Aula Teórica 14

1. Aula Teórica 14 Escoamento de Couette, i.e., escoamento entre duasplacasplanas.

2. Couette Flow • We will assume stationary, incompressible and that the plates have infinite length and depth along the direction normal to the paper. This is equivalent to say that we are far away from the entrance and the exit and from the walls perpendicular to x3. In this case the velocity as a single component, along x1. • The BC are u=0 at y=0 and u=U0 at y=h • The continuity equation becomes: • The NS equation becomes:

3. y z gx g 𝜶 𝜶 gy x

4. Integrating along yy • The BC are u=0 at y=0 and u=U0 at y=h

5. Interpretation Defining: is the straight line • This flow could exist between: • The piston of a car and the cylinder, • A tire and the road, • A foot and the soil, • …..

6. Flow over a inclined plane • We will assume stationary, incompressible that the plates have infinite length along the direction normal to the paper and that we are far from the entrance and the exit. In this case the velocity as a single component, along x1. • The BC are u=0 at y=0 and τ=0 aty=h h

7. The continuity equation becomes: • The NS equation becomes:

8. Integrating along yy • The BC are u=0 at y=0 and τ=0 at y=h • The velocity profile is a parabola and shear stress is a straight line

9. Average velocity, Maximum shear • Does it make sense maximum shear to be independent of the viscosity?