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# Engineering Q - dimensional analysis/conversions?

The pertinent variables in describing the behavior of a gas are taken as pressure (P, lbf/ft^2), volume (V, ft^3), number of moles (n, moles), and RT (ft-lbf/mole). On the basis of dimensional analysis, derive a relation among these variables. Note: You must formally derive your answer by following the procedure described in lecture.

I have no clue where to start.

### 2 Answers

- 7 years agoFavorite Answer
Dimensional analysis sounds scary, but it should be taught in high school. Basically, it means don't bother memorizing a bunch of stupid formulae, often you don't need them! Just include the units in your calculations, and make sure they work out.

So in this example, you have 4 variables:

P[lbf/ft^2]

V[ft^3]

n[mole]

RT[ft-lbf/mole]

"derive a relation among these variables" ... ie. write down an equals sign, try to make the right hand side (RHS) equal the left hand side (LHS). To start, just pick one variable for one side, and put the others on the other side

(1) P = VnRT

Now substitute the units and see what happens. Note: you can combine units by multiplying or dividing them out, just like numbers: ft * ft = ft^2 etc... Notice mole/mole=1, they cancel out

[lbf/ft^2] = [ft^3][mole][ft-lbf/mole] -------> [lbf/ft^2] = ft^4-lbf

Therefore, equation (1) is a complete lie because RHS does not equal LHS. Once you get the right equation, LHS = RHS like it should.

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- kleppingerLv 43 years ago
to resolve this, you should rework miles to km, and hrs to seconds. i hit upon it least complicated to resolve those complications by utilising drawing a horizontal line, and putting the instruments of the numerator on accurate, and the denominator instruments less than. Convert the instruments by utilising making the instruments take position on accurate and on bottom only so that they cancel out (reminiscent of how 9/9 cancels out to at least a million). for instance: seventy 3 mi_x a million km__x a million hr___= 0.0326 km __ hr__0.6214mi___3600 sec____________sec (It would not seem fairly typed out, yet drawn out on paper it seems nicer, and it retains you waiting; plus, you should use the conversion component or its reciprocal, i.e. km to mi or mi to km)

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