()0 ( )0 vh v y ± =⇒ = We expect this but it is good to see the math confirm it. Now, let’s look at momentum y .
Background image of page 2
Image of page 3
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 / 4

16100lectre27_cg - Poiseuille Flow Through a Duct in 2-D y...

This preview shows document pages 1 - 3. Sign up to view the full document.

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