In engineering, the application of fluid mechanics in designs, make much of the use of empirical results from many experiments. This data is often difficult to present in a readable form. Even from graphs, it may be difficult to interpret. Dimensional analysis provides a strategy for choosing relevant data and its presentation. This is a useful technique in all experimentally based areas of engineering. If it is possible to identify the factors involved in a physical situation, dimensional analysis can form a relationship between them. The resulting expressions may not at look rigorous but these qualitative results converted to quantitative forms can be used to obtain any unknown factors from experimental analysis.

Dimensions and units

Carl Friedrich Gauss (1777-1855) and Wilhelm Eduard Weber (1804-1891) had reduced all units, which became necessary during their work in electricity and magnetism to the units of length, mass, and time. Any physical situation can be described, by length, mass, and time. These are, all known as dimensions.

Of course, dimensions are of no use without a magnitude being attached. We must know more than that something has a length. It must also have a standardized unit - such as a meter, a foot, a yard etc. Dimensions are properties, which can be measured. Units are the standard elements we use to quantify these dimensions. In the dimensional analysis, we are only concerned with the nature of the dimension i.e. its quality, not its quantity. The following common abbreviation is used:

Length = L

Mass = M

Time = T

In this section, we are only concerned with M, L, and T. We can represent all the physical properties we are interested in with M, L and T. Some quantities have no dimensions. For example, the sine of an angle is defined as the ratio of the lengths of two particular sides of a triangle. Thus, the dimensions of the sine are L/L, or 1. Therefore, the sine function is "dimensionless". There are many other examples of "dimensionless" quantities are:

1. All trigonometric functions

2. Exponential functions

3. Logarithms

4. Angles

5. Quantities such as the number of people in the room

6. Numbers (like 2, 61552; etc.)

The following table lists dimensions of some common physical quantities:

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In other words E = P x V.

ML2T-2 = ML-1T-2 x L3

We know that volume V is expressed as L3 and pressure P is expressed as ML-1T-2.

So energy E is expressed as ML2T-2.

Thus, we can have a definite volume or size even after our physical death because energy is everlasting.

Now it is very interesting to see that in Chemistry E = P x V is the Gas Equation in Dimensional Analysis as PV = nRT and n and R are constant whereas temperature is an objective comparative measure heat or energy. Heat is expressed as ML2T-2.

Bible says in Genesis 2:7 that God instilled gas into the nostrils of man and man became a living soul. Bible shows the connection of Gas and Soul. And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life, and man became a living soul. (Gen 2:7)

Bible also says that when Jesus will come again in clouds, we will meet him in the air. It also connects that concept of energy to a soul.

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