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2 cards from this section. Quick, good the night before a test.
What is the purpose of using dimensional analysis?
Think about how dimensions help in combining variables.
Name the dependent variable in the paint can problem.
Look for what is being affected in this problem.
What does the Buckingham Pi theorem help us with?
Recall the theorem's purpose in relation to variables.
True or false: The dependent variable can change based on the independent variable's manipulation.
Consider how one variable's change affects another.
Given a cylindrical can with diameter D = 0.3m, depth h = 1m, thickness d = 0.01m, specific weight γ = 9800 N/m³, and modulus of elasticity E = 25000 N/m², express the vertical deflection in functional form using Pi terms.
Start by calculating each dimensionless term using their relationships.
Analyze how a change in depth from 1m to 0.5m affects the vertical deflection of the can while maintaining D and d constant. What does this suggest about pressure effects?
Think about how less depth will change the stress exerted on the bottom.
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