Download presentation

Presentation is loading. Please wait.

Published byJoslyn Shillington Modified over 4 years ago

1
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST von Kárman Equation for flat plates (dp e /dx≠0) u For laminar or turbulent flows: in the turbulent case we take time-average velocity and pressure. u Procedure: Mass and momentum balance of the following control volume: dx x x+dx

2
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST dx u Mass balance: Steady Flow o Flow rate: von Kárman Equation forflat plates (dp e /dx≠0)

3
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST dx o x Momentum flow rate through y=δ: u Mass balance : von Kárman Equation for flat plates (dp e /dx≠0)

4
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST o Difference : u x momentum balance: Steady flow von Kárman Equation for flat plates (dp e /dx≠0)

5
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST u x momentum balance: von Kárman Equation for flat plates (dp e /dx≠0)

6
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST u Forces along x: p+dpp p+ 1/2 dp τ0τ0 von Kárman Equation for flat plates (dp e /dx≠0)

7
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST u Final result: u Using the definition of d and δ m : von Kárman Equation for flat plates (dp e /dx≠0)

8
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST u When dp e /dx=0 (dU/dx=0): von Kárman Equation for flat plates (dp e /dx≠0) u When dp e /dx=0 (dU/dx=0) we have m =a (a takes different values in laminar and turbulent flow): Boundary layer grows faster when C f is higher

9
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST Approximate solutions for laminar boundary layer for dp e /dx=0 u Blasius solution shows that with and a – constant along the BD

10
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST Approximate solutions for laminar boundary layer for dp e /dx=0 u von Kárman Equation: but β - constant Integrating

11
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST Approximate solutions for laminar boundary layer for dp e /dx=0 u Remark: a and β depend on the velocity profile, however δ/x, c f and C D do not vary much with profile shape u We have and

12
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST Approximate solutions for laminar boundary layer for dp e /dx=0

13
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST u Contents: –von Kármàn Equation; –Simplification for ; –Approximate solutions for laminar Boundary Layers with zero pressure gradient. Blasius Solution for Laminar Boundary Layer Equation over a flat plate with dp e /dx=0

14
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST u Recommended Study Elements: –Sabersky – Fluid Flow: 8.6, 8.7 –White – Fluid Mechanics: 7.3, 7.4 Von Kárman Equation for a flat plate

15
2004Mecânica dos Fluidos II Prof. António Sarmento - DEM/IST Problem on the Von Kármàn Equation

Similar presentations

OK

A Numerical Solution to the Flow Near an Infinite Rotating Disk White, Section 3-8.2 MAE 5130: Viscous Flows December 12, 2006 Adam Linsenbardt.

A Numerical Solution to the Flow Near an Infinite Rotating Disk White, Section 3-8.2 MAE 5130: Viscous Flows December 12, 2006 Adam Linsenbardt.

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google