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.

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Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.