Friction drag coefficient for steady, constant property, 2-D, uniform flow over a flat plate:
Reℓ < 5 × 105
Laminar:
CDf = 1.328 Reℓ−1/2
Mixed or Transitional:
CDf = 0.0743 Reℓ−1/5 −
€
CDf =
€
0.455
(log Reℓ )
2.58
−
1740
Reℓ €
5 ×10 5 < Reℓ < 10 7
1700
Reℓ
5 ×10 5 < Reℓ < 10 9
CDf = 0.0743 Reℓ−1/5
Turbulent (smooth plate):
€
CDf =
€
Turbulent (completely turbulent):
€
CDf
5 ×10 5 < Reℓ < 10 7
0.455
2.58
5 ×10 5 < Reℓ < 10 9
−2.5
⎡
⎛ ε ⎞⎤
= ⎢1.89 −1.62 log ⎜ ⎟⎥
⎝ ℓ ⎠⎦
⎣
see Table 8.1 for ε
(log Reℓ )
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
€
Streamlines for cylinder in uniform cross flow for a range of Reynolds numbers.
CD =
1
2
D
ρ U 2 Ap
€
Drag coefficient, CD, versus Reynolds number, Re, where D is total drag, U is uniform
velocity, D is diameter, Ap is projected frontal area, ρ is density, and µ is viscosity.
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˚
Wing with trailing vortices.
stall at high α
(a) uniform flow
past a cylinder
(b) free vortex at
center of cylinder
(c) uniform flow past
rotating cylinder
Rotating cylinder
with separation
D
Lift coefficient, CL, and drag coefficient,
CD, versus spin ratio, SR = (ω D) (2 U ) ,
for a spinning smooth sphere where:
ω
D
U
Re
ρ
ν
D
L
rate of rotation
€
diameter
uniform velocity
Reynolds number
density
kinematic viscosity
drag
lift
L