Solved: Consider steady, incompressible, laminar flow of a Newtonian fluid in an

Chapter 9, Problem 9-105

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Consider steady, incompressible, laminar flow of a Newtonian fluid in an infinitely long round pipe of diameter D or radius R 5 D/2 inclined at angle a (Fig. P9105). There is no applied pressure gradient (P/x 5 0). Instead, the fluid flows down the pipe due to gravity alone. We adopt the coordinate system shown, with x down the axis of the pipe. Derive an expression for the x-component of velocity u as a function of radius r and the other parameters of the problem. Calculate the volume flow rate and average axial velocity through the pipe.