INTRODUCTION OF DIMENSIONAL ANALYSIS

                                                                                                                                       

Dimensional analysis is one of the approach to solve fluid mechanics problems by using dimensions. We first review the concept of dimensions and units then review the fundamental principle of dimensional homogeneity. We also describe a powerful tool for engineers called dimensional analysis, in which the combination of dimensional variables and  non dimensional variables and study a technique to reduce the number of variables using Raleigh Method and Theorem Pi Buckingham. In dimensional analysis , we need to predict the physical parameters that will influence the flow then group these parameters into dimensionless combinations.

DIMENSION	SYMBOL	SI UNIT	ENGLISH UNIT
Mass	M	kg	lb
Length	L	m	Ft
Time	T	s	s
Temperature	θ	℃	℉

TABLE 1 : Primary dimensions and their associated primary SI and English units.

The significant of dimensional analysis are;

1. Useful for research study especially in design work by reducing the number of variables.
2. To express in dimensionless equation to find the significant of each parameters.
3. To simplify the analysis of complex phenomenon in systematic order.

*All equations related to a physical phenomenon must be dimensionally homogeneous. This is known as Principle of Dimensional Homogeneity.

2.         DIMENSIONAL HOMOGENEITY

An equation which expresses the proper relationship between the variables in a physical phenomenon will be dimensionally homogenous. This means that each of additive terms in an equation should have the same dimension. 

Example: P (kg/ms) = ρgh (kg/ms), where both sides are in same units.

In MLTθ system, M, length L, time T, and temperature θ. 
For FLTθ system, mass M is replaced by force F.
 For instance;

 Area for rectangular, A = Length, L x width, b = m² (SI unit). 

But in D.A, value is not important. 

Thus, Area = Length, L x width, L = L²

Table 2 shows quantities of fluid mechanics and hydraulic in MLTθ system.

Table 2

3.         METHODS

There are a lot of methods can be use to reduce into a smaller number of dimensionless parameters such as Raleigh method (basic principle) and Theorem Pi Buckingham.

Most popular methods used in dimensional analysis are Rayleigh method (basic principle) and Buckingham’s Pi Theorem