Krull–Schmidt category: Difference between revisions

Revision as of 10:04, 28 November 2013

Rayleigh's method of dimensional analysis is a conceptual tool used in physics, chemistry, and engineering. This form of dimensional analysis expresses a functional relationship of some variables in the form of an exponential equation. It was named after Lord Rayleigh.

The method involves the following steps:

Gather all the independent variables that are likely to influence the dependent variable.
If R is a variable that depends upon independent variables R₁, R₂, R₃, ..., R_n, then the functional equation can be written as R = F(R₁, R₂, R₃, ..., R_n).
Write the above equation in the form $X = C X_{1}^{a} X_{2}^{b} X_{3}^{c} \dots X_{n}^{m}$ where C is a dimensionless constant and a, b, c, ..., m are arbitrary exponents.
Express each of the quantities in the equation in some fundamental units in which the solution is required.
By using dimensional homogeneity, obtain a set of simultaneous equations involving the exponents a, b, c, ..., m.
Solve these equations to obtain the value of exponents a, b, c, ..., m.
Substitute the values of exponents in the main equation, and form the non-dimensional parameters by grouping the variables with like exponents.

Drawback – It doesn't provide any information regarding number of dimensionless groups to be obtained as a result of dimension analysis

@@ Line 1: / Line 1: @@
-Greetings! I am Jimmy. He currently lives in Wisconsin and his family loves it. In my professional life I am an administrative assistant. Canoeing is what that he is totally dependent on. If you in order to find out more away his website: http://Www.Facebook.com/Cafeland2014CheatsHack<br><br>Stop by my blog :: [http://Www.Facebook.com/Cafeland2014CheatsHack cafeland hack]
+'''Rayleigh's method of dimensional analysis''' is a conceptual tool used in [[physics]], [[chemistry]], and [[engineering]]. This form of [[dimensional analysis]] expresses a [[functional relationship]] of some [[variable (mathematics)|variables]] in the form of an [[exponential equation]]. It was named after [[John Strutt, 3rd Baron Rayleigh|Lord Rayleigh]].
+The method involves the following steps:
+# Gather all the [[independent variable]]s that are likely to influence the [[dependent variable]].
+# If ''R'' is a variable that depends upon independent variables ''R''<sub>1</sub>,&nbsp;''R''<sub>2</sub>,&nbsp;''R''<sub>3</sub>,&nbsp;...,&nbsp;''R''<sub>''n''</sub>, then the [[functional equation]] can be written as ''R'' =&nbsp;''F''(''R''<sub>1</sub>,&nbsp;''R''<sub>2</sub>,&nbsp;''R''<sub>3</sub>,&nbsp;...,&nbsp;''R''<sub>''n''</sub>).
+# Write the above equation in the form <math>X = C X_1^a X_2^b X_3^c \cdots X_n^m \,</math> where ''C'' is a [[dimensionless constant]] and ''a'',&nbsp;''b'',&nbsp;''c'',&nbsp;...,&nbsp;''m'' are arbitrary exponents.
+# Express each of the quantities in the equation in some [[fundamental unit]]s in which the solution is required.
+# By using [[Dimensional analysis#Commensurability|dimensional homogeneity]], obtain a [[set (mathematics)|set]] of [[simultaneous equations]] involving the exponents&nbsp;''a'',&nbsp;''b'',&nbsp;''c'',&nbsp;...,&nbsp;''m''.
+# [[Equation solving|Solve]] these equations to obtain the value of exponents&nbsp;''a'',&nbsp;''b'',&nbsp;''c'',&nbsp;...,&nbsp;''m''.
+# [[Simultaneous equations#Substitution method|Substitute]] the values of exponents in the main equation, and form the [[non-dimensional]] [[parameter]]s by [[Combining like terms|grouping]] the variables with like exponents.
+'''Drawback''' – It doesn't provide any information regarding number of dimensionless groups to be obtained as a result of dimension analysis
+== See also ==
+* [[Physical quantity]]
+* [[Buckingham pi theorem]]
+[[Category:Dimensional analysis]]
+{{applied-math-stub}}

Krull–Schmidt category: Difference between revisions

Revision as of 10:04, 28 November 2013

See also

Navigation menu

Search