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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. The numbers along the line indicate several flow regimes and associated changes in the drag coefficient:
For the case of a sphere in a uniform far field flow, it is advantageous to use a cylindrical coordinate system (r, φ, z). The z –axis is through the centre of the sphere and aligned with the mean flow direction, while r is the radius as measured perpendicular to the z –axis. The origin is at the sphere centre.
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).
Shown is a sphere in Stokes flow, at very low Reynolds number. Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, [1] is a type of fluid flow where advective inertial forces are small compared with viscous forces. [2] The Reynolds number is low, i.e. . This is a typical situation in flows where the ...
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. Drag depends on the properties of the fluid and on the size, shape, and speed of the object.
The flow is proportional to the absolute inlet pressure, so the flow in scfm would equal the C v flow coefficient if the inlet pressure were reduced to 2 psia and the outlet were connected to a vacuum with less than 1 psi absolute pressure (1.0 scfm when C v = 1.0, 2 psia input).
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 ...