Drag and Lift Coefficients

These are defined as

where D and L are drag and lift forces respectively.

Some of the common non-dimensional numbers in Fluid Mechanics have been listed in Table 5.1.

Non-Dimensional Number Definition Significance Application
Reynolds Number, Re $ {\rho~V~L} \over {\mu}$ $ {Inertial~ Force} \over {Viscous~ Force}$ All  branches  of  Fluid  Dynamics
Mach  Number, M $ ~{V} \over {a}$ $ {flow ~speed} \over {speed
sound}$ Compressible  Flow
Froude Number, Fr $ {V^2} \over {g~L} $ $ {Inertia~ Force}
\over {Gravity~ Force}$ Free Surface Flows
Prandtl Number, Pr $ {\mu~C_p} \over k $ $ {Viscous~
dissipation} \over {Conduction}$ Heat Transfer
Ration of Specific Heats, k $ {c_p} \over {c_v}$ $ Enthalpy
\over {Internal~Energy}$ Compressible Flow
Roughness Ratio $ \epsilon \over L $ $ {Height~of~Roughness}
\over {Body~Length} $ Turbulent Flows
Pressure Coefficient, Cp $ {p~-~p_\infty} \over
{1/2~\rho~V^2}$ $ {Static~Pressure} \over {Dynamic~Pressure}$ Aerodynamics, Hydrodynamics
Drag Coefficient, CD $ {D} \over
{1/2~\rho~V^2~A}$ $ {Drag} \over {Dynamic~Force}$ Aerodynamics, Hydrodynamics
Lift Coefficient, CL $ {L} \over
{1/2~\rho~V^2~A}$ $ {Lift} \over {Dynamic~Force}$ Aerodynamics, Hydrodynamics
Skin Friction, cf $ {\tau_{wall}} \over {1/2~\rho~V^2}$ $ {Wall~Shear~Stress} \over {Dynamic~pressure}$ Boundary Layer Flow

Table 5.1: Important Non-Dimensional Numbers

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney