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If the number of fundamental dimensions equals 'm', then the repeating variables shall be equal to:
- a)m and none of the repeating variables shall represent the dependentvariable.
- b)m + 1 and one of the repeating variables shall represent the dependentvariable
- c)m + 1 and none of the repeating variables shall represent the dependentvariable.
- d)m and one of the repeating variables shall represent the dependent variable
Correct answer is option 'C'. Can you explain this answer?
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If the number of fundamental dimensions equals m, then the repeating v...
Ans. (c)
In dimensional analysis, particularly in the Buckingham π theorem, the number of repeating variables is equal to the number of fundamental dimensions, m, plus one. These repeating variables are chosen from the independent variables and should not include the dependent variable. Therefore, the repeating variables shall be m+1 and none of them should represent the dependent variable.
In dimensional analysis, particularly in the Buckingham π theorem, the number of repeating variables is equal to the number of fundamental dimensions, m, plus one. These repeating variables are chosen from the independent variables and should not include the dependent variable. Therefore, the repeating variables shall be m+1 and none of them should represent the dependent variable.
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If the number of fundamental dimensions equals m, then the repeating v...
Answer:
In dimensional analysis, the fundamental dimensions are the base dimensions that cannot be expressed in terms of other dimensions. Let's assume the number of fundamental dimensions is m.
The repeating variables are those variables in a problem that have the same dimension as the fundamental dimensions. These variables are repeated in the derived equations and can be used to represent the physical quantities involved in the problem.
To find the relationship between the number of fundamental dimensions (m) and the repeating variables, we need to consider two cases:
Case 1: None of the repeating variables represent the dependent variable.
In this case, the repeating variables are independent of each other and do not represent the quantity being solved for. Therefore, the repeating variables are equal to m.
Case 2: One of the repeating variables represents the dependent variable.
In this case, one of the repeating variables is the quantity being solved for, and the other repeating variables are independent variables. Therefore, the repeating variables are equal to m-1.
Conclusion:
Based on the above analysis, we can conclude that if the number of fundamental dimensions equals m, then the repeating variables shall be equal to m and none of the repeating variables shall represent the dependent variable. Therefore, the correct answer is option 'C': m and none of the repeating variables shall represent the dependent variable.
In dimensional analysis, the fundamental dimensions are the base dimensions that cannot be expressed in terms of other dimensions. Let's assume the number of fundamental dimensions is m.
The repeating variables are those variables in a problem that have the same dimension as the fundamental dimensions. These variables are repeated in the derived equations and can be used to represent the physical quantities involved in the problem.
To find the relationship between the number of fundamental dimensions (m) and the repeating variables, we need to consider two cases:
Case 1: None of the repeating variables represent the dependent variable.
In this case, the repeating variables are independent of each other and do not represent the quantity being solved for. Therefore, the repeating variables are equal to m.
Case 2: One of the repeating variables represents the dependent variable.
In this case, one of the repeating variables is the quantity being solved for, and the other repeating variables are independent variables. Therefore, the repeating variables are equal to m-1.
Conclusion:
Based on the above analysis, we can conclude that if the number of fundamental dimensions equals m, then the repeating variables shall be equal to m and none of the repeating variables shall represent the dependent variable. Therefore, the correct answer is option 'C': m and none of the repeating variables shall represent the dependent variable.
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If the number of fundamental dimensions equals m, then the repeating variables shall be equal to:a)m and none of the repeating variables shall represent the dependentvariable.b)m + 1 and one of the repeating variables shall represent the dependentvariablec)m + 1 and none of the repeating variables shall represent the dependentvariable.d)m and one of the repeating variables shall represent the dependent variableCorrect answer is option 'C'. Can you explain this answer?
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