The velocity distribution in a fully developed laminar pipe flow is given by where UCL is the velocity at the centerline, and R is the pipe radius. The fluid density is ρ, and its viscosity is µ. (a) Find the average velocity  . (b) Write down the Reynolds number Re based on average velocity and pipe diameter. At what approximate value of this Reynolds number would you expect the flow to become turbulent? Why is this value only approximate? (c) Assume that the stress/strain rate relationship for the fluid is Newtonian. Find the wall shear stress τw in terms of µ, R and UCL. Express the local skin friction coeffient Cf in terms of the Reynolds number Re.

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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.