Mechanics of Fluids

334 Boundary layers, wakes and other shear layers
Fig. 8.15 Drag relations for
isolated smooth spheres.
calculate d. On the other hand, if uT is initially unknown we may determine
{ 3
4CD(Re) 2 } 1/3 = d{ϱ(�ϱ)g/µ 2 } 1/3 and then obtain uT from the
corresponding value of Re.
It will be noted, however, that for a given value of { 3
4CD(Re) 2 } 1/3 in
the approximate range 2.3 × 105 < Re < 3.8 × 105 there appear to be three
possible values of Re, and therefore of velocity. The kink in the graph here
is of course a consequence of the abrupt fall in CD that occurs when the
boundary layer becomes turbulent. The middle one of these three values
of velocity represents an unstable condition because over the section AB of
the curve a small increase of velocity leads to a reduction of drag and thus
to further acceleration; therefore steady conditions cannot be maintained.
Although both the outer values are stable, it is normally the lower one that
is attained in practice, unless it is very close to the peak A or there is some
pronounced unsteadiness in the fluid itself such as upward gusts of air if the