Two fluid layers are located between two parallel plates. The upper layer, A$,$ is a Newtonian fluid with a viscosity of $1cp.$ The lower fluid B has rheological properties described by the following equation:

$(\frac{{}_0}{})-1=(\frac{}{{}_C}{)}^{\frac{1}{2}}$

where $=$ viscosity of the fluid, $=$ shear stress, ${}_0=$ limiting viscosity $=9cp$

${}_C=$ characteristic stress $=1$ dynes $\frac{?}{c{m}^2}$

The lower plate is held fixed and a stress of $4$ dynes $\frac{?}{c{m}^2}$ is placed on the upper plate. What is the steady$-$state velocity of the upper plate?

Note: There is no pressure gradient in this system and the flow is perpendicular to the gravity direction.