SIMILARITY

In hydraulic and aeronautical engineering valuable results are obtained at relatively small cost by performing tests on small scale models of full size systems (prototypes). Similarity laws help us to interpret the results of model studies. The relation between model and prototype is classified into three:

1. Geometry Similarity
2. Kinematics Similarity
3. Dynamic Similarity

M o d e l 

Model is similar with object/structure required in certain scale ratio. It is need to be tested in laboratory with similar condition in real phenomenon. The size of model is not necessary smaller than prototype.

1. Not necessarily functional (don’t need to work).
2. Can be to any scale (usually smaller but can also be of the original size or bigger).
3. Used for Display or/and [Visual] Demonstration of product.
4. May consist of only the exterior of the object/product it replicates.
5. Relatively cheap to manufacture.

 P r o t o t y p e 

Prototype is an object/actual structure in full size. It is need properly tested in actual phenomenon.

1. Is fully functional, but not fault-proof.
2. Is an actual version of the intended product.
3. Used for performance evaluation and further improvement of product.
4. Contains complete interior and exterior.
5. Is relatively expensive to produce.
6. Often used as a technology demonstrator

An Example: Flow Past a Sphere

Flow Past a Sphere: Geometric and

Kinematic Similitude

https://ecourses.ou.edu/cgi-bin/view_anime.cgi?file=m06221.swf&course=fl&chap_sec=06.2

Flow Past a Sphere: Dynamic Similitude

https://ecourses.ou.edu/cgi-bin/view_anime.cgi?file=m06222.swf&course=fl&chap_sec=06.2

Types of Similarities

Geometry similarity

The prototype and model have identical shapes but differ only in size. Ratio of corresponding length in prototype and model show as,

Kinematic Similarity

In addition to geometric similarity, ratio of velocities at all corresponding points in flow are the same.

Dynamic Similarity

Two systems have dynamic similarity if, in addition to dynamic similarity, corresponding forces are in the same ratio in both. The force scale ratio is 

Basically, if the geometric and kinematics similarities exist, it shows two system are dynamically similar. The ratios of these systems of all corresponding forces are the same. The respective forces includes:

1. Gravity
2. Viscosity
3. Elasticity
4. Surface tension
5. Inertia

Advantages of Using Similarities

1. Performances of object can be predicted.
2. Economy and easy to build, where design of model can be done many times until reach a certain values.
3. Non-functional structure also can be measured such as dam.

 NON-DIMENSIONAL PARAMETER

By using Raleigh’s Method or the Buckingham Phi Theorem, the number of dimensional variables such as mass, length and time used in an analysis of flow is reduced to a few non-dimensional variables.

Listed below are the five non-dimensional parameters that represent the ratio of forces per unit volume.

1.    Reynolds Number

2.    Froude Number

3.    Mach Number

4.    Euler Number

5.    Weber Number