Handbook of air conditioning and refrigeration / Shan K

x � distance from surface of outlet to a cross-sectional plane having centerline velocity
v c, ft (m)
In Eq. (18.8), A o, in ft 2 (m 2 ), represents the effective area of the airstream, i.e., the minimum area at
the vena contracta. It can be calculated as
(18.9)
where Ac � core area of outlet, i.e., surface area of opening, ft2 (m2 Ao � AcCd Rfa )
vcore � face velocity at core of outlet, fpm (m/s)
Cd � discharge coefficient, usually between 0.65 and 0.9
Rfa � ratio of free area to gross area (free area is net area of opening through which air can
pass)
When v o is 500 to 1000 fpm (2.5 to 5 m/s), for round free openings, K � 5; for rectangular openings
and linear slot diffusers, K� �4.9. When v o is 2000 to 5000 fpm (10 to 25 m/s), for round free
openings, K � 6.2.
When multiple air jets are discharged into a conditioned space at the same level, each air jet
behaves independently until the jets meet. From the point where the jets meet, the velocities between
the centerlines of the air jets increase until they are equal to the centerline velocities of the
air jets.
Throw, Entrainment Ratio, and Characteristic Length
Throw in ft (m), is defined as the horizontal or vertical axial distance from the outlet to a cross-sectional
plane where the maximum velocity of the airstream at the terminal zone has been reduced to
50 fpm (0.25 m/s), 100 fpm (0.5 m/s), or 150 fpm (0.75 m/s). The throw is indicated by T v, and
the subscript denotes the terminal velocity for which the throw is measured. For instance, T 50 (T 0.25)
indicates the throw with a terminal velocity of 50 fpm (0.25 m/s).
From Eqs. (18.8) and (18.9), throw can be calculated as
where vt,max � maximum velocity of airstream at terminal zone, fpm (m/s)
� supply volume flow rate at outlet, cfm (m3 /s)
V˙ s
(18.10)
For a specific configuration of supply outlet, throw Tv depends on both the supply volume flow rate
V˙ s and supply outlet velocity vcore. The entrainment ratio Ren is the ratio of the volume flow rate of the total air at a specific crosssectional
plane of the air jet V˙ x to the volume flow rate of the supply air V˙ o discharged from the outlet
,which is sometimes called primary air. Total air is the sum of supply air and induced air.
The entrainment ratio is proportional to the distance or square root of the distance from the outlet.
For circular jets in the main zone, the entrainment ratio can be calculated as
For a long slot, the entrainment ratio is
R en � V˙ x
V˙ o
R en � V˙ x
V˙ o
v o � v coreC d R fa
T v �
K�V˙ s
v t, max√AcC d R fa
� 2x
K√A o
� √ 2x
K�H o
AIR SYSTEMS: SPACE AIR DIFFUSION 18.7
� 2v o
v c
� √ 2v o
v c
(18.11)