Dynamic Similarity of Flows with Gravity, Pressure and Inertia Forces
A flow of the type in which significant forces are gravity force, pressure force and inertia force, is found when a free surface is present.
Examples can be
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the flow of a liquid in an open channel.
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the wave motion caused by the passage of a ship through water.
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the flows over weirs and spillways.
The condition for dynamic similarity of such flows requires
and
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(18.2e) |
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In practice, it is often convenient to use the square root of this ratio so to deal with the first power of the velocity.
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From a physical point of view, equality of
implies equality of
as regard to the concept of dynamic similarity.
The reciprocal of the term
is known as Froude number ( after William Froude who first suggested the use of this number in the study of naval architecture. )
Hence Froude number,
.
Therefore, the primary requirement for dynamic similarity between the prototype and the model involving flow of fluid with gravity as the significant force, is the equality of Froude number, Fr, i.e.,
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(18.2f) |
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