Explain what is dimensional analysis? what are its applications & what are its limitations?

Asked by mehreennisar | 24th Feb, 2010, 08:05: AM

Expert Answer:

Dear student,

In maths and science, dimensional analysis is a tool to understand the properties of physical quantities independent of the units used to measure them. Technique used in the physical sciences and engineering to reduce physical properties such as acceleration, viscosity, energy, and others to their fundamental dimensions of length, mass, and time. This technique facilitates the study of interrelationships of systems (or models of systems) and their properties. Acceleration, for example, is expressed as length per unit of time squared. Dimensional analysis is often the basis of mathematical models of real situations.

Application:

A typical application of dimensional analysis occurs in fluid dynamics. If a moving fluid meets an object, it exerts a force on the object, according to a complicated (and not completely understood) law. The variables involved are: the speed, density and viscosity of the fluid, the size of the body (expressed in terms of its frontal area ), and the force. Using the algorithm of the π-theorem, one can reduce these five variables to two dimensionless parameters: the drag coefficient and the Reynold's number.

Limitation:

  • Dimensional analysis has no information on dimensionless constants.
  • If a quantity is dependent on trigonometric or exponential functions, this method cannot be used.
  • In some cases, it is difficult to guess the factors while deriving the relation connecting two or more physical quantities.
  • This method cannot be used in an equation containing two or more variables with same dimensions.
  • It cannot be used if the physical quantity is dependent on more than three unknown variables.
  • This method cannot be used if the physical quantity contains more than one term, say sum or difference of two terms.

Hope this helps.

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Answered by  | 24th Feb, 2010, 09:32: AM

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