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drag force F d. Using the algorithm of the Buckingham π theorem, these five variables can be reduced to two dimensionless groups: drag coefficient c d and; Reynolds number Re. That this is so becomes apparent when the drag force F d is expressed as part of a function of the other variables in the problem:
Isocontours of the ψ function (values in contour labels). 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.
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.
The derivation of Stokes' law, which is used to calculate the drag force on small particles, assumes a no-slip condition which is no longer correct at high Knudsen numbers. The Cunningham slip correction factor allows predicting the drag force on a particle moving a fluid with Knudsen number between the continuum regime and free molecular flow.
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.
Blue line: drag force; red line: inertia force; black line: total force according to the Morison equation. Note that the inertia force is in front of the phase of the drag force: the flow velocity is a sine wave, while the local acceleration is a cosine wave as a function of time.
The first reference drag curve is based purely on the Siacci/Mayevski retardation rate function. The second reference drag curve is adjusted to equal the Siacci/Mayevski retardation rate function at a projectile velocity of 2600 fps (792.5 m/s) using a .30-06 Springfield Cartridge, Ball, Caliber .30 M2 152 grains (9.8 g) rifle spitzer bullet ...
A schematic diagram of the Blasius flow profile. The streamwise velocity component () / is shown, as a function of the similarity variable .. Using scaling arguments, Ludwig Prandtl [1] argued that about half of the terms in the Navier-Stokes equations are negligible in boundary layer flows (except in a small region near the leading edge of the plate).