Consider steady, incompressible, two-dimensional flow of

Chapter 10, Problem 41P

(choose chapter or problem)

Problem 41P

Consider steady, incompressible, two-dimensional flow of fluid into a converging duct with straight walls (Fig. P10-46). The volume flow rate is ν, and the velocity is in the radial direction only, with u r a function of r only. Let b be the width into the page. At the inlet into the converging duct (r = R), u r is known; u r = u r(R). Assuming inviscid flow everywhere, generate an expression for u r as a function of r, R, and

FIGURE P10-46

u r(R) only. Sketch what the velocity profile at radius r would look like if friction were not neglected (i.e.. a real flow) at the same volume flow rate.