SET II SHORT QUESTIONS

1. What do you mean by dimensionless numbers? Name some of it.

Dimensionless numbers are those numbers which are obtained by dividing the inertia force by viscous force or gravity force or pressure force or surface tension force or elastic force.  As this is a ratio of two forces, it will be dimensionless number.  These dimensionless numbers are also called non – dimensional parameters.

The following are the important dimension less numbers:

    1.      Reynolds numbers

2. Froude’s number
3. Euler’s number
4. Weber’s number
5. Mach’s number

2. What are the different laws on which models are designed for dynamic similarity?

Model laws or laws of similarity are the laws  on which the models are designed for dynamic similarity.  Models are designed on the basis of ratio of the force, which is dominating in the phenomenon.

The following are the model laws:

1. Reynolds model law
2. Froude model law
3. Euler model law
4. Weber model law
5. Mach model law 

3. Explain the terms: distorted models and undistorted models.  What is the use of distorted models?

Undistorted Models: Undistorted models are those models which are geometrically similar to their prototypes or in other words the scale ratio for the linear dimensions of the model and its prototype is same.  The behaviour of the prototype can be easily predicted from the results of undistorted model.

Distorted Model:

            A model is said to be distorted if it is not geometrically similar to its prototyped model. Different scale ratios for the linear dimensions are adopted.  For example, incase to rivers, harbours, reservoirs etc.  two different scale ratios, one for horizontal dimensions and other for vertical dimensions are taken. Thus the models of revivers, harbors and reservoirs will become distorted models.

The followings are the advantages of distorted models.

1. The vertical dimensions of the model can be measured accurately.
2. The cost of the model can be reduced.
3. Turbulent flow in the model can be maintained. 

4. Write the drawbacks of analytical methods.

            The following are the disadvantages of analytical methods used for study and analysis of many problems in fluid mechanics.

1.          It involves a number of approximations and assumptions and hence application of the analytical methods are restricted.

2.                  It involves highly complicated equations which cannot be solved.

3.                  The solutions to various complex flow patterns cannot be obtained by analytical methods alone.

4.              It is impossible or impracticable in some cases to make a satisfactory and complete mathematical analysis of the problems 

5. What you mean by hydraulic similitude?

            The observations made on the performance of the model are useful to predict the performance of the prototype. Hence it is very necessary that the model should represent the prototype in every respect i.e. the model should represent the prototype should have similar properties. The similarity between a prototype and its model is called similitude.

            For absolute similitude between a model and the prototype the following types of similarities should exist.

 a)      Geometric similarity

 b)      Kinematics similarity and

 c)      Dynamic similarity 

6. What are the demerits of distorted models?

The following are the demerits of distorted models:

i)                    Due to unequal horizontal and vertical scales the pressure and velocity distribution are not truly reproduced in the model.

ii)                  The wave pattern in the model will be different from that in the prototype due to depth distortion.

iii)                Slopes, bends and earth cuts are not truly reproduced.

7. What do you mean by scale effect?

            This is a defect which occurs in certain models due to which the computed properties of the prototype from model experiments deviate much from the actual properties of the prototype.

            For example, a model cannot match with prototype if it large depths, high velocities, surface tension factor, flow conditions and force. Here the models do not have exact properties with prototype. Hence, the scale effect occurs.

8. What are the different types of forces acting in moving fluid?

Types of Forces Acting in Moving Fluid:

For the fluid flow problems, the forces acting on fluid mass may be any one, or a combination of several of the following forces :

1. Inertia Force F_i.
2. Viscous force F_v.
3. Gravity force F_g.
4. Pressure force F_p.
5. Surface tension force,
6. F_s Elastic force F_e.

1. Inertia Force (F₁) :

 It is equal to the product of mass and acceleration of the flowing fluid and acts in the direction opposite to the direction of acceleration. It is always existing in the fluid flow problems.

2. Viscous Force (F_v) :

 It is equal to the product of shear stress (t) due to viscosity and surface area of the flow. It is present in fluid flow problems where viscosity is having an important role to play.

3. Gravity Force (F_g) :

 It is equal to the product of mass and acceleration due to gravity of the flowing fluid. It is present in case of open surface flow.

4. Pressure Force (F_p)  :

 It is equal to the product of pressure intensity and cross sectional area of the flowing fluid. It is present in case pipe flow.

5. Surface Tension Force(F_s) :

 It is equal to the product of surface tension and length of surface of the flowing fluid.

6. Elastic Force (F_e) :

 It is equal to the product of elastic stress and area of the flowing fluid.

For a flowing fluid, the above – mentioned forces may not always be present. And also the forces, which are present in a fluid flow problem, are not of equal magnitude. There are always one or two forces which dominate the other forces. These dominating forces govern the flow of fluid.