Applications of Navier-Stokes Equations

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Presentation transcript:

Applications of Navier-Stokes Equations Aula teória 12 Applications of Navier-Stokes Equations

Film over a plane surface X2 X1

Boundary conditions: Null velocity at the bottom (x2=0) null friction at the surface (x2=h)

Why h cubic?

The Couette Flow Is the flow between two parallel plates, with relative velocity and with or without pressure gradient.

Boundary conditions u=U0 at y=h, u=0 at y=0

A negative pressure gradient implies a parabolic velocity profile, contributing for a positive velocity, A positive pressure gradient implies a parabolic velocity profile, contributing for a negative velocity, A plate velocity contributes with a linear profile. The resulting velocity profile is: + =

(da sebenta de Mec. Fluidos I)