Document KJDLODgbr2v9pRDV9w53eDmkQ

622 CHAPTER 30 1950. Guide Throw : r\,: Equations forthe throw of straight flow side wall' outlets have beende- - veloped on the basis of'the momentum theory. Equation'4 states the throw in terms of the area of the outlet and the primary air volume :* 1 where L = 0.82 -=Ci= vili. ; (4) L = throw, feet. .! Ai = effective outlet area, in square inches = (gross measured area) X (percentage of free area/100) X (discharge coefficient). The discharge coefficient is approximately 0.8. i Equation 4 has been developed under the assumption that the tempera ture of the supply, air is the same as the temperature of-the room air. It applies only to straight flow outlets with aspect ratios less than 16. Equation 5 for the performance; of straight flow outlets evolved from research* allows the calculation of the .maximum residual velocity at any distance perpendicular to the outlet face.- It applies for aspect ratios up to 50. V, ViVt, = ,, Ci x xVa\ (5) where V, ~ maximum'residual velocity in air stream, i.e.,.the highest maintained velocity at the given cross section in the room, feet per minute.; Vi average initial velocity across outlet, feet per minute. K = constant of proportionality. i A, = effective outlet area in square feet *= (gross measured area) X (percentage of free area/100) X (discharge'coefficient). -- X = normal distance from outlet face, feet. , Equation 5 together with Equation !6 (which reduces to Equation 7 if the jet angle is 20 deg) for'the entrainment ratio, 0.785 K Entrainment Ratio = BXVTt + 2 X tan e\ -1 2/ 1 (8) where R = ratio of maximum residual velocity to average residual velocity, 8 = jet angle or spread angle in degrees. 0.785 K . Entrainment Ratio (20 deg jet angle) RX^/Ai J- + 0.35 X) - 1 .0.785. (7) has.been used to develop charts* which provide illie/graphiiial 'soliitibpdf problems involving the determination of thb throwbf air 'from'dots and'jets, the Iresidual. velocity, and the size of opemhgij^See' ilgs;;2`and 3,)V' The charts apply only to qtr discharging into room'air of sanrn feTnpwature as the They can be used to determine the throw of air and ehtraihment Alt`Distribution ' . 623 ratio8 upto 40 :l Vrith initial velocities ofTOOO to 6000 fpm, andwithresidual velocities of . 100 to 1000 fpm. The charts furthermore are for use:with sharp-edged orifices of'slots, and include the caefficient of; discharge:, Ifair is discharged from an orifice with a well-rounded entrance or from a lehjgth . of straight.duct, the coefficient of discharge is unity and.the actual area of ' the opening is the effective area. For such rectangular openings the' effective diameter is the diameter of a circle with an area equal to the actual area of the rectangle. The following examples will illustrate the use of the charts: . ' . ' Example!: Air is delivered to a cooler through independent slots each 24.uk x 2 in. 4>--------------- ;--1---------------- ^ . \------------------------------ :--I---------1--------1----I-- MGO ` ISO 200 2SO 300 400 500 600 700800.. 1,000 .MAXIMUM ' RESIDUAL VELOCITY- FPM . Fig.: 2. Relation Between Initial Velocity, Residual Velocity; ......Entrainment1 Ratio and Thbow op Aib prom Jetb and Slots' ; ?: ; : ; ; with an initial; velocity of 2000 fpm. Determine the maximum residual velocity and the entrainment ratio at a distance of 15 ft from the slot.' i From Fig. 3 the effective diameter = 6.2 in. = 0.52:ft.: The number of effective diameters in 15 ft = 15/0152 = 28:8. ' .......... From Fig. 2 at 2000 ft initial velocity read entrainment ratio = 6.6 and maximum residual velocity = 390 fpm. From tests it has been shown that the average residual velocity may be taken as 1 of the maxtmuVn or 130 fpm in this'case: 1 - Example t: Using the data from Example l determine the distance at which the maximum residual velocity will be 150 fpm. From Fig. 2 atFi= 200b and Vr = 150, the number of effective diameters is read directly as 73 and the throw of the air is therefore 73 x 0.52 = 38 ft. .. _ . , .. , " .., Example 3: rAir issues from a round orifice plate with an initial average velocity of 4000 fpm. It is to have a maximum residual velocity of 400 fpm at a distance of 30 ft from the opening. Calculate the size of the opening required and the entrainment ratio. '"v_i s>On'Fig. 2 at'the intersectionof the curve of 4000 fpm, the entrainment'ratio is read directlyaailS and the effective diametersof throw => 55.- -.ii.-p