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Civil - Mechanics Of Fluids - Dimensional Analysis And Model Studies

**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.

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