# Dimensional Analysis Problem

## Homework Statement

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, bbl/yr; p is the true vapor pressure at the bulk temperature, psia; 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?

Unit conversions

## The Attempt at a Solution

I have a doubt with the (p/(14.7-p))^0.68 term. I think it should be dimensionless, but I am not totally sure as there is a 14.7 with no units minus a pressure in psia...

• ayeshanaved23

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kuruman
Homework Helper
Gold Member
... as there is a 14.7 with no units minus a pressure in psia...
What is atmospheric pressure in psi?

gneill
Mentor
I have a doubt with the (p/(14.7-p))^0.68 term. I think it should be dimensionless, but I am not totally sure as there is a 14.7 with no units minus a pressure in psia...
It's terms like that that indicate that this is not an equation, but a formula. There are many such formulas for different disciplines, typically compiled into handbooks, where you must enter the variable values as dimensionless magnitudes of quantities that are given in specific units. A formula is "true" only so long as you specify all quantities in the required units and don't entry the units A formula's constants typically have no units so you can't trivially "translate" the formula to work with other units, and since you have to interpret the result of the formula in particular units you can't just treat the expression as an equation and "solve" for any of the variables in terms of the others without putting some thought into what you're doing.