Calculating Air Flush Time for Airliner Cabin with 30000 cuft and 10000 ppm of X

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To calculate the air flush time for an airliner cabin of 30,000 cubic feet with an initial concentration of 10,000 ppm of substance X, the goal is to reduce this concentration to 100 ppm using a fresh air flow rate of 600 ft³/min. The discussion suggests modeling the problem with a differential equation that accounts for the inflow and outflow of substance X. The inflow concentration of X remains constant, while the outflow concentration depends on the current amount of X in the cabin. Participants are encouraged to derive the equation and solve for the time required to reach the target concentration. The conversation emphasizes the importance of understanding the flow dynamics in this air flushing scenario.
juice34
A airliner cabin with 30000 cuft containing 10000 ppm of x is to be flushed with fresh air until the concentration is 100ppm of x. The flow rate is 600ft^3/min. How many minutes till the concentration is at 100ppm. Could somebody help me or guide me in solving this problem.
 
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juice34 said:
A airliner cabin with 30000 cuft containing 10000 ppm of x is to be flushed with fresh air until the concentration is 100ppm of x. The flow rate is 600ft^3/min. How many minutes till the concentration is at 100ppm. Could somebody help me or guide me in solving this problem.

Hi juice34! :smile:

You can assume that the flow rate in equals the flow rate out.

Hint: call the amount of x "p".

Then the flow in contains [how much?] of x/min (doesn't depend on p), and the flow out contains [how much?] of x/min (does depend on p) … make a differential equation for p and t. :smile:
 

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