HVAC - Primary airflow temperatre

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Puzzled
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TL;DR
Air Temperature affects.
Hi team,
I am after some assistance. When I am amending the primary airflow temperature on diffusers from 22°C to 13°C, it is my opinion that all the Draught rating (DR) and comfort criteria calcs will all change as the air will become more dense. Is this correct?
 
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As far as I understand, the DR equation does not consider the density of air.
Temperature and turbulence of the supplied air are factors of more influence.
Normally, 22 degrees is closer to the temperature of the air already in the occupied space, while 13 degrees is closer to the temperature of the air that is supplied into the space via diffusers and being mixed with the warmer air, being the difference in density of 0.2 kg/m3 aproximately.