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If k is an irrational number, then the curve never closes, and fills the space between the larger circle and a circle of radius R − 2r. Each hypocycloid (for any value of r) is a brachistochrone for the gravitational potential inside a homogeneous sphere of radius R. [6] The area enclosed by a hypocycloid is given by: [3] [7]
The red curve is an epicycloid traced as the small circle (radius r = 1) rolls around the outside of the large circle (radius R = 3).. In geometry, an epicycloid (also called hypercycloid) [1] is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle.
At the end of each tracheal branch, a special cell provides a thin, moist interface for the exchange of gases between atmospheric air and a living cell. Oxygen in the tracheal tube first dissolves in the liquid of the tracheole and then diffuses across the cell membrane into the cytoplasm of an adjacent cell. At the same time, carbon dioxide ...
A cycloid generated by a rolling circle. In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve.
A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion. Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other methods. The concepts of total pressure and dynamic pressure arise from Bernoulli's equation and are
Where air is flowing in a laminar manner it has less resistance than when it is flowing in a turbulent manner. If flow becomes turbulent, and the pressure difference is increased to maintain flow, this response itself increases resistance. This means that a large increase in pressure difference is required to maintain flow if it becomes turbulent.
The starting point for a mathematical description of almost any type of fluid flow is the classical set of Navier–Stokes equations.To describe particle-laden flows, we must modify these equations to account for the effect of the particles on the carrier, or vice versa, or both - a suitable choice of such added complications depend on a variety of the parameters, for instance, how dense the ...
In physics, the Young–Laplace equation (/ l ə ˈ p l ɑː s /) is an algebraic equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although use of the latter is only applicable if assuming that the wall is very thin.