Two concentric cylinders of radii a and b respectively (a > b) have their common axis lying along the z-axis. The space between them   b < r < a contains fluid of viscosity µ. A flow is generated by moving the outer cylinder with constant speed U parallel to its axis whilst the inner cylinder remains at rest. 1. Use cylindrical polar coordinates (r, θ, z) and consider an elementary fluid element of lengths dr and dz and angle dθ (measured from the z-axis). Draw a diagram showing the forces acting on the surfaces of the fluid element. 2. Determine the velocity distribution u in the z-direction, stating any assumptions you make.

Two concentric cylinders of radii a and b respectively (a > b) have their common axis
lying along the z-axis. The space between them   b < r < a contains fluid of viscosity µ.
A flow is generated by moving the outer cylinder with constant speed U parallel to its
axis whilst the inner cylinder remains at rest.

1. Use cylindrical polar coordinates (r, θ, z) and consider an elementary fluid element
of lengths dr and dz and angle dθ (measured from the z-axis). Draw a diagram
showing the forces acting on the surfaces of the fluid element.

2. Determine the velocity distribution u in the
z-direction, stating any assumptions you make.