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Drag Coefficient (Cd)

A dimensionless quantity representing the resistance of an object to motion through a fluid. Cd is dependent on shape and Reynolds number.
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The statement of the theorem

The Drag Coefficient, CdC_d, is defined as the dimensionless ratio of the total drag force, DD, acting on a body BB immersed in a fluid, to the dynamic pressure multiplied by a defined reference area ArefA_{ref}. Mathematically, the drag force DD is derived from the surface integral of the stress tensor τij\tau_{ij} over the boundary surface SS of the body BB:\n\nD=∬S(σ⃗⋅n⃗)⋅i⃗flow dSD = \iint_{S} (\vec{\sigma} \cdot \vec{n}) \cdot \vec{i}_{flow} \, dS\n\nwhere σ⃗\vec{\sigma} is the Cauchy stress tensor, n⃗\vec{n} is the outward unit normal vector to SS, and i⃗flow\vec{i}_{flow} is the unit vector in the direction of the relative flow velocity v⃗\vec{v}.\n\nAssuming the flow is steady and incompressible, the drag force DD simplifies to:\n\nD=12ρv2ArefCdD = \frac{1}{2} \rho v^2 A_{ref} C_d\n\nTherefore, the rigorous definition of the Drag Coefficient is given by:\n\nCd=D12ρv2Aref=∬S(pn⃗+τ⃗)⋅i⃗flow dS12ρv2ArefC_d = \frac{D}{\frac{1}{2} \rho v^2 A_{ref}} = \frac{\iint_{S} (p \vec{n} + \vec{\tau}) \cdot \vec{i}_{flow} \, dS}{\frac{1}{2} \rho v^2 A_{ref}}\n\nHere, ρ\rho is the fluid density, vv is the characteristic flow velocity, ArefA_{ref} is the reference area (e.g., projected area), and pp and τ⃗\vec{\tau} are the pressure and viscous stress components, respectively.
Source: Wikipedia