Importance of Dimensional Homogeneity In Engineering Calculations

Engineering is a very extensive area that there are different kinds of professions in them. One of them is mechanical engineering which this website is built upon! And in mechanical engineering, there are various kinds of areas such as design engineering, manufacturing engineering, materials engineering, etc. 

But all of these engineering areas have a very important common… It is EQUATIONS! We are using lots of kinds of equations to find answers to our questions. Or, we are deriving special equations to find the desired solutions to our problems. These equations can have different parameters. And while we are defining our parameters, we need to take care of dimensional homogeneity to find correct results.

What Is The Dimensional Homogeneity?

While we are calculating an equation to find a result, we are doing different mathematical operations such as additions, subtractions, multiplications, and divisions. 

In terms of dimensional homogeneity, additions and subtractions are important ones. We can divide and multiply the values have different units. 

When you are calculating anything, you need to have the same dimensions if you are making additions or subtractions. Otherwise, calculations will not be correct. You will have irrelevant values without any specific unit.

For example, you are adding different stress values that you found from different calculations to find out the total value in the strength of the materials problem. All the stress values must be in the same dimension, for example, MPa. If you add different values that have MPa, GPa, and Pa, you will have a meaningless value which will be not the correct result. 

If we give another example for multiplications and divisions, assume that you are calculating the force value with Newton’s law. you need to multiply the acceleration and the mass which have different dimensions and units. But with this formula, you are trying to find a new value. 

Conclusion

In detailed and special engineering calculations, you need to give special care to dimensional homogeneity to obtain correct results in your calculations. 

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