Seeking help from experts to solve a small problem
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As shown in the figure, there is a make-up air fan in front of container A and an exhaust fan behind it, keeping container A under negative pressure. When the make-up air volume remains constant and the exhaust air volume is increased, the negative pressure in container A increases (from -50 pa to -100 pa). Does this mean that the residence time of the gas in container A decreases? What changes have occurred in the gas flow rate? What is the basis?
Residence time and flow rate are not the same; when the flow rate increases, the residence time decreases. With the same volume of A, according to PV=nRT, when the pressure decreases, the volume must increase. Where does this increased volume go? It gets pumped out.
It’s related to this residence time algorithm, right? Volume residence time or mass residence time?
I think when the exhaust volume is first increased, the residence time is short and the pressure decreases gradually. To maintain this negative pressure, the same amount of air that is introduced must be removed, so as to keep the pressure balanced. For the gas in the container, using the ideal gas law PV=nRT, with P constant and the volume V of the container constant, then n must also remain constant. During the pressure reduction process, which is also the process of increasing the amount of gas being removed, P decreases while V remains constant; as a result, n decreases, meaning that a portion of the gas in the container is removed.
With the inlet flow unchanged and the exhaust flow increased, the gas velocity will inevitably increase, resulting in a shorter average residence time. However, the values that change are quite complex and cannot be determined through simple arithmetic calculations. From an energy perspective, increasing the vacuum creates more energy, and an increase in kinetic energy means that the gas velocity increases
Can changing values be solved using calculus?
First, the exhaust volume increases, and the make-up air volume increases accordingly. An increase in system negative pressure results in a higher power requirement for the exhaust fan, while the power requirement for the make-up fan decreases. Since the air volume increases, the flow velocity naturally increases as well, resulting in a shorter residence time per unit mass of gas.