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Consider the following statements:  
1. Dimensional analysis is used to determine the number of variables involved in a certain phenomenon
2. The group of repeating variables in dimensional analysis should include all the fundamental units.
3. Buckingham's π theorem stipulates the number of dimensionless groups for a given phenomenon.
4. The coefficient in Chezy's equation has no dimension.
Which of these are correct?
  • a)
    1, 2, 3 and 4
  • b)
    2, 3 and 4
  • c)
    1 and 4
  • d)
    2 and 3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Consider the following statements:1. Dimensional analysis is used to d...
Ans. (d) 1 and 4 are wrong, coefficient in Chezy's equation has dimension [L1/2T-1]
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Consider the following statements:1. Dimensional analysis is used to d...
Dimensional Analysis in Fluid Mechanics

Statement 1: Dimensional analysis is used to determine the number of variables involved in a certain phenomenon.

- This statement is correct. Dimensional analysis is a technique used to determine the number of variables involved in a certain phenomenon by expressing them in terms of fundamental dimensions.

Statement 2: The group of repeating variables in dimensional analysis should include all the fundamental units.

- This statement is incorrect. The group of repeating variables in dimensional analysis should only include non-fundamental units that are derived from the fundamental units.

Statement 3: Buckingham's theorem stipulates the number of dimensionless groups for a given phenomenon.

- This statement is correct. Buckingham's Pi theorem states that the number of dimensionless groups for a given phenomenon is equal to the number of variables involved minus the number of fundamental dimensions.

Statement 4: The coefficient in Chezy's equation has no dimension.

- This statement is correct. The coefficient in Chezy's equation is a dimensionless constant that relates the friction factor to the roughness height of a pipe.

Conclusion

- Option D is the correct answer as it includes the two correct statements, 2 and 3.
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Consider the following statements:1. Dimensional analysis is used to determine the number of variables involved in a certain phenomenon2. The group of repeating variables in dimensional analysis should include all the fundamental units.3. Buckingham's π theorem stipulates the number of dimensionless groups for a given phenomenon.4. The coefficient in Chezy's equation has no dimension.Which of these are correct?a)1, 2, 3 and 4b)2, 3 and 4c)1 and 4d)2 and 3Correct answer is option 'D'. Can you explain this answer?
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