Insane Dimensional Analysis Problem

1. Jun 4, 2013

cytochrome

1. The problem statement, all variables and given/known data
• The American Petroleum Institute has published a correlation for determining the hydrocarbon emissions from fixed-roof storage tanks

Ly = (24/1000) * (p/(14.7-p))^0.68 * D^1.73 * H^0.51 * T^0.5 * Fp * C

where: Ly is breathing emissions, gallons/yr; p is the true vapor pressure at the bulk temperature, psi; D is the tank diameter, ft; H is the height in ft; T is the average tank outage corrected for roof volume, ft; Fp is the dimensionless paint factor; and C is the dimensionless adjustment factor.

Is this equation dimensionally consistent? Is it possible, based on a unit analysis, that the equation is correct? If not, what units must be added to the term 24/1000 to make it dimensionally consistent?

2. Relevant equations

Dimensional analysis and conversions

3. The attempt at a solution

I simply rewrote the equation but I am totally stuck on what to do with the (p/(14.7-p))^0.68 term... how do you have a unit to a power like 0.68?

2. Jun 4, 2013

voko

It is not really different from a integer power like 2, which you find in acceleration, pressure, etc.

3. Jun 4, 2013

SteamKing

Staff Emeritus
The term (p/(14.7-p)) is dimensionless, as you have pressure divided by pressure. Raising a dimensionless number to a power does not change the fact that it is dimensionless.

4. Feb 25, 2017

popoff

Does anyone have the solution to this problem? I do not even know how to start to solve it!

Thank you :)

5. Feb 25, 2017

Staff: Mentor

Hi popoff. No one here will give you the solution to a homework question. That would be against the forum rules.

If you have the same homework question and you need help with it you'll have to show your own attempt at solution (show what your understanding is of the problem and what approaches you have already tried) before help can be offered. The best way to do this when a thread is as old as this is to start your own, new thread.