(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There are two storage rooms, (A) and (B) connected by a single doorway. Only room (B)

has an outward vent, so all air exiting the rooms does so through this vent in room (B). The

ventilator you will install drives outside air (78% nitrogen) at a certain flow rate through

a duct that splits into two and distributes the total flow evenly between an inward vent in

room (A) an an inward vent in room (B). All air exiting room (A) does so through the door

and then mixes with the air in room (B) before leaving through the vent in room (B). No air

ever flows from (B) to (A). You may assume that the air entering each room (either through

the vent or in the case of (B) also through the door from (A)) mixes instantaneously with the

rest of the air in the room. The dimensions of room (A) are 20 feet × 15 feet × 12 feet

(3600 cu ft) and the dimensions or room (B) are 20 feet × 18 feet × 12 feet (4320 cu ft).

The laboratory knows that if there is a leak in room (A) then by the time the atmosphere

in (A) reaches 85%, the atmosphere in (B) will have reached 81%. This is the situation you

are hired to deal with: (A) starting at 85%, (B) at 81% and you need to reduce both to 79%.

Support your conclusions with graphs.

2. Relevant equations

In the first situation, the ventilator forces air through the main duct (before it splits

into two) at 400 cu ft/min on high. How long does it take for this ventilator to reduce

the atmosphere in both rooms to below 79%?

3. The attempt at a solution

Okay, so I understand that the initial conditions are A(0)=.85 and B(0)=.81 and that A(t) and B(t) both =.79

Saying x is the nitrogen level, I need to form an equation something like dx/dt = 200(.79)-200(.85t) but that's where I get confused. I feel like this should be fairly simple but I keep getting stumped. Any help you can give is greatly appreciated!

-Sam

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# Homework Help: Building Ventilation ODE

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