Document RamQoaM07nqawXn2op3zJgkjV

674 CHAPTER 31 1954 Guide the basic relation of Equation 2, and a nomogram for calculating the pa rameters vxX_ Ao and V* V. from X Vx and Vo through Rta and Ca 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 Zones 1 and 2. Fx/F0 is plotted against X/flo and, for a range of aspect ratios, against X/\TA for the single value of K' = 7.0. Values of Vj/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 I: A grille has a core area 12 in. x 18.75 in., Hu -- 0.90, (',< -- 0.80, and K' - 5.0. Find V r (velocity through core area) when Vx is 50 fpm for throw of 50 feet (X = 50). Solution: A,, 12 X 18.75 144 1.56 sq ft Air Distribution For Vx = 50, X . 50 --= =----- = 40 vX 1.25 An = 1.56 X 0.80 X 0.90 = 1.123 X 50 = 47.2 vX ~ i.06 Vx K'.VTo 5-v/l.l23 = 0.106 Vo X 50 Vx Vx F,,(Cd 0.106 = 0.147 0.80 X 0.90 675 fpm- The quantity of air discharged is then, Q = V0AC = 340 X 1.56 = 530 cfm. Throw ------------ Equation 2a can be used to determine the throw X of ah outlet, if the dis charge volume and the center velocity are known. or, if Q Vx Vac XCdX Ru (4) Z -- v'Cd X Rt* y = K- Q Vx' ZVAo (4a) The maximum throw L is usually defined as the distance from the outlet face where the centerline velocity is 50 fpm. Therefore, for Fx = 50 fpm, LQ Zy/X, (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 logy* (5) r -- the radial distance of the point under consideration from the centerline of the jet.