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In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or comparisons are performed.
An example of dimensional analysis can be found for the case of the mechanics of a thin, solid and parallel-sided rotating disc. There are five variables involved which reduce to two non-dimensional groups. The relationship between these can be determined by numerical experiment using, for example, the finite element method. [10]
The following two problems demonstrate the finite element method. P1 is a one-dimensional problem : {″ = (,), = =, where is given, is an unknown function of , and ″ is the second derivative of with respect to .
A portion of the two dimensional grid used for Discretization is shown below: Graph of 2 dimensional plot. In addition to the east (E) and west (W) neighbors, a general grid node P, now also has north (N) and south (S) neighbors. The same notation is used here for all faces and cell dimensions as in one dimensional analysis.
The analysis of results is performed by determining the ratio of elements from within the sample and working out a chemical formula that fits with those results. This process is useful as it helps determine if a sample sent is the desired compound and confirms the purity of a compound.
A Fermi problem (or Fermi question, Fermi quiz), also known as an order-of-magnitude problem, is an estimation problem in physics or engineering education, designed to teach dimensional analysis or approximation of extreme scientific calculations. Fermi problems are usually back-of-the-envelope calculations.
Gravimetric analysis describes a set of methods used in analytical chemistry for the quantitative determination of an analyte (the ion being analyzed) based on its mass. The principle of this type of analysis is that once an ion's mass has been determined as a unique compound, that known measurement can then be used to determine the same analyte's mass in a mixture, as long as the relative ...
The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of the total mass transfer rate (convection + diffusion) to the rate of diffusive mass transport, [1] and is named in honor of Thomas Kilgore Sherwood.