Chapter 6
: Principles of Physical Similarity and Dimensional Analysis
Lecture 17 :
Dynamic Similarity
Dynamic similarity is the similarity of forces .
In dynamically similar systems, the magnitudes of forces at correspondingly similar points in each system are in a fixed ratio.
In a system involving flow of fluid, different forces due to different causes may act on a fluid element. These forces are as follows:
Viscous Force (due to viscosity)
Pressure Force ( due to different in pressure)
Gravity Force (due to gravitational attraction)
Capillary Force (due to surface tension)
Compressibility Force ( due to elasticity)
According to Newton 's law, the resultant FR of all these forces, will cause the acceleration of a fluid element. Hence
(17.1)
Moreover, the inertia force is defined as equal and opposite to the resultant accelerating force
= -
Therefore Eq. 17.1 can be expressed as
For dynamic similarity, the magnitude ratios of these forces have to be same for both the prototype and the model.
The inertia force is usually taken as the common one to describe the ratios as (or putting in other form we equate the the non dimensionalised forces in the two systems)
End of Lecture 17!
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is defined as equal and opposite to the resultant accelerating force 
