A viscous liquid fills the annular gap between vertical concentric cylinders. The outer cylinder is stationary, and the inner cylinder equations rotates at speed annular velocity . The flow is laminar. Simplify for the continuity, Navier-Stokes, and shear tangential shear equations to model this flow field. Obtain expressions for the liquid velocity profile and the stress distribution. Compare the shear stress at the surface of the inner cylinder with that of the outer cylinder. Determine which is greater. The continuity equation in cylindrical coordinates for constant density is r1r(rur)+r1(v)+z(vz)=0 Normal and shear stresses in cylindrical coordinates for constant density and viscosity are rr=p+2rvz0=p+2(r1uv+ru)zz=p+2zvzn=[rr(r)+r1ur]z=(zv+r1vz)zz=(zuz+rvz) The Navier-Stokes equations in cylindrical coordinates viscosity are r component: (tur+vrrur+rwurru2+uzzur)=grrp+{r(r1r[rur])+r2122vrr22u+z22vr} component: (tv+vrrv0+rubv+ruru+v2zv)=gr1p+{r(r1r[rv])+r2122u+r22vr+z22v}zcomponent:(tvz+vrrvz+rv0uz+vzzuz)=gzzp+{r1r(rrvz)+r2122vz+z22vz}