Similitude

The three types of similarities are,

1.   Geometric similarity

2.   Kinematic similarity

3.   Dynamic similarity

Scale ratio.

Scale ratio is the ratio of linear dimension in the model and prototype which are equal in a geometric similarity. It is denoted by Lr.

Lr = Lp/Lm = bp/bm = Dp/Dm

Dynamic similarity.

It means the similarity of forces at corresponding points in the model and prototype is equal.

Types of forces in a moving fluid.

The types of forces in a moving fluid are,

1.   Inertia force (fi)

2.   Viscous force (fv)

3.   Gravity force (Fg)

4.   Pressure force (Fp)

5.   surface tension (Fs)

6.   Elastic force (Fe)

Dimensionless numbers.

Dimensionless numbers are the numbers obtained by dividing inertia force or gravity force or pressure force or elastic force or surface tension. They are called as non-dimensional parameters.

Surface tension.

Surface tension force is defined as the product of surface tension and length of surface of flowing fluid.

Pressure force.

Pressure force is the product of pressure intensity and cross-sectional area of the flowing fluid in case of pipe flow.

Elastic force.

Elastic force is defined as the product of elastic stress and the area of flowing fluid.

Types of dimensionless numbers.

The types of dimensionless numbers are:

1.   Reynold’s number

2.   Froude’s number

3.   Euler’s number

4.   Weber’s number

5.   Mach’s number

Reynold’s number.

Reynold’s number is defined as the ratio of inertia force of flowing fluid and viscous force of the fluid. It is denoted by (Re)

Re = V x d / v = ? V d / ?

Froude’s number

Froude’s number is defined as square root of ratio of inertia force of flowing fluid to gravity. It is denoted as Fe 

Classification of models

The classifications of models are

i.             Undistorted models

ii.    Distorted models

Undistorted model

If the scale ratio for the linear dimensions of the model and prototype is same, then the model is said to be undistorted model.

Distorted model

A distorted model is said to be a distorted model only when it is not geometrically similar to prototype.

Advantages of distorted models.

The advantages of distorted models are,

1.   The vertical dimensions of the model can be measured accurately.

2.   The cost of model can be reduced.

3.   Turbulent flow in the model can be maintained.

Types of model laws

The types of model laws are

1.   Reynolds’s model laws

2.   Froude’s model laws

3.   Euler’s model laws

4.   Weber’s model laws

5.   Mach’s model laws

Application of Froude’s model laws

Froude’s model laws is applied in

1.Free surface flow such as flow over spillways, weirs, sluices, channels etc

2.Flow of jet from an orifice or nozzle

3.Where waves are likely to be formed on surface

4.Where fluids of different densities flow over one anther

Weber’s model laws

When surface tensile forces alone are predominant a model may be taken to be dynamically similar to the prototype when ratio of inertial to the surface tensile forces is the same in the model and prototype.

(We) model = (We) prototype