7.1 - Linearization of the Bernoulli's Equation
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Practice Questions
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What does a fixed bottom boundary in fluid dynamics imply for fluid flow?
💡 Hint: Think about how a riverbed prevents water from going beneath.
Define dynamic free surface.
💡 Hint: Consider how ocean waves rise and fall.
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Interactive Quizzes
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What is the primary condition assumed when linearizing Bernoulli's equation?
💡 Hint: Think about how small waves behave compared to larger waves.
True or False: A dynamic free surface can sustain pressure changes without distortion.
💡 Hint: Consider characteristics of still water versus waves.
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Challenge Problems
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In a river with a known bottom slope, derive the velocity profile under the assumption of a small amplitude wave. Explain each step of your derivation.
💡 Hint: Start with fundamental equations and relate changes through derivatives.
Construct a computational model factoring linearized Bernoulli’s equation for wave movement in a channel with varying depth and slope. Discuss expected outcomes and behaviors.
💡 Hint: Consider using software or simulations to illustrate changing conditions.
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