The discharge of air from a duct system

Air in the plane of the open end of the discharge duct must be at virtually atmospheric pressure—since there is no longer any resisting force to prevent the equalisation of pressure. We can therefore say that the potential energy of the air leaving the system through an open end is zero. The kinetic energy is not zero however. There is an outflow of mass from the system. Applying Bernoulli’s theorem, it is seen that the total energy of the airstream leaving the ducting must be equal to its kinetic energy or velocity pressure.

If a grille or diffuser is placed over the open end of the duct, the total pressure on its upstream side must be greater than that on its downstream side by an amount equal to the frictional loss incurred by the flow of air through the grille. If any change of velocity that may take place as the air flows between the bars of the grille is ignored, the velocity pressure upstream must equal the velocity pressure downstream. It follows that the static pressure of the upstream air is used to overcome the frictional loss through the grille. This is illustrated in Figure 15.6.

Denoting the upstream side of the grille by the subscript 1 and the downstream side by subscript 2, and assuming face velocities at the grille, we can write

Pt = Pi2 + frictional loss past the grille Pl + Psi = P2 + Ps2 + frictional loss past the grille

But

Ps 1 = Prt

Hence

Discharge duct Discharge duct

Without a grille —► with a grille

Fig. 15.6 Airflow from a discharge opening, (a) without a grille and (b) with a grille.

Psi ~ Ps2 = frictional loss past the grille

Since p$2 is virtually the same as atmospheric pressure—the zero datum—this becomes

Psl = frictional loss past the grille

To sum up: the fan has to make good the energy loss at the end of the system incurred by the kinetic energy of the airstream leaving the system and the friction past the last grille.

Posted in Engineering Fifth Edition