Dilution (equation)

The dilution equation, also known as the Basic Room Purge Equation, is used in industrial hygiene. It determines the time required to reduce a known vapor concentration existing in a closed space to a lower vapor concentration. The equation can only be applied when the purged volume of vapor or gas is replaced with "clean" air or gas. For example, the equation can be used to calculate the time required at a certain ventilation rate to reduce a high carbon monoxide concentration in a room.


 * $$\ D_t=\left [ \frac{V}{Q} \right ]\quad \cdot ln\left [ \frac{C_{initial}}{C_{ending}}\right ] \quad $$

Sometimes the equation is also written as:


 * $$\ ln\left [ \frac{C_{ending}}{C_{initial}}\right ] \quad={-}\frac{Q}{V} \cdot (t_{ending}-t_{initial})\quad $$          where tinitial = 0

Dt = Time required; the unit of time used is the same as is used for Q.

V = Air or gas volume of the closed space or room in cubic feet, cubic meters or liters

Q = Ventilation rate into or out of the room in cubic feet per minute, cubic meters per hour or liters per second

Cinitial = Initial concentration of a vapor inside the room measured in ppm

Cending = Final reduced concentration of the vapor inside the room in ppm