The air flow inside the duct

In the case of natural ventilation the flow rate is determined by the heat field, the duct geometry, the fluid dynamic head losses and the wind velocity and direction. If the effects due to the wind are neglected the mean air velocity W0 at the ventilated duct inlet section can be expressed by the following relation [8, 10]:

with <T> and <1/T> mean temperature values calculated along the wall full length and Tou=T (x=L).

In Eq. (2) by f the friction factor of the duct, by Xin and Xou the friction factors of the head losses located on the inlet and outlet sections and by g the acceleration due to gravity are indicated. In the Eq. (2) the factor a, defined as the ratio between the mean value of the velocity square and the square of the velocity mean value, has been considered for the calculation of the kinetic energy of the air flowing into the duct [10]. In the case of laminar flow and parabolic velocity profile it results that a=6/5.

For the friction factor f the relation f=96/Re [12] has been used. The friction factors Xin and Xoj are characterized by the following minimum values: Xin=0.5 (sudden air inlet from the atmosphere) and Xou=1 (sudden air outlet into the atmosphere); the presence of narrowings, obstructions, various shapings, protection grills, dirt accumulation, determines a considerable increase in these values.