Drag and Lift Coefficients

These are defined as

$$C_D~=~\left({ {D}\over {1/2 \rho~V^2~A}}\right);~~C_L~=~\left({ {L}\over {1/2 \rho~V^2~A}}\right)$$ (5.15)

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	$~{V} \over {a}$	${flow ~speed} \over {speed ~of~ sound}$	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