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Mechanical - Fluid Mechanics And Machinery - Dimensional Analysis

**DIMENSIONAL
ANALYSIS**

**1. What are the methods of
dimensional analysis**

There are
two methods of dimensional analysis.
They are,

a. Rayleigh
- Retz method

b. Buckingham's theotem method.

Nowadays
Buckingham's theorem method is only
used.

**2. Describe the Rayleigh's method for dimensional
analysis.**

Rayleigh's method is used for
determining the expression for a variable which depends upon maximum three or
four variables only. If the number of independent variables becomes more than
four, then it is very difficult to find the expression for dependent variable.

**3. What do you mean by dimensionless number**

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 or elastic force. As this is
a ratio of one force to other force, it will be a dimensionless number.

**4. Name the
different forces present in fluid flow**

Inertia force Viscous force Surface tension force
Gravity force

**5. State
Buckingham****’****s ****Π**** theorem**

It states that if there are ‘n’
variables in a dimensionally homogeneous equation and if these variables
contain ‘m’
fundamental dimensions (M,L,T), then they are grouped into (n-m), dimensionless
independent Π-terms.

**6. ****State the
limitations of dimensional analysis. **

1. Dimensional
analysis does not give any due regarding the selection of variables. 2.The
complete information is not provided by dimensional analysis.

3.The values of coefficient and the nature of function can be
obtained only by experiments or from mathematical analysis.

**7.****Define
Similitude **

Similitude is defined as the complete similarity between the
model and prototype.

**8. ****State Froude’s model
law**

Only Gravitational force is more predominant force.
The law states ‘The Froude’s number is same for both model and prototype’

**9.What are the similarities between model and
prototype?**

(i)
Geometric Similarity

(ii)
Kinematicc Similarity

(iii)
Dynamic Similarity

**10.Define Weber number.**

It is the ratio of the square
root of the inertia force to the surface tension force.

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