Page 185 - Wind Energy Handbook

DRAG COEFFICIENT 159

Figure A3.5 Separated Flow Pressure Distribution Around a Cylinder

A3.2 Drag coefficient

If Stokes’ drag Equation (A3.2) for the sphere is re-arranged, giving

ì ðd 2
Drag ¼ 3ðìUd ¼ 24 1 rU 2 (A3:3)
rUd 2 4

1
2
it is then in the standard form of drag coefficient (C d )3 dynamic pressure ( rU ) 3
2
frontal area (A). The drag coefficient is then defined as
Drag
C d ¼ (A3:4)
1 2
rU A
2
Note that, rUd=ì is known as the Reynolds number (Re) and represents the ratio of
the inertia force acting on a unit volume of fluid, as it is accelerated by a pressure
gradient, and the viscous force on the same volume of fluid which is resisting the
motion of the fluid. For high Reynolds numbers viscous forces are low and vice
versa. The drag coefficient term in Equation (A3.3) is C d ¼ 24=Re and is clearly a
function only of the Reynolds number; this turns out to be valid for all bodies in
incompressible flow but the functional relationship is not usually as simple as in
the above case. However, it can be stated, generally, that C d falls with increasing
Reynolds number.