Water flows down a long, straight, inclined pipe of diameter D and length L (Fig

Chapter 9, Problem 9-125

(choose chapter or problem)

Water flows down a long, straight, inclined pipe of diameter D and length L (Fig. P9125). There is no forced pressure gradient between points 1 and 2; in other words, the water flows through the pipe by gravity alone, and P1 5 P2 5 Patm. The flow is steady, fully developed, and laminar. We adopt a coordinate system in which x follows the axis of the pipe. (a) Use the control volume technique of Chap. 8 to generate an expression for average velocity V as a function of the given parameters r, g, D, Dz, m, and L. (b) Use differential analysis to generate an expression for V as a function of the given parameters. Compare with your result of part (a) and discuss. (c) Use dimensional analysis to generate a dimensionless expression for V as a function of the given parameters. Construct a relationship between your Ps that matches the exact analytical expression.