Water flows through a circular pipe with diameter d. The velocity profile of the water is given as: u(r) 4μ 4 ), where r

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Water flows through a circular pipe with diameter d. The velocity profile of the water is given as: u(r) 4μ 4 ), where r is the radius of the tube, u is the viscosity, and a is a constant. a) Show that this velocity profile satisfies the boundary conditions of a fully developed laminar flow. b) Which units must the constant a have for u (r) to express velocity in m/s? c) Find an expression for the shear stress at the point where r = d / 4 d) Find an expression for the shear force acting on a piece of pipe of length L. e) What is the difference between a turbulent and a laminar flow? (z + - +/-) 1/2+2 =