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About Mathematical Modeling
Published in Sandip Banerjee, Mathematical Modeling, 2021
When the dimension of a quantity is found and expressed in the form of an equation, the equation is called the dimensional equation. Dimensional analysis is a method of using the fact that the dimension of each term in an equation must be the same, to suggest a relationship between the physical quantities involved.
Algebra 1
Published in Surinder S. Virdi, Advanced Construction Mathematics, 2019
In science and engineering, a number of methods can be used to solve problems. Dimensional analysis is an effective method that can be used not only to establish relationship among physical quantities using their dimensions, but also to check the dimensional correctness of a given equation.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
Dimensional analysis is a mathematical tool whose use will enable the scientist and engineer to save time in planning experiments and correlating results of experiments. The method arose in the science of mechanics. In this science three units are regarded as fundamental, namely, length, mass, and time. Other employed units are called derived units. For example, velocity and acceleration are derived units defined by reference to the two fundamental units - length and time. The units of force-momentum, mechanical energy, and power are dependent on all three of the fundamental units. The study of electricity, heat transfer, and so forth requires the inclusion of other fundamental units such as charge.
Steady-state temperature distribution in a tetragonal solid
Published in International Journal of Ambient Energy, 2020
P. Sankarganesh, P. Gowtham, J. Thamilarasan, K. Karthik
Dimensional analysis is a mathematical technique which makes use of the study of the dimensions for solving several engineering problems. Each physical phenomenon can be expressed by an equation giving relationship between differential quantities; such quantities are dimensional and non-dimensional. It helps determining systematic arrangements of the variables and to form non-dimensional parameters. It is based on the principle of dimensional homogeneity and uses the dimensions of the relevant variables affecting the phenomenon.
Effects of the attrition of bed material on the solid circulation rate in a recirculating fluidized bed
Published in Particulate Science and Technology, 2018
Shivali Chourasia, Babu J. Alappat
Dimensional analysis is a mathematical technique that deals with the dimensions of the physical quantities involved in the phenomenon. This is the method of analysis based on the mathematics of the dimensions of variables. The dimensionless variables are fewer than the original dimensional variables. According to the principle of dimensional homogeneity, the solution of a problem must be a dimensional homogeneous equation in terms of specified variables (Buckingham 1915).
Light intensity as mechanical potential: a symmetry-based approach
Published in Liquid Crystals, 2019
Tianyi Guo, Xiaoyu Zheng, Peter Palffy-Muhoray
In the case of dimensional analysis, the emphasis is on units; one inquires about how the relevant quantities can be combined to form an expression with the right units – that is, the units of the unknown quantity being solved for.