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CHAPTER 31
1956 Guide
the basic relation of Equation 2, and a nomogram for calculating the par rameters
and
Vx . -
V. . from
X
VAc
and
Vx
Vo
Fig. 3. Chart; for Determining Centerline Velocities op
i
Axial and Radial Jets
Zones 1 and 2. Fx/Fo is plotted against X/Ho and, for a range of aspect ratios, against X/vVt for the single value of K' = 7.0. Values of Fx/Fo for_other values of K' may be obtained by direct proportioning of VK' to
V7.0. The following Example 1 which is solved on Fig. 3 will illustrate the use
of the chart.
Example 1: A grille has a core area 12 in. x 18.75 in., Ru = 0.90, Ce = 0.80, and
K' = 5.0. Find V, (velocity through core area) when V,, is 50 fpm for throw of 50 feet (X - 50).
Solution:
12 X. 18.75 A, 1.56 aq ft
. 144 . .
Air Distribution
709
X
VT,
--50- = 40 1.25
Ao : 1.56 X 0.80 X 0.90 = 1.123
X 50
Va,
--- = 47.2 1.06
Vx K'VTv 5\/El23
y. * X
0.106 50
For V, = 50,
Vx Vx ve = V(CdAJ
0.106 = 0.147
0.80X0.90
V.
=
50 0.147
:
The quantity of air discharged is then,
340 fpm.
Throw
Q = V.AC = 340 X 1.56 = 530 cfm.
Equation 2a can be used to determine the throw X of an outlet, if the dis charge volume and the center velocity are known.
or, if
Q Vx VA.X Ci X fif.
(4)
z = VCd x Rt.
Y-K q
V,' ZVT'
(4a)
The maximum throw L is usually defined as. the distance from the outlet face where the centerline velocity is 50 fpm. Therefore, for F* = 50 fpm,
K' L=X=
50
Q
Z*/Z
(4b)
Velocity Profiles of Jets,
In Zone 3 of both axial and radial jets, the velocity distribution may be
expressed by a single curve (Fig. 4) in terms of dimensionless coordinates,
and this same curve can be used as a good; approximation for adjacent por tions of Zones 2 and 4. Experiments have shown that temperature and
density differences have but a small effect on cross-sectional velocity pro files.
Velocity distribution in Zone 3 can be expressed by the Gauss error-
function or probability curve which is approximated by a simple equation
using common logarithms
-
where
r
3.3 log j
(5)
the radial distance of the point under consideration from the centerline of the jet.