Document X74Gb4QeO5YGvKqVobbo2L3zw

546 CHAPTER 29 1965 Guide And Data Book outlet, if the discharge volume and the_ center' velocity are known. v-.jK'. -Q " V.'-y/A, XCi X Rf. (7) or, if .- Z = VCt X Rf. V Q_ X V.Zs/A. (8) The maximum throw-L is usually defined as the distance from the outlet face where-the centerline velocity is 50 fpm. Therefore, for Va--50 fpm. L _K[ - Q_ "_50 Zy/A* (9) Any other terminal centerlincvelocity e.g., 100, 150, 200, etc., fpmcouIdbe'inserted-inEquatioh'8fbr<V..-c. .-i" Velocity Profiles of Jets . i- In Zone 3 of both a*ial and radial jets, the velocity,distrir bution may be expressed by a single curve (Fig. 9) in terms pf dimensionless coordinates, and this same curve can be used as a'good approximatioh'for adjacent portions of Zones 2 and 4/Experiments have`shown, that temperature and " density differences have but a smaU effect on 'cross-sectional velocity profiled' ' ' 1 Space AIr Distribution 547 Velocity distribution in- Zone 3 can be expressed by. the Gauss error-function or probability ,curve which is approxi mated by a simple equation using common logarithms . (tt.)'" 33l08v (,0) when r -- the radial distance of the point under consideration from the centerline of the jet. ' r " the radial distance in the same croon sectional plane from the to the point where the velocity is half the centerline velocity. (V -0.5 7,)'. V * the centerline 'velocity- in the same cross-sectional plane, feet per minute. V m the actual velocity at the point being considered, feet pa minute. , Experiments show that the conical angle for 0.5 F, and r,, is approximately one-half of the total'angle of divergence of a jet: The velocity profile curve for one-half-of a straight- flow turbulent jet (the other half being a symmetrical dupli cate) is shown in Fig. 9. For multiple-opening outlets,' such as grilles, or perforated panels, the velocity profiles are simi lar, but the angles of divergence are smaller. ` Entrainment Ratios' Equations for the entrainment of circular jets and of jets from long slots have been mathematically derived.14 They.are: For third zone expansion of circular jets, Ql JL Q, " Kr VA, M) By substituting from Equation 4. ' 0 V; (12) For a long'slot . Q, / 2 nt 0 " * K''V H. (13) And by substituting from Equation 2 at the beginning of Zone 3 .i ft-VT V, Q v. (14) tokere Qt -- total volume flow rate at distance X from face of out let, cubic feet per minute. Q -- discharge from outlet, cubic feet per minute. X -- distance from face of outlet, feet K' proportionality constant. -- - ~ A* TM effective area of stream at discharge from an- open- end duct or at a contracted section, square feet. H% -- width of slot, feet. w01 a-king dot. Comparing Equations 11-and-13 shows that the long slot should have a greater rate of induction. It should ala* be noted thatithe entrainment ratio at a given-distance is less with a large./?' than with a small K'. Effect, pf Walls and Ceilings . .. - Jets discharging parallelto a wall with one edge'of the out let coinciding with the wall, take the form of one-half of an axial jet discharging from-an outlet twice as large, similar to radial, jets horn ceiling plaques. Entrainment takes place practically' only along the surface of a half cone and'the mnvimiim velocity remains close to the walL7 Values of K and K' are approximately those for a free jet multiplied by V2, that is to say, the normal maximum of 7.0 for K' for free jets becomes 9.9 for a similar jet adjacent to, and discharged parallel to, a wall, and X/V2A, should be used in place of Xv'Ao in Fig. 8. When a jet is discharged parallel to, but at some distance from a wall, its expansion in the direction of the wall is re duced and entrained air must be obtained by recirculation from -the jet itself instead of from ambient air.**u The jet gypanda' normally to within a short distance from the wall, which nearer to the outlet only affects velocity distiibution in the outer shell of the jet, but further on also affects centerline velocities. This happens at some distance horn a plane where the jet outline becomes parallel to the wall, and where the'jet enters its fourth or terminal zone. Few engineering data are available on this important phase of jet expansion.* Air Velocities in Two Parallel Ventilating Jets1' In each air jet of twin parallel air jets, there is a maximum velocity core and the jet behaves independently until the point is reached at which the two interfere. The point- of interference and its distance out from the outlets varies with the distance between the outlets: FYom the outlets to the point of interference the maximum velocity, as for a single jet, will be on the centerline of each jet. Then the velocity on a line midway between and parallel Entrainment ratios are important from the standpoint of the total air movement at a given distance from an outlet. It jrill be noted that with a given outlet, the entrainment ratio is proportional to the distance X (Equation 11)' or pro portional to the square root of the distance X (Equation 13) from the outlet. FWin.Equations 12 and 14, it will be noted that for a fixed centerline velocity, the entrainment ratio is directly proportional to. the outlet velocity. They also show that at the same centerline ahd outlet velocity; a circular jet will have a greater entrainment and total air movement than Stock 14 in.* Cm. Outlet* 14*9 fa. , Stock Vdodfy 500 fpa A. Rounded Omrt and Rounded Sort. . a Rounded Throat and Bade and 2 Spfrfter*.' C Square Throat and Sock and 6 Garde-Vane*. Fig. 10 .... Outlet Velocity and Air Direction Diagrams for - Stack Heads with Expanding Outlets