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The surface-area-to-volume ratio has physical dimension inverse length (L −1) and is therefore expressed in units of inverse metre (m −1) or its prefixed unit multiples and submultiples. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm 2 and a volume of 1 cm 3. The surface to volume ratio for this cube is thus
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 excluded volume of a hard sphere is eight times its volume—however, for a two-molecule system, this volume is distributed among the two particles, giving the conventional result of four times the volume; [2] this is an important quantity in the Van der Waals equation of state. The calculation of the excluded volume for particles with non ...
Examples include number of particles and population size. In mathematics, the "number of elements" in a set is termed cardinality. Countable nouns is a related linguistics concept. Counting numbers, such as number of bits, can be compounded with units of frequency (inverse second) to derive units of count rate, such as bits per second.
The damage on the metal sheet or characteristic pattern illustrates an "uneven surface," a change in the sheet material's plastic behavior and involves a larger deformed volume compared to mere flattening of the surface oxides. Galling is a form of wear caused by adhesion between sliding surfaces.
In two dimensions, volume is just area, and a volume element gives a way to determine the area of parts of the surface. Thus a volume element is an expression of the form (,) that allows one to compute the area of a set B lying on the surface by computing the integral = (,).
Two common methods for finding the volume of a solid of revolution are the disc method and the shell method of integration.To apply these methods, it is easiest to draw the graph in question; identify the area that is to be revolved about the axis of revolution; determine the volume of either a disc-shaped slice of the solid, with thickness δx, or a cylindrical shell of width δx; and then ...
A ruled surface is one which can be generated by the motion of a straight line in E 3. [46] Choosing a directrix on the surface, i.e. a smooth unit speed curve c(t) orthogonal to the straight lines, and then choosing u(t) to be unit vectors along the curve in the direction of the lines, the velocity vector v = c t and u satisfy