# Assumptions And Derivations

• posted

Many times in deriving formulaes and equation we come across assuming as UNIT LENGTH , UNIT MASS , OR SOME UNIT QUANTITY . i want to know why this term is used and what is its significance and how useful it really is?

• posted

Dear babu:

To make magnitude a separate value. Note the similarity to "unit vector" + "speed" and velocity.

How useful is pricing vegetables "per pound" or "per kilogram"? How useful is density, which is mass per unit volume?

It allows you the ability to separate the measurements from the specific "thing", and compare different things on some property, to try and discover correlations. Such as "specific gravity"...

The next step is "dimensional analysis" and the "Buckingham Pi Theorem". How did Reynold's come up with his number?

David A. Smith

• posted

Actually sir you point is not clear to me. Can you mail me any example ?

• posted

Dear babu:

Surely you cannot mean to ask for an example of this?

... or this?

As used in mechanical engineering...

a dimenionless number that has much to do with pipe flow.

Why is it important to compare things on equal quantity basis?

Is a "unit mass" or "per unit mass" any different in the contexts you were asking about?

Would the results be any different if you were comparing "ten units mass" of one thing to "ten units mass" of another thing?

So usually the unit designator is simply to *remove* differences in length, or mass, or whatever from the comparison, so that you can observe some other relationship. Density is mass per unit volume. You can buy steel by the unit mass, knowing that a certain shape has a known mass per unit length.

"Unit" in engineering contexts is usually synonymous with ("means the same as") "one".

unit length = one meter OR one centimeter OR one unit of length unit time = one year OR one second OR one unit of time unit mass = one kilogram OR one microgram OR one unit of mass

Look at your original question... does it make sense to make rules that can only be applied to "mass = 143 units"?

Wouldn't it make sense to do something like: total_force = total_mass times acceleration force per unit mass = acceleration

I hope that helps.

David A. Smith

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