Ventilation rate calculation There are 20 people in a dinning room, each produces 200 W total heat. The carbon dioxide concentration in the supply air is 500 ppmv. Assume the supply air temperature is 15 °C and relative humidity 50 %. The room air is to be maintained at 22 °C and 60 % relative

Question

Ventilation rate calculation
There are 20 people in a dinning room, each produces 200 W total heat. The carbon dioxide concentration in the supply air is 500 ppmv. Assume the supply air temperature is 15 °C and relative humidity 50 %. The room air is to be maintained at 22 °C and 60 % relative humidity. If the required maximum [latex]CO_{2}[/latex] concentration in the room is 1000 ppmv, estimate the minimum ventilation rate based on the [latex]CO_{2}[/latex] concentration.

Accepted Answer

Based on the supply air temperature of 15 °C and 50 % relative humidity we can get the specific volume of supply air using a psychrometric chart,
[latex]v_{s}=0.822 m^{3}[/latex]/kg dry air

The specific volume of exhaust air at 22 °C and 60 % relative humidity is
[latex]v_{e}=0.855 m^{3}[/latex]/kg dry air

The total heat production rate by 20 people in the dining room is,
THP = 20 × 200 W= 4000 W or 4 kJ/s

Then the mass production rate of [latex]CO_{2}[/latex] is estimated using Eq. (14.9)
[latex]\dot{s}_{CO_{2}}= ho _{CO_{2}}\frac{THP}{24,600}=1.83 imes\frac{4}{24,600}=2.98 imes 10^{-4}(kg/s)[/latex]

Then the minimum ventilation rate fan is determined using Eq. (14.17)
[latex]\dot{s}_{CO_{2}}=Q_{e}c_{e}\left(1 - \frac{v_{s}c_{s}}{v_{e}c_{e}} ight)=Q_{s}c_{s}\left(\frac{v_{e}c_{e}}{v_{s}c_{s}} - 1 ight)[/latex] (14.17)

Since [latex]v_{s} < v_{e}[/latex], the minimum ventilation rate should be calculated based on the exhaust air. However, we need to convert the unit of concentration c from ppmv to kg [latex]CO_{2}/m³[/latex] air.
[latex]c_{e}=\frac{1.000 m^{3} CO_{2} imes 1.83 kg CO_{2}/m^{3} CO_{2}}{10^{6} m^{3} air}=1.83 imes 10^{-3} kgCO_{2}/m^{3} air[/latex]

The exhaust ventilation rate is
[latex]Q_{e}=\frac{\dot{s}_{CO_{2}}}{c_{e}\left(1 - \frac{v_{s}c_{s}}{v_{e}c_{e}} ight)}[/latex]

[latex]=\frac{2.98 imes 10^{-4} kg CO_{2}/s}{\left(\frac{1000 m^{3} CO_{2} imes 1.83 kg CO_{2}/m^{3} CO_{2}}{10^{6} m^{3} air} ight)\left(1 - \frac{0.822}{0.855} imes \frac{500}{1000} ight)}[/latex]
[latex]=0.31 m^{3} air/s[/latex]

Question 14.3: Ventilation rate calculation There are 20 people in a dinnin...

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