Consider steady flow of air through the diffuser portion of a wind tunnel (Fig. P11–20). Along the centerline of the diffuser, the air speed decreases from uentrance to uexit as sketched. Measurements reveal that the centerline air speed decreases parabolically through the diffuser. Write an equation for centerline speed u(x), based on the parameters given here, from x = 0 to x = L.

### Solution to 22P

Step 1

We need to write an equation of centerline speed u(x) where x=0 and x=L. We are given that the fluid flow is decreasing parabolically while flowing through the diffuser.