PPT: Dimensional Analysis | Fluid Mechanics for Mechanical Engineering PDF Download

 Page 1


Learning Objectives
1. Introduction to Dimensions & Units
2. Use of Dimensional Analysis
3. Dimensional Homogeneity
4. Methods of Dimensional Analysis
5. Rayleigh’s Method
Page 2


Learning Objectives
1. Introduction to Dimensions & Units
2. Use of Dimensional Analysis
3. Dimensional Homogeneity
4. Methods of Dimensional Analysis
5. Rayleigh’s Method
Learning Objectives
6. Buckingham’s Method
7. Model Analysis
8. Similitude
9. Model Laws or Similarity Laws
10. Model and Prototype Relations
Page 3


Learning Objectives
1. Introduction to Dimensions & Units
2. Use of Dimensional Analysis
3. Dimensional Homogeneity
4. Methods of Dimensional Analysis
5. Rayleigh’s Method
Learning Objectives
6. Buckingham’s Method
7. Model Analysis
8. Similitude
9. Model Laws or Similarity Laws
10. Model and Prototype Relations
? Many practical real flow problems in fluid mechanics can be solved by using 
equations and analytical procedures. However, solutions of some real flow 
problems depend heavily on experimental data. 
? Sometimes, the experimental work in the laboratory is not only time-consuming, 
but also expensive. So, the main goal is to extract maximum information from 
fewest experiments. 
?In this regard, dimensional analysis is an important tool that helps in correlating 
analytical results with experimental data and to predict the prototype behavior from 
the measurements on the model.
Introduction
Page 4


Learning Objectives
1. Introduction to Dimensions & Units
2. Use of Dimensional Analysis
3. Dimensional Homogeneity
4. Methods of Dimensional Analysis
5. Rayleigh’s Method
Learning Objectives
6. Buckingham’s Method
7. Model Analysis
8. Similitude
9. Model Laws or Similarity Laws
10. Model and Prototype Relations
? Many practical real flow problems in fluid mechanics can be solved by using 
equations and analytical procedures. However, solutions of some real flow 
problems depend heavily on experimental data. 
? Sometimes, the experimental work in the laboratory is not only time-consuming, 
but also expensive. So, the main goal is to extract maximum information from 
fewest experiments. 
?In this regard, dimensional analysis is an important tool that helps in correlating 
analytical results with experimental data and to predict the prototype behavior from 
the measurements on the model.
Introduction Dimensions and Units
In dimensional analysis we are only concerned with the nature of the 
dimension i.e. its quality not its quantity. 
? Dimensions are properties which can be measured. 
Ex.: Mass, Length, Time etc.,
? Units are the standard elements we use to quantify these dimensions.
Ex.: Kg, Metre, Seconds etc.,
The following are the Fundamental Dimensions (MLT)
? Mass kg M
? Length m L
? Time s T
Page 5


Learning Objectives
1. Introduction to Dimensions & Units
2. Use of Dimensional Analysis
3. Dimensional Homogeneity
4. Methods of Dimensional Analysis
5. Rayleigh’s Method
Learning Objectives
6. Buckingham’s Method
7. Model Analysis
8. Similitude
9. Model Laws or Similarity Laws
10. Model and Prototype Relations
? Many practical real flow problems in fluid mechanics can be solved by using 
equations and analytical procedures. However, solutions of some real flow 
problems depend heavily on experimental data. 
? Sometimes, the experimental work in the laboratory is not only time-consuming, 
but also expensive. So, the main goal is to extract maximum information from 
fewest experiments. 
?In this regard, dimensional analysis is an important tool that helps in correlating 
analytical results with experimental data and to predict the prototype behavior from 
the measurements on the model.
Introduction Dimensions and Units
In dimensional analysis we are only concerned with the nature of the 
dimension i.e. its quality not its quantity. 
? Dimensions are properties which can be measured. 
Ex.: Mass, Length, Time etc.,
? Units are the standard elements we use to quantify these dimensions.
Ex.: Kg, Metre, Seconds etc.,
The following are the Fundamental Dimensions (MLT)
? Mass kg M
? Length m L
? Time s T
Secondary or Derived Dimensions
Secondary dimensions are those quantities which posses more than one 
fundamental dimensions. 
1. Geometric
a) Area m
2
L
2
b) Volume m
3
L
3
2. Kinematic
a) Velocity m/s L/T L.T
-1
b) Acceleration m/s
2
L/T
2
L.T
-2
3. Dynamic
a) Force N ML/T M.L.T
-1
b) Density kg/m
3 
M/L
3
M.L
-3