In: Civil Engineering
a predominant force or most significant force is selected and model is designed on the basis of ratio of this force. What is the reason for this? What happens to other forces?
Ideally all dimensionless number should be equal for model and prototype. But by doing so, practically it is not possible to build a model. We go for incomplete similarity. For Example:
We illustrate incomplete similarity with the problem of
measuring the aerodynamic
drag force on a model truck in a wind tunnel. Suppose
we purchase a one-sixteenth scale die-cast model of a
tractor-trailer rig .
The model is geometrically similar to the prototype. The model
truck is 0.991 m
long, corresponding to a full-scale prototype length of 15.9 m. The
model
truck is to be tested in a wind tunnel that has a maximum speed of
70 m/s.
The wind tunnel test section is 1.0 m tall and 1.2 m wide—big
enough to
accommodate the model without needing to worry about wall
interference
or blockage effects. The air in the wind tunnel is at the same
temperature
and pressure as the air flowing around the prototype. We want to
simulate
flow at Vp = 60 mi/h (26.8 m/s) over the full-scale prototype
truck.
The first thing we do is match the Reynolds numbers.Thus, to match
the Reynolds number between model and prototype, the wind tunnel
should be run at 429 m/s (to three significant digits). We
obviously
have a problem here, since this speed is more than six times
greater
than the maximum achievable wind tunnel speed. Moreover, even if
we
could run the wind tunnel that fast, the flow would be supersonic,
since the
speed of sound in air at room temperature is about 346 m/s.
It is clearly not possible to match the model Reynolds number to
that of
the prototype with this model and wind tunnel facility.
So in actual the force which govern the problem , corresponding dimensional number is made equal. Other forcs are insignificant and hence neglected.