Drag Force

Oseen approximated the inertial effect and developed a correction to the Stokes drag given in Equation (4). This is shown in Figure 2.

(4)

For 1 < R < 1000, which is referred to as the transition regime, the following expressions may be used (Clift et al., 1978):

(5)

(6)

For 10³<R_D<2.5x10⁵, the drag coefficient is roughly constant. (C_D=0.4) This regime is referred to as the Newton regime. At Re≈2.5x10⁵, the drag coefficient decreases sharply due to the transition from laminar to turbulent boundary layer around the sphere. That causes the separation point to shift downstream as shown in Figure 3.

Figure 3: Laminar and turbulent boundary layer separation.