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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define dimensional homogeneity in your own words.
💡 Hint: Focus on the importance of units being consistent.
Question 2
Easy
What is Buckingham's Pi Theorem used for?
💡 Hint: Think about the number of variables and dimensions.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does dimensional homogeneity ensure in an equation?
- Different dimensions can coexist
- All terms have the same dimensions
- Dimensions do not matter
💡 Hint: Think about how you check units across an equation.
Question 2
True or False: The Reynolds number is a fundamental dimension.
- True
- False
💡 Hint: Recall the definitions of dimensions vs groups.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A new fluid is introduced for an experiment involving drag on a sphere. The density of the fluid is 1200 kg/m³, and the dynamic viscosity is 0.0012 Pa.s. Calculate the dimensionless Reynolds number if the diameter is 0.1 m and the flow velocity is 3 m/s.
💡 Hint: Recall the formula for Reynolds number and substitute the values properly.
Question 2
Using Buckingham's Pi Theorem, if you have 6 variables in a fluid dynamics problem with 3 essential dimensions, how many independent dimensionless groups can you find? Explain your reasoning.
💡 Hint: Remember n is the count of variables, k is the number of dimensions.
Challenge and get performance evaluation