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Drag coefficients in fluids with Reynolds number approximately 10 4 [1] [2] Shapes are depicted with the same projected frontal area. In fluid dynamics, the drag coefficient (commonly denoted as: , or ) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water.
is the drag coefficient – a dimensionless coefficient related to the object's geometry and taking into account both skin friction and form drag. If the fluid is a liquid, c d {\displaystyle c_{\rm {d}}} depends on the Reynolds number ; if the fluid is a gas, c d {\displaystyle c_{\rm {d}}} depends on both the Reynolds number and the Mach number .
For an object with well-defined fixed separation points, like a circular disk with its plane normal to the flow direction, the drag coefficient is constant for Re > 3,500. [17] The further the drag coefficient C d is, in general, a function of the orientation of the flow with respect to the object (apart from symmetrical objects like a sphere).
Note the minus sign in the equation, the drag force points in the opposite direction to the relative velocity: drag opposes the motion. Stokes' law makes the following assumptions for the behavior of a particle in a fluid: Laminar flow; No inertial effects (zero Reynolds number) Spherical particles; Homogeneous (uniform in composition) material
Universal sedimentation equation — drag coefficient, a function of Reynolds number and shape factor, 2D diagram Universal sedimentation equation — drag coefficient, a function of Reynolds number and shape factor, 3D diagram. This is why mathematically all Newtonian, incompressible flows with the same Reynolds number are comparable.
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The more general form of the equation in the classical case is [6] =, where D is the diffusion coefficient; μ is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, μ = v d /F; k B is the Boltzmann constant; T is the absolute temperature.
The Morison equation contains two empirical hydrodynamic coefficients—an inertia coefficient and a drag coefficient—which are determined from experimental data. As shown by dimensional analysis and in experiments by Sarpkaya, these coefficients depend in general on the Keulegan–Carpenter number, Reynolds number and surface roughness. [4] [5]