Which of the following rules are used in choosing the repeating variables in dimensional analysis :
1. Repeating variables should include the dependent variables
2. Repeating variables should contain all primary units used in describing the variables in the problem
3. Repeating variables should combine among themselves.
4. Repeating variables should not contain the dependent variables.
Answers
In 2 repeating variables must be chosen in such a way that they should contain geometric property,flow property and fluid property
In 3 Repeating variables together must have same number of fundamental dimensions. Also No Two repeating group should have same dimentions
4 is true dependent variable should not be selected as repeating variable
/* note :refer R.K.Bansal book on fluid mechanics */
Answer: Statement 1 is False, Statement 2 is partially true, Statement 3 is partially true and Statement 4 is True.
Dimensional analysis: In dimensional analysis, a set of units is used either to determine the form of an equation or, more frequently, to verify that the solution to a computation serves as a safeguard against a variety of straightforward mistakes.
Explanation:
Step 1: Statement 1 is False
Step 2: Statement 2, In this case, the choices for the two recurring variables have to be made in such a way as to ensure that they include all three of the following properties: geometric property, flow property, and fluid property.
Step 3: Statement 3, In 3 Repeating variables together, the same number of basic dimensions is required to be present. In addition, no two groups of recurring elements should have the same dimensions.
Step 4: Statement 4 is t, reliant on whether or not a statement is true should not be chosen as a recurring variable.