We were discussing the basic concept of streamline and equipotential line, dimensional homogeneity, Buckingham pi theorem and difference between model and prototype
in the subject of fluid mechanics, in our recent posts.

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Now we will go ahead to understand the basic
principle of similitude i.e. types of similarity in the field of fluid
mechanics with the help of this post.

Let us have a brief look over the basics of model
and prototypes

In order to secure the information about the
performance of any hydraulic structure such as dam or any hydraulic machine
such as turbine, before going for construction and manufacturing of actual of
structure or machine, models are prepared of the actual structure or machine
and experiments are carried out on the models to secure the desired result.

Therefore we can define the model as the small scale
replica of the actual structure or machine. Actual structure or machine will be
termed as prototype.

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**Similitude
– Types of similarities**

Similitude is basically defined as the similarity
between model and its prototype in each and every respect. It suggests us that
model and prototype will have similar properties or we can say that similitude
explains that model and prototype will be completely similar.

Three types of similarities must exist between model
and prototype and these similarities are as mentioned here.

Geometric similarity

Kinemtaic similarity

Dynamic similarity

We will discuss each type of similarity one by one
in detail. Let us first see here geometric similarity.

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**Geometric
similarity**

Geometric similarity is the similarity of shape.
Geometric similarity is said to exist between model and prototype, if the ratio
of all respective linear dimension in model and prototype are equal.

Ratio of dimension of model and corresponding
dimension of prototype will be termed as scale ratio i.e. Lr.

Let us assume the following linear dimension in
model and prototype.

Lm = Length of model, L

_{P }= Length of prototype
B

_{m }= Breadth of model, B_{P }= Breadth prototype
D

_{m }= Diameter of model, D_{P }= Diameter of prototype
A

_{m }= Area of model, A_{P }= Area of prototype
V

_{m }= Volume of model, V_{P }= Volume of prototype###
**Kinematic
Similarity**

The Kinemetic similarity is said to exist between
model and prototype, if the ratios of velocity and acceleration at a point in
model and at the respective point in the prototype are the same.

We must note it here that the direction of velocity
and acceleration in the model and prototype must be identical.

V

_{m }= Velocity of fluid at a point in model, V_{P }= Velocity of fluid at respective point in prototype
a

_{m }= Acceleration of fluid at a point in model, a_{P }= Acceleration of fluid at respective point in prototype###
**Dynamic
Similarity**

The dynamic similarity is said to exist between
model and prototype, if the ratios of corresponding forces acting at the
corresponding points are the same.

We must note it here that the direction of forces at
the corresponding points in the model and prototype must be same.

F

_{m }= Force at a point in model, F_{P }= Force at respective point in prototype
We will see another important topic
in the field of fluid mechanics i.e. Types of forces acting in moving
fluid with the help of our next post.

Do you have any suggestions? Please write in comment
box.

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**Reference:**

Fluid mechanics, By R. K. Bansal

Image Courtesy: Google