Consider steady, incompressible, two-dimensional flow of fluid into a converging duct with straight walls (Fig. P10–47). The volume flow rate is V̇, 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 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.

FIGURE P10–47

Transcribed Image Text:

| r = R ΔΘ