13.1.1 - Dimensional Homogeneity
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Practice Questions
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What are the fundamental dimensions used in fluid mechanics?
💡 Hint: Think of basic measurements.
Define dimensional homogeneity.
💡 Hint: Consider what happens if units don’t match.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does dimensional homogeneity ensure in an equation?
💡 Hint: Think about the relationship of units.
True or False: The Reynolds number is a dimensionless quantity.
💡 Hint: Think about its role in fluid dynamics.
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Challenge Problems
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Consider a system with three dependent variables: pressure (p), velocity (V), and dynamic viscosity (μ). Using Buckingham’s Pi theorem, find the number of dimensionless groups.
💡 Hint: Count variables and use the theorem.
If the drag force on a cylinder depends on its diameter, fluid velocity, density, and viscosity, describe how you would form a dimensionless group.
💡 Hint: Focus on balancing out units.
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