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Creeping flow past a falling sphere in a fluid (e.g., a droplet of fog falling through the air): streamlines, drag force F d and force by gravity F g. At terminal (or settling) velocity, the excess force F e due to the difference between the weight and buoyancy of the sphere (both caused by gravity [7]) is given by:
The drag equation may be derived to within a multiplicative constant by the method of dimensional analysis. If a moving fluid meets an object, it exerts a force on the object. Suppose that the fluid is a liquid, and the variables involved – under some conditions – are the: speed u, fluid density ρ, kinematic viscosity ν of the fluid,
At low , is asymptotically proportional to , which means that the drag is linearly proportional to the speed, i.e. the drag force on a small sphere moving through a viscous fluid is given by the Stokes Law: = At high , is more or less constant, but drag will vary as the square of the speed varies.
An object moving through a gas or liquid experiences a force in direction opposite to its motion. Terminal velocity is achieved when the drag force is equal in magnitude but opposite in direction to the force propelling the object. Shown is a sphere in Stokes flow, at very low Reynolds 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.
The downward force of gravity (F g) equals the restraining force of drag (F d) plus the buoyancy. The net force on the object is zero, and the result is that the velocity of the object remains constant. Terminal velocity is the maximum speed attainable by an object as it falls through a fluid (air is the most common example).
In fluid dynamics, Epstein drag is a theoretical result, for the drag force exerted on spheres in high Knudsen number flow (i.e., rarefied gas flow). [1] This may apply, for example, to sub-micron droplets in air, or to larger spherical objects moving in gases more rarefied than air at standard temperature and pressure.
Jean le Rond d'Alembert (1717-1783) From experiments it is known that there is always – except in case of superfluidity – a drag force for a body placed in a steady fluid onflow. The figure shows 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 ...