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Answers for “为什么 $\Pi_1^{(p)} = \Pi_1^{(m)}$ 被称为预测方程?”

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Dynamic similarity is satisfied by looking at the force distribution at corresponding locations in the flow. The forces must have the same direction and their magnitudes must be constant multiples of each other.

Conditions: Presented after geometric and kinematic similarity have been established.; Concerns force distribution at corresponding locations in the flow.; Force directions must match.; Force magnitudes must be constant multiples of one another.

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To relate prototype and model behavior, the lecture matches each dimensionless group in the prototype expression to the corresponding group in the model expression. The equalities for Π2,…,ΠN−1\Pi_2, \ldots, \Pi_{N-1} are the similarity requirements, and the first equality Π1(p)=Π1(m)\Pi_1^{(p)} = \Pi_1^{(m)} is the prediction equation.

Conditions: Applied to the prototype-model pair written on the board.; The method separates the first group, used for prediction, from the remaining groups, used as similarity requirements.; The underlying physics governing the flow must be identical for both the prototype and the model.