Document rBaw7rqm09GK4jEjjGdxoKZbV

758 CHAPTER 30 1957 Guide the basic relation of Equation 2, and a nomogram for calculating the pa rameters X Aq and v* v from X- VaI and V, Vo through R)o and C& 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. 3 for Fig. 3. Chart fob Determining Centerline Velocities op Axial and Radial Jets Zones l and 2. Fx/Fo is plotted against X/H0 and, for a range of aspect ratios, against X/vGi for the single value of K' -- 7.0. Values of Vx/V for other values of K' may be obtained by direct proportioning of VK' to V7X). 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, C'd = 0.80, and K' =* 5.0. Find V. (velocity through core area) whenV. is 50 fpm for throw of 50 feet (X = 50). Solution: Ac 12 X 18.75 144 1.56 sq ft Air Distribution For V* = 50, X 50 vr, _ i.25 "40 Ao = 1.56 X 0.80 X 0.90 = 1.123 * *U47.2 VAo 106 V. K'VTo 5\/l.l23 OA06 X 50 V, V, 0.106 0.147 Vc Vo(Cd RtJ 0.80 X 0.90 = o"S^ = 340 fpm- 759 The quantity of air discharged is then, Q = V.A. = 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, T VA. X Cd X Ric (4) z " Vcd X Ru X EQ V. ` 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, EL. = X = 50 Q zVTc (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 errorfunction or probability curve which is approximated by a simple equation using common logarithms where 3 3 log (5) r = the radial distance of the point under consideration from the centerline of the jet.