Determine the flow rate using the differential pressure

Question

Assuming an input air flow rate, the room volume and an underpressure (let's say 5%) is known, is it possible to determine the output air flow rate? What law can I use, or what additional info would I need?
Background:
I'm aiming to track the energy flows within a room as part of a research project. The input volume flow is coming from one source and can be determined by evaluating the signals of the respective volume flow controller. The outflow on the other hand is very difficult since 32 digestors are located in the room, each with its own funnel. I do have accurate temperature readings, so with the precise volume flows it should be easy to track energy flows.

Nick · Accepted Answer

If we're at steady state, the mass flow in must equal the mass flow out. You have only given the flow rate in, I'm going to assume it's at ambient density of about $1.2,mathrm{kg/m}^3$, so the mass flow in is $1,200,mathrm{kg/h}$.
To calculate the density in the room we can use the ideal gas law, $p=rho RT$. At a 5% underpressure relative to atmospheric, the pressure in the room is $0.95times101,325=96260,mathrm{Pa}$. Assuming dry air with $R=287,mathrm{J/kg/K}$ and a temperature of $300,mathrm{K}$, the density in the room is $1.12,mathrm{kg/m}^3$.
The volume flow out is therefore $1,200/1.12=1,070,mathrm{m}^3/mathrm{h}$.

Determine the flow rate using the differential pressure

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