57:020 Fluid Mechanics
29
Similarity and model
testing
• Definition
: Flow conditions for a model test are completely
similar if all relevant dimensionless
parameters have the same corresponding values for model and prototype.
• Pi model = Pi
prototype i = 1
• Enables
extrapolation from model to full scale
• However,
complete similarity usually not possible. Therefore, often it is necessary
to
use Re, or
Fr, or Ma scaling, i.e., select most important P and
accommodate others
as best
possible.
• Types of similarity:
• Geometric Similarity : all body dimensions in all
three coordinates have the same
linear-scale ratios.
• Kinematic
Similarity : homologous (same relative position) particles lie at
homologous
points at
homologous times.
• Dynamic
Similarity : in addition to the requirements for kinematic similarity the
model
and
prototype forces must be in a constant ratio.
