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Viscous drag of fluid in a pipe: Drag force on the immobile pipe restricts the velocity of the fluid through the pipe. [4] [5] In the physics of sports, drag force is necessary to explain the motion of balls, javelins, arrows, and frisbees and the performance of runners and swimmers. [6]
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]
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 .
An object falling through water or oil would slow down at a greater rate, until eventually reaching a steady-state velocity as the drag force comes into equilibrium with the force from gravity. This is the concept of viscous drag, which for example is applied in automatic doors or anti-slam doors. [14]
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]
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.
The Navier–Stokes equations (/ n æ v ˈ j eɪ s t oʊ k s / nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes.