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In fluid dynamics, Stokes' law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. [1] It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations. [2]
Parasitic drag is made up of multiple components including viscous pressure drag (form drag), and drag due to surface roughness (skin friction drag). Additionally, the presence of multiple bodies in relative proximity may incur so called interference drag , which is sometimes described as a component of parasitic drag.
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 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.
Skin friction drag is generally expressed in terms of the Reynolds number, which is the ratio between inertial force and viscous force. Total drag can be decomposed into a skin friction drag component and a pressure drag component, where pressure drag includes all other sources of drag including lift-induced drag. [1]
In fluid dynamics, the Oseen equations (or Oseen flow) describe the flow of a viscous and incompressible fluid at small Reynolds numbers, as formulated by Carl Wilhelm Oseen in 1910. Oseen flow is an improved description of these flows, as compared to Stokes flow, with the (partial) inclusion of convective acceleration. [1]
is the shear stress ("skin drag") in the fluid, μ {\displaystyle \mu } is a scalar constant of proportionality, the dynamic viscosity of the fluid d u d y {\displaystyle {\frac {du}{dy}}} is the derivative in the direction y, normal to x, of the flow velocity component u that is oriented along the direction x.
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.