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2 cards from this section. Quick, good the night before a test.
Define the potential function and its role in fluid dynamics.
Think about how it relates to flow velocity.
What does the Laplace equation represent in fluid dynamics?
Consider the relationship to fluid conservation.
What represents the potential function?
Focus on flow conditions.
True or False: The Laplace equation can be satisfied by any scalar function.
Consider conditions for application.
Consider a potential function Φ(x, y) = 4x^2 + 3y^2 - 5xy. Determine the velocity components and check if this satisfies Laplace's equation.
Differentiate with respect to x and y to find components.
Given a velocity potential Φ = x^3 - 3xy^2, compute the streamlines and determine the flow rate between two points.
Use the formulas you've learned for u and v to analyze flow between points.
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