Document Ke84b5ppvLdE5NeLMVQKrYnx

766 CHAPTER 30 ; 1958 Guide the basic relation of Equation 2, and a nomogram for calculating the pa rameters * . F, X ... -- and -- from --= and Ao f. Va, through Ru and Cd is given in the same illustration. Fx -- f0 Zones 1 and 2. Vx/Vii is plotted against X/Ho and, for a range of aspect ratios, against X/yfA for the single'value of K' = 7.0. Values of VjVo for other values of K' may be obtained by direct proportioning of y/K' 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., R(, = 0.90, Cd = 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 sq ft 144 Air Distribution 767 For Fx = 50, 50 = 40 VAi 125 Ao = 1.56 X 0.80 X 0.90 1.123 X 50 = 47.2 VM 1.06 K _ K'VA, 5\/l.l23 0.106 Vo X 50 F, Fx 0.106 0.147 F,, Fo(CdR<,). 0.80 X 0.90 v'= ofb = 340 fpm; The quantity of air discharged is then,- ' Q = FoA. = 340 X 1.56 = 530 cfm. Throw 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 0 X= Fx Vac X Cd X Bf. (4) Z = VCd X B,. X-- Q " Fx Zy/Ac (4a) The maximum throw L is usually defined as the distance from the outlet face where the centerline velocity is 50 fpm. Therefore, for Vx = 50 fpm, K' Q (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 erroriunction or probability curve which is approximated by a simple equation using common logarithms fey- Fx 3.3 log where (5) r - the radial distance of the point under consideration from the centerline of the jet.