solved problem in resistance to flow

solved problem in resistance to flow
For a thin wing moving parallel to its chord line, transition to a turbulent boundary
layer occurs at a “local” Reynolds number Rex, where x is the distance from the leading
edge of the wing. The critical Reynolds number depends upon the intensity of turbulent
fluctuations in the stream and equals 2.8E6 if the stream is very quiet. A semiempirical
correlation for this case [Ref. 3 of Ch. 6] is
crit
2 1/2
1/2
2
1 (1 13.25 )
Re
0.00392 x
?
?
? ? + +
where ? is the tunnel-turbulence intensity in percent. If V = 20 m/s in air at 20°C, use this
formula to plot the transition position on the wing versus stream turbulence for ? between
0 and 2 percent. At what value of ? is xcrit decreased 50 percent from its value at ? = 0?
Solution: This problem is merely to illustrate the strong effect of stream turbulence on
the transition point. For air at 20°C, take ? = 1.2 kg/m3 and ? = 1.8E?5 kg/m?s. Compute
Rex,crit from the correlation and plot xtr = ?Rex/[?(20 m/s)] versus percent turbulence:

In flow past a body or wall, early
transition to turbulence can be induced by
placing a trip wire on the wall across the
flow, as in Fig. P6.5. If the trip wire in
Fig. P6.5 is placed where the local velocity
is U, it will trigger turbulence if Ud/? = 850,
where d is the wire diameter [Ref. 3 of Ch. 6].
If the sphere diameter is 20 cm and transition
is observed at ReD = 90,000, what is the
diameter of the trip wire in mm?