Question

Scale ratio for vertical dimensions id (lr),the scale ratio for velocity is

Answer 1

Geometric Similarity implies the similarity of shape such that, the ratio of any length in one system to the corresponding length in other system is the same everywhere.

This ratio is usually known as scale factor.

Therefore, geometrically similar objects are similar in their shapes, i.e., proportionate in their physical dimensions, but differ in size.

In investigations of physical similarity,

·          the full size or actual scale systems are known as prototypes

·          the laboratory scale systems are referred to as models

·          use of the same fluid with both the prototype and the model is not necessary

·           model need not be necessarily smaller than the prototype. The flow of fluid through an injection nozzle or a carburettor , for example, would be more easily studied by using a model much larger than the prototype.

·          the model and prototype may be of identical size, although the two may then differ in regard to other factors such as velocity, and properties of the fluid.

If l1 and l2 are the two characteristic physical dimensions of any object, then the requirement of geometrical similarity is

    (model ratio)

(The second suffices m and p refer to model and prototype respectively) where lr is the scale factor or sometimes known as the model ratio. Figure 5.1 shows three pairs of geometrically similar objects, namely, a right circular cylinder, a parallelopiped, and a triangular prism.