what is dimensional analysis
http://www.chem.tamu.edu/class/fyp/mathrev/mr-da.html
Dimensional analysis is the use of units in an equation/derivation to check the validity of the process. In practical terms, many use the term to mean using a conversion factor. For example, suppose we wish to convert 100 cm to 1 m and we know the factor is 1 m = 100 cm. Therefore,
100 cm x (1 m/100 cm) = 1 meter. Note how the cm unit in the numerator cancels with the cm unit in the denominator leaving the unit we want to keep all alone.
Here is more information for you to read. http://en.wikipedia.org/wiki/Dimensional_analysis
Dimensional analysis is a mathematical method used in physics and engineering to check the consistency of physical equations and to convert between different units of measurement. It helps to ensure that the units of different physical quantities in an equation align correctly, which is important for the equation to make sense and be accurate.
The basic principle of dimensional analysis is that physical quantities can be expressed in terms of their fundamental dimensions, such as length, time, mass, temperature, electric charge, and so on. Each of these fundamental dimensions has a specific unit associated with it, like meters for length, seconds for time, kilograms for mass, and so on.
To perform dimensional analysis, you need to follow these steps:
1. Identify the physical equation or relationship you want to analyze. This could be an equation given in a problem or a formula you are using to solve a specific question.
2. Break down each physical quantity in the equation into its fundamental dimensions. For instance, if you have a velocity, you would break it down into length (L) divided by time (T).
3. Assign units to each fundamental dimension. For example, you might use meters for length and seconds for time.
4. Check if the units on both sides of the equation match. If they do, then the equation is dimensionally consistent. If not, there might be an error in the equation or in the units used.
Dimensional analysis is also used to convert between different units. By multiplying or dividing a quantity by conversion factors, which are ratios of equivalent units, you can convert from one unit to another. For example, to convert from meters to feet, you would use the conversion factor 1 meter = 3.28084 feet.
Overall, dimensional analysis provides a systematic and reliable approach to verify the correctness of equations, understand the relationships between physical quantities, and convert between different units of measurement.