Q. Define Dimensional analysis.
It gives a mathematical relation between various variables of a process in dimensionless form.

Q. Describe the  utility of dimensional analysis.
(i) It gives a simplified theoretical solution of a flow problem by proper selection of variables in non dimensional form.
(ii) It helps in developing correlation for experimental data which help in the design of the process.

Q. Name the various methods of dimensional analysis.
Two methods
(a) Rayleigh’s method
(b) Buckingham’s Pi Method

Q. What is Rayleigh’s Method?
It develops a relation between dependent and independent variables in a flow process on the basis of dimensional homogeneity. The maximum total number of variables should be four or less. Otherwise it becomes very cumbersome and complex. Mathematically
X=f(X1, X2,X3) where X is dependent variable and X1, X2, X3 are independent variables.

Q. Define Buckingham’s (π) Method.
It is an improvement over Rayleigh’s method. It can be applied to any number of variables. Suppose total variables are n. There are, say, total dimensions involved are m(say 4). Number of non dimensional pi terms will be = n-m= n-4. Mathematically
X1 =f(x2,X3,X4,……….Xn)
then write it as follows
f (X1,X2,X3,X4,…….. Xn)=0
Then it becomes
f (π1,π2,π3, π4,……..πn-m)=0
In case m=4 and n=8 ,the term becomes
f (π1,π2,π3, π4)=0

Q. How to find various Pi (π) terms?
Each non-dimensional π term is formed by combining m dimensional parameters with one of the remaining (n-m) variables i.e each π term contains (m+1 ) variables. These m variables are repeating variables for each π term. These m variables chosen should not form a dimensionless parameter.Preferably repeating variables are
(i) Length, velocity and density
(ii) Diameter, velocity and density
(iii) Length, velocity and viscosity
(iv) Diameter, velocity and viscosity
Suppose variables are l,v,ρ,µ,k,g,cp
M=4 L,M,T, and ϴ
No of π terms=n-m=7-4=3
According to π theorem
π1= f(π2, π3, π4)
π2= f(π1, π3, π4)
π3= f(π1, π2, π4)
π4= f(π2, π3, π1)

Q. List the advantages of dimensional analysis.
(i) It gives a functional relationship between independent and dependent variables in dimensionless form.
(ii)By proper selection of repeating variables, dimensionless parameters can be easily found.
( iii) Curves can be drawn for the experimental data easily.
( iv) It gives a theoretical solution for complicated problem.

Q. What are the limitations of dimensional analysis?
(i) It does give any idea about the selection of repeating variables.
(ii) It does not complete information about the variables. It gives only how these are related.
( iii) It does give any physical explanation of the process or phenomenon.
( iv) It does give any information regarding the effect of one variable over other variables