SIMILITUDE AND SIMILARITY IN FLUID MECHANICS

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.

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.

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.

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.