1 (2pt), If a model and prototype have similar shapes, angles, and length ratios

Question

1 (2pt), If a model and prototype have similar shapes, angles, and length ratios we say they are ______ similar. (a) dynamically (b) kinematically (c) geometrically (d) centrifugally

2 (2pt), If the flow patterns in a geometrically similar model and prototype have similar shapes we say the model and prototype have ______ similarity. (a) dynamic (b) kinematic (c) geometric (d) centrifugal

3 (2pt) If the forces in a geometrically similar model and prototype have the same scale we say the model and prototype are ______ similar. (a) dynamically (b) kinematically (c) geometrically (d) centrifugally

4 (2pt) In determining Pi terms by inspection list 2 rules governing the development of Pi terms. (e.g. Pi terms must be ________________________) ____________________________________________________________________________________________________________________________________________________________________________________________________________________

Explanation / Answer

?1. Geometrically similar 2. Kinematic similarity 3. Dynamic similarity 4. A. Variables which are already dimensionless (such as angles) should not be picked. Such variables are already dimensionless Pi groups, and cannot contribute to formulating the remaining Pi groups. B. The Pi groups are written in final functional form, typically as the first Pi as a function of the remaining Pi groups. If only one Pi is found, it must be a constant, since it is a function of nothing else.
C. The Pi groups are formulated by multiplying each of the remaining variables (those that were not chosen as repeating variables) in turn by the repeating variables, each in turn raised to some unknown exponent. The exponents are found algebraically by forcing the Pi to be dimensionless. The convention is to form the first Pi using the dependent variable.

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