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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.
For an object with a smooth surface, and non-fixed separation points (like a sphere or circular cylinder), the drag coefficient may vary with Reynolds number Re, up to extremely high values (Re of the order 10 7).
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 .
Drag coefficient C d for a sphere as a function of Reynolds number Re, as obtained from laboratory experiments. The dark line is for a sphere with a smooth surface, while the lighter line is for the case of a rough surface (e.g. with small dimples).
Although the inertia and drag coefficients can be tuned to give the correct extreme values of the force. [ 8 ] Third, when extended to orbital flow which is a case of non uni-directional flow, for instance encountered by a horizontal cylinder under waves, the Morison equation does not give a good representation of the forces as a function of time.
The volume flux, through a tube bounded by a surface of some constant value ψ, is equal to 2πψ and is constant. [ 9 ] For this case of an axisymmetric flow, the only non-zero component of the vorticity vector ω is the azimuthal φ –component ω φ [ 11 ] [ 12 ]
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
A drag coefficient can also be calculated mathematically: = [8] where: C d, drag coefficient., density of the projectile. v, projectile velocity at range. π (pi) = 3.14159... d, measured cross-sectional diameter of projectile; or