Dynamic Similarity of Flows with Gravity, Pressure and Inertia Forces part 2

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

1.   the flow of a liquid in an open channel.
2.  the wave motion caused by the passage of a ship through water.
3.   the flows over weirs and spillways.

The condition for dynamic similarity of such flows requires

•  the equality of the Euler number Eu (the magnitude ratio of pressure to inertia force),

                                                                                   and

• the equality of the magnitude ratio of gravity to inertia force at corresponding points in the systems being compared.
         Thus ,

(18.2e)

• In practice, it is often convenient to use the square root of this ratio  so to deal with the first power of the velocity.
• 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.,

(18.2f)