Document zQMNz9BKb7ZLGDX2BEKO3JLg3

270 CHAPTER 20 1959 Guide be experimentally determined. Values of C* and Rf, are required for determining V#, Do, and A, for orifice-type and multiple-opening outlets, and should, therefore, be included in catalog data of these outlets. In- the case of multiple-opening outlets and annular-ring outlets, the streams coalesce into a solid jet before actual jet expansion takes place. This coalescence affects the experimen tally determined proportionality constants K or K' and ac counts for some of the divergence in reported values for simi lar outlets. Centerline Velocities in Zones 1 and 2 Experimental evidence indicates that in Zone 2 where H ** width of jet at outlet or at vena contract*. Approximately the same values of K' apply as for Zone 3 expansion from axial outlets. In Zone 1, the ratio F./F# is constant and equal to the ratio of the center velocity of the jet at start of expansion to the average velocity, ranging from approximately 1.0 for roundedentrance nozzles to about 1.2 for straight pipe discharge, but with much higher values for diverging-discharge outlets. Determining Centerline Velocities To permit correlation of data from all four zones, centerline velocity ratios are plotted against distance from outlet in Pig. 2 in accordance with the basic relation of Equation 2, and a nomogram for calculating the parameters X A* and V, Vt from X VT. and F, V, through Rf* and Cd is given in the same illustration. The variation of the centerline velocity ratio with distance from outlet, or more properly, from start of jet expansion, is also shown on Pig. 2 for Zones 1 and 2. V./V, is plotted against X/U, and, for a range of aspect ratios, against X/\/a for the single value of K' -- 7.0. Values of F./F for other values of K.' may be obtained by direct proportion ing of y/K' to V7.0. Air Distribution Straightflow Turbulent Jets The following Example 1 which is solved on Pig. 2 will illustrate the. use of the chart. Example 1: A grille has a core area 12 in. x 18.75 in., ft/. = 0.90, Cd * 0.80, and K.' = 5.0. Find V, (velocity through core area) when V, is SO fpm for throw of 50 feet (X = 50). Solution: 12 X 18.75 A. => ------------ = 1.56 sq ft X 50 SI ~ 1-25 " 40 A* - 1.56 X 0.80 X 0.90 = 1.123 = 7-- -- 4/.Z VT, 1.O6 F, K'VA, 5vTl23 V, X 50 vr 0.106 F. V,(C<RfJ 0.80 X 0.90 50, 50 Ve * 340 fpm. 0.147 The quantity of air discharged is then, Q = VJL, - 340 X 1.S6 - 530 cfm. Throw - Equation 2a can be used to determine the throw X of an outlet, if tite discharge volume and the center velocity are known. K' Q X v. Va, X Cd X Rf (4) or, if z - VCd x ft/. 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 V, = 50 fpm. L-X C 5Q'zVA< (4b) 271 Velocity Profiles of Jets In Zone 3 of both axial and radial jets, the velocity distri bution may be expressed by a single curve (Pig. 3) in terms of dimensionless coordinates, and this curve ^ used as a good approximation for adjacent portions of Zones 2 and 4. Experiments have shown that temperature and density differences have but a small effect on cross-sectional velocity profiles. Velocity distribution in Zone 3 can be expressed by the Gauss error-function or probability curve which is approxi mated by a simple equation tiring common logarithms Ct;)'-""*=? <*> where r = the radial distance of the point under consideration from the centerline of the jet. rt.s = the radial distance in the same cross-sectional from the axis to the point where the velocity is half the centerline velocity. (F -> 0.5 F,.) F, = the oenterline velocity in the same cross-sectional plane, feet per minute. F - the actual velocity at the point being considered, feet per minute. Experiments show that the conical angle for 0.5 V, and r,.% is approximately one-half of the total angle of divergence of a jet. The velocity profile curve for one-half of a straightflow turbulent jet (the other half being a symmetrical dupli cate) is shown in Pig. 3. For multiple-opening outlets, such as grilles, or perforated panels, the velocity profiles are simi lar, but tire angles of divergence are smaller. Radial Jets In the radial jet the cross-sectional area at any Htstanci* from the outlet varies as the square of this Hist/mr*, the * as for an axial jet Experiments have shown that the centerline velocity gradients and the cross-sectional velocity profiles are similar to those of Zone 3 of *TMl jets and that the angles of divergence are about the same. In ring Fig. 2, X/H should be used as abscissa instead of X/V~A- Jets from ceiling plaques have the same form as one-half of a free radial jet. The jet is wider and longer than a free jet, with the maximum velocity close to the wall. This is demon strated in Fig. 4 which also indicates that under the conditions shown the width of the slot between ceiling and plaque NOZZLE I lOOO \V -t.------------ SHAOCO AREAS REPRESENT kCASUREO VELOCITY PROPR.ES S/2* NOZZLE f M" --tr-- Rg. 4... Air Jets from a 14-in. Ceiling Plaque for Two Slot Widths with Some Rate of Row