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2.2 Gas Fluid Dynamics 47

thickness of the boundary layer dðxÞ is taken as the distance above the solid surface
where the velocity reaches 0.99 u 1 . The boundary layer grows with the distance
from the leading edge until it reaches a constant thickness. Then, we call it fully
developed boundary layer.
The flow within a boundary layer also changes gradually from laminar to tur-
bulent. And it is characterized with boundary layer Reynolds number Re x based on
u 1 and x

qu 1 x
Re x ¼ ð2:75Þ
l
The velocity profile within the laminar boundary layer is simplified as

u 2y y 2
¼ 2 ð2:76Þ
u 1 d d
The skin drag is resulted from the shear stress on the solid surface (wetted area).
For the real bluff bodies, flow separation occurs and it results in another drag effect
called form drag or pressure drag. Overall, the drag is

1 2
F D ¼ C D qu A ð2:77Þ
2 1
where C D is the drag coefficient based on the reference area, A.

Fig. 2.4 Drag coefficient versus Reynolds number for a sphere (Data source [11])