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The similarity requirements are the equalities of corresponding non-left-hand-side dimensionless groups between the prototype and the model. Specifically, $\Pi_2^{(p)} = \Pi_2^{(m)}$, $\Pi_3^{(p)} = \Pi_3^{(m)}$, and $\Pi_{N-1}^{(p)} = \Pi_{N-1}^{(m)}$.

Conditions: Defined here for the groups $\Pi_2$ through $\Pi_{N-1}$.; The lecturer ties this naming to the convention that the left-hand-side parameter is placed in $\Pi_1$.; Applies to the prototype and model flow problems shown on the board.

The similarity requirements are the equalities of corresponding non-left-hand-side dimensionless groups between the prototype and the model. Specifically, $\Pi_2^{(p)} = \Pi_2^{(m)}$, $\Pi_3^{(p)} = \Pi_3^{(m)}$, and $\Pi_{N-1}^{(p)} = \Pi_{N-1}^{(m)}$.

Conditions: Defined here for the groups $\Pi_2$ through $\Pi_{N-1}$.; The lecturer ties this naming to the convention that the left-hand-side parameter is placed in $\Pi_1$.; Applies to the prototype and model flow problems shown on the board.

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.

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.

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 $\Pi_2, \ldots, \Pi_{N-1}$ are the similarity requirements, and the first equality $\Pi_1^{(p)} = \Pi_1^{(m)}$ 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.

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 $\Pi_2, \ldots, \Pi_{N-1}$ are the similarity requirements, and the first equality $\Pi_1^{(p)} = \Pi_1^{(m)}$ 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.

Kinematic similarity requires that velocities and accelerations at corresponding points in the two flows have the same direction and their magnitudes must be constant multiples of one another. It is the next requirement after geometric similarity.

Conditions: Requires geometric similarity as a prior condition.; Concerns corresponding points in the two flows.; Velocity and acceleration directions must match.; Velocity and acceleration magnitudes must be constant multiples of one another.

Kinematic similarity requires that velocities and accelerations at corresponding points in the two flows have the same direction and their magnitudes must be constant multiples of one another. It is the next requirement after geometric similarity.

Conditions: Requires geometric similarity as a prior condition.; Concerns corresponding points in the two flows.; Velocity and acceleration directions must match.; Velocity and acceleration magnitudes must be constant multiples of one another.

Geometric similarity requires that the ratios of corresponding linear dimensions between the model and prototype are equal. For the two rectangular-box examples shown, the condition is expressed as $\frac{B}{b} = \frac{H}{h} = \frac{W}{w}$.

Conditions: The compared objects must have corresponding linear dimensions.; Each ratio pairs a prototype length with the matching model length.; Applies to corresponding linear dimensions of two objects or domains.

Geometric similarity requires that the ratios of corresponding linear dimensions between the model and prototype are equal. For the two rectangular-box examples shown, the condition is expressed as $\frac{B}{b} = \frac{H}{h} = \frac{W}{w}$.

Conditions: The compared objects must have corresponding linear dimensions.; Each ratio pairs a prototype length with the matching model length.; Applies to corresponding linear dimensions of two objects or domains.

The equality between the first dimensionless group of the prototype and that of the model is called the prediction equation because it is used to recover the quantity of interest once the other groups have been matched. The lecturer states that the left-hand-side parameter appears only in $\Pi_1$.

Conditions: Used after the corresponding similarity requirements are imposed.; The lecturer states that the left-hand-side parameter appears only in $\Pi_1$.; Applies to the prototype and model flow problems shown on the board.

The equality between the first dimensionless group of the prototype and that of the model is called the prediction equation because it is used to recover the quantity of interest once the other groups have been matched. The lecturer states that the left-hand-side parameter appears only in $\Pi_1$.

Conditions: Used after the corresponding similarity requirements are imposed.; The lecturer states that the left-hand-side parameter appears only in $\Pi_1$.; Applies to the prototype and model flow problems shown on the board.