DIMENSIONAL ANALYSIS AND MODEL STUDIES

1. Define dimensional analysis.

Dimensional analysis is a mathematical technique which makes use of the study of dimensions as an aid to solution of several engineering problems. It plays an important role in research work.

2. Write the uses of dimension analysis?

�    It helps in testing the dimensional homogeneity of any equation of fluid motion.

� It helps in deriving equations expressed in terms of non-dimensional parameters.

� It helps in planning model tests and presenting experimental results in a systematic manner.

3. Define dimensional homogeneity.

An equation is said to be dimensionally homogeneous if the dimensions of the terms on its LHS are same as the dimensions of the terms on its RHS.

4. Mention the methods available for dimensional analysis. Rayleigh method,

Buckinghum ? method

5. State Buckingham’s ? theorem.

It states that ‘if there are ‘n’ variables (both independent & dependent variables) in a physical phenomenon and if these variables contain ‘m’ functional dimensions and are related by a dimensionally homogeneous equation, then the variables are arranged into n-m dimensionless terms. Each term is called ? term’.

6. List the repeating variables used in Buckingham ? theorem. Geometrical Properties – l, d, H, h, etc, Flow Properties – v, a, g, ?, Q, etc,

Fluid Properties – ?, ?, ?, etc.

7. Define model and prototype.

The small scale replica of an actual structure or the machine is known as its Model, while the actual structure or machine is called as its Prototype. Mostly models are much smaller than the corresponding prototype.

8. Write the advantages of model analysis.

� Model test are quite economical and convenient.

� Alterations can be continued until most suitable design is obtained.

� Modification of prototype based on the model results.

� The information about the performance of prototype can be obtained well in advance.

9. List the types of similarities or similitude used in model anlaysis.

Geometric similarities, Kinematic similarities, Dynamic similarities 10. Define geometric similarities

It exists between the model and prototype if the ratio of corresponding lengths, dimensions in the model and the prototype are equal. Such a ratio is known as ‘Scale Ratio’.

11. Define kinematic similarities

It exists between the model and prototype if the paths of the homogeneous moving particles are geometrically similar and if the ratio of the flow properties is equal.

12. Define dynamic similarities

It exits between model and the prototype which are geometrically and kinematic similar and if the ratio of all forces acting on the model and prototype are equal.

13.                                     Mention the various forces considered in fluid flow. Inertia force,

Viscous force, Gravity force, Pressure force,

Surface Tension force, Elasticity force

14.Define model law or similarity law.

The condition for existence of completely dynamic similarity between a model and its prototype are denoted by equation obtained from dimensionless numbers. The laws on which the models are designed for dynamic similarity are called Model laws or Laws of Similarity.

15.                                     List the various model laws applied in model analysis. Reynold’s Model Law,

Froude’s Model Law, Euler’s Model Law, Weber Model Law, Mach Model Law

16.State Euler’s model law

In a fluid system where supplied pressures are the controlling forces in addition to inertia forces and other forces are either entirely absent or in-significant the Euler’s number for both the model and prototype which known as Euler Model Law.

17. State Weber’s model law

When surface tension effect predominates in addition to inertia force then the dynamic similarity is obtained by equating the Weber’s number for both model and its prototype, which is called as Weber Model Law.

18. State Mach’s model law

If in any phenomenon only the forces resulting from elastic compression are significant in addition to inertia forces and all other forces may be neglected, then the dynamic similarity between model and its prototype may be achieved by equating the Mach’s number for both the systems. This is known Mach Model Law.

19. Classify the hydraulic models.

The hydraulic models are classified as: Undistorted model & Distorted model 20. Define undistorted model

An undistorted model is that which is geometrically similar to its prototype, i.e. the scale ratio for corresponding linear dimensions of the model and its prototype are same.

21. Define distorted model

Distorted models are those in which one or more terms of the model are not identical with their counterparts in the prototype.

22. Define Scale effect

An effect in fluid flow that results from changing the scale, but not the shape, of a body around which the flow passes.