Friction drag coefficient for steady, constant property, 2 ...

Friction drag coefficient for steady, constant property, 2-D, uniform flow over a flat plate:

Laminar: CDf = 1.328 Reℓ−1/2 Reℓ < 5 × 105
5 ×105 < Reℓ < 107
Mixed or Transitional: CDf = 0.0743 Reℓ−1/5 − 1740 5 ×105 < Reℓ < 109
Reℓ
€ €

0.455 1700
log Reℓ −2.58 Reℓ
( )CDf=

€

Turbulent (smooth plate): CDf = 0.0743 Reℓ−1/5 5 ×105 < Reℓ < 107
€ 5 ×105 < Reℓ < 109
0.455
€ log Reℓ 2.58
( )CDf=

Turbulent (completely turbulent): CDf = ⎢⎣⎡1.89 − 1.62 log ⎛ ε ⎞⎤−2.5 see Table 8.1 for ε
€ ⎜⎝ ℓ ⎟⎠⎦⎥

where Reℓ = U ℓ ν is Reynolds number, U is free stream velocity, ν is kinematic viscosity, ℓ is
plate length, b is plate width€, ε is plate roughness, and D f is drag force due to friction.

€€
€

ℓ

€

Reℓ = U ℓ ν
€



Strong differences in laminar and turbulent separation on an 8.5-in. bowling ball entering water
at 25 ft/s: (a) smooth ball, laminar boundary layer; (b) same entry, turbulent flow induced by
patch of nose-sand roughness (NAVAIR Weapons Division Historical Archives.)

CD = 1.2 CD = 0.12

Two objects of considerably different size that have the same drag force.

Drag coefficient as a function of Froude number and hull characteristics for that portion of the
drag due to the generation of waves (Inui, Wave Making Resistance of Ships, 1962).

Effect of angle of attack, α, and aspect ratio, A = b/c where b is span and c is chord length,
on lift coefficient, CL, and drag coefficient, CD, for typical airfoils.

α = 0˚ stall at high α

Wing with trailing vortices.

(a) uniform flow (b) free vortex at (c) uniform flow past
past a cylinder center of cylinder rotating cylinder

Rotating cylinder D
with separation L

Lift coefficient, CL, and drag coefficient,

CD, versus spin ratio, SR = (ω D) (2 U ),

for a spinning smooth sphere where:
ω rate of rotation
D diam€eter
U uniform velocity
Re Reynolds number
ρ density
ν kinematic viscosity
D drag
L lift