8.40 A fully developed two-dimensional duct flow of width W and height D has a parabolic velocity profile, as shown in F
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8.40 A fully developed two-dimensional duct flow of width W and height D has a parabolic velocity profile, as shown in Figure P8.40. (a) If w» D, show that the wall shear stress Tw is related to the pressure gradient dp/dx according to dp/dx = -2T/D. (b) Express the pressure gradient in terms of the velocity on the centerline, the fluid viscos- ity , and the duct height D. (c) How does the z-component of vorticity vary with y?
yį 0 319 = 1-2² D Figure P8.40
8.40 (b)-8Uoμ/D², (c) -8Uoy/D²