Question

A viscous liquid is sheared between two parallel disks of radius �, one of which rotates with angular speed Ω, while the other is fixed. The velocity field is purely tangential, and the velocity varies linearly with z from: �; = 0 at � = 0 (the fixed disk) to the velocity of the rotating disk at its surface (� = ℎ). Derive an expression for the velocity field between the disks.

Answer 1

Answer:

Upper disk rotates at a constant angular velocity. The velocity at any height from stationery disk, say at x metres

$U_o=v(\frac {x}{h})$ where v is tangential velocity at radius r from the centre of disk

$U_o=r\omega (\frac {x}{h})$

The radial component of velocity is given as

$U_r=0$

The z component of velocity is also given as  

W=0

Total velocity, $v= r\omega (\frac {x}{h})\hat e_{o}$