Document Ra4JxG9Mp25kMQ3g3DOOyngEz

280 CHAPTER 20 1960 Guide be experimentally determined. Values of C< and R<* are required for determining V*, Da, and At 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 if'-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 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 ail four zones, centerline velocity ratios are plotted against distance from outlet in fig. 2.in accordance with the basic relation of Equation 2, and a nomogram for calculating the parameters X V, X V, . :A, and vt from vj and V9 Ht width ofjet at outlet or at vena contracts. Approximately the same values of iT':apply-as for Zone 3 'expansion from aria! outlets. In Zone l;-the ratio Va/Vis constant and equal to the ratio through R/, and Ct 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 Fig. 2 for Zones 1 and 2. V,/V is plotted against X/Ht and, for a range of aspect ratios, against Xfy/~A for the single value of K' -- 7.0. Values of V,/V ' for other values of K' may be obtained by direct proportion ing of VA'-to VV.O. `3 Air Distribution 281 Velocity Profiles of Jets In Zone 3 of both axial and radial jets, the velocity distri bution may be expressed by a single curve (Fig.' 3) in terms of dimensionless coordinates, and this same curve can be 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 b approxi mated by a simple equation using common logarithms The following Example l which is solved on Fig. 2 will illustrate the use of the. chart. Example 1: A grille has a core area 12 in- x 18.75in.; Rt * 0.90, C4 0.80, and K' *= 5.0. Find V, (velocity through core area) when Vm is 50 fpm for throw of 50 feet (X -- 50). 12 X 18.75 ----- ------- = 1.56 sq ft X 50 VT* 1.25 ' At *=* 1.56 X 0.80 X 0.90 = 1.123 X 50 Va. ' LOO 472 r. V, V, Vc - so, K'y/A, 5 '/nS n X so p. 0.106 Vt(C<R,J 0.80 X 0.90 v` ds - 340 fpm- . The,quantity of air discharged is then, Throw Q - VMc - 340 X 1.56 = 530 cfm. Equation 2a can be used to determine the throw X of an outlet, if tiie discharge volume and the center velocity are known. where r the radial distance of the point under consideration from the centerline of the jet. r#.i " the radial distance in the same cross-sectional plane from the axis to the point where the velocity is half the centerline velocity. (V * 0.5 V,.) V, = the centerline velocity in the same cross-sectional plane, feet per minute. V = the actual velocity at the point bciDg considered, feet per minute. Experiments show that the conical Angle for 0.5 V, and Tt.% is approximately one-half of the total angle of.divergence of a jet. The velocity profile curye for one-half of a straightflow turbulent jet (the other half being a symmetrical dupli cate) is shown in Fig. 3. For multiple-opening outlets, such as grilles, or perforated panels, the velocity profiles are simi lar, but the angles of divergence are' smaller. Radial Jets In the radial jet the cross-sectional area at any dbfoqpA from the outlet varies as the square of this distance, the as for an axial jet Experiments have shown that the centerline velocity gradients and the cross-sectional velocity profiles are Fpputo* to those of Zone 3 of axial jets and that the arigTpg of divergence are about the same. In using Fig. 2, X/H should be used as abscissa instead of Xfs/T. 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 b demon strated in Fig. 4 which also indicates that under the conditions shown tiie width of the slot between ceiling and plaque has V, VA. X Ct X Ru (4) z - Vcd X R,, Xa__Q_ v, ZVT. -(4a) - The maximum throw L is usually defined as the distant from the outlet face where the centerline velocity is 50 fpm. Therefore, for F, - 50 fpm, ,x- Q so zVTt (4b) LOUE i- *--____ SHADED AREAS REPRESENT MEASURED VELOCITY PROPR.ES S/2' NOZZLE 14'PLAQUE M= 262 CFM USO FPU Rg. 4.... Air Jets from a 14-iri. Ceiling Plaque for Two Slot. Widths with Same Rote of Roiw