Model-Prototype Performance http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...
8.7 Model-Prototype Performance
Geometric (scale model) and dynamic (same Ä„-groups) similitude mean that the dependent Ä„-groups are the
same for both the model and the prototype. For this reason, measurements made with the model can be applied
directly to the prototype. Such correspondence is illustrated in this section.
Example 8.6 shows how the pressure difference measured in a model test can be used to find the pressure
difference between the corresponding two points on the prototype.
EXAMPLE 8.6 APPLICATIO OF PRESSURE
COEFFICIE T
A 1/10 scale model of a blimp is tested in a wind tunnel under dynamically similar conditions. The
speed of the blimp through still air is 10 m/s. A 17.8 kPa pressure difference is measured between
two points on the model. What will be the pressure difference between the two corresponding points
on the prototype? The temperature and pressure in the wind tunnel is the same as the prototype.
Problem Definition
Situation: A 1/10 scale of a blimp is tested in a wind tunnel under dynamically similar conditions. A
pressure difference of 17.8 kPa is measured on model.
Find: Corresponding pressure difference (Pa) on prototype.
Properties: Pressure and temperature are the same for wind tunnel test and prototype, so ½m = ½p.
Plan
Reynolds number is the only significant Ä„-group. Thus Eq. 8.4 reduces to
For dynamic similitude, Rem = Rep. Then with geometric similitude, Cpm = Cpp.
1. Calculate the model/prototype velocity ratio.
2. Calculate pressure difference on prototype.
Solution
1. Reynolds-number similitude
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2. Pressure coefficient correspondence
Pressure difference on prototype
Example 8.7 illustrates calculating the fluid dynamic force on a prototype blimp from wind tunnel data using
similitude.
EXAMPLE 8.7 DRAG FORCE FROM WI D TU EL
TESTI G
A 1/10 scale of a blimp is tested in a wind tunnel under dynamically similar conditions. If the drag
force on the model blimp is measured to be 1530 N, what corresponding force could be expected on
the prototype? The air pressure and temperature are the same for both model and prototype.
Problem Definition
Situation: A 1/10 scale model of blimp is tested in a wind tunnel, and a drag force of 1530 N is
measured.
Find: The drag force (in newtons) on the prototype.
Properties: Pressure and temperature are the same, ½m = ½p.
Plan
Reynolds number is the only significant Ä„-group, so Eq. 8.4 reduces to CF = f(Re). For dynamic
similtude, Rem = Rep. Thus with geometric similitude CF,m = CF,p.
1. Find velocity ratio by equating Reynolds numbers.
2. Find the force ratio from force coefficient.
Solution
1. Reynolds-number similitude
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2. Force coefficient correspondence
Therefore
Review
The result that the model force is the same as the prototype force is interesting. When Reynolds-
number similitude is used, and the fluid properties are the same fluid for model and prototype, the
forces on the model will always be the same as the forces on the prototype.
Copyright © 2009 John Wiley & Sons, Inc. All rights reserved.
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