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708 CHAPTER 32 t -. 3. Variation in Fan Size: .. At Constant RPM--Constant Air Density Constant Fan Proportions--Fixed Point of Rating () Q: Varies as cube of wheel diameter. () P: Varies as square of wheel diameter. .(c). Tip Speed: Varies as wheel diameter. . (d) Power: Varies as fifth power of diameter. 1952 Guide A.'Variation in Air Density: Constant Volume--Constant System Fixed Fan Size--Constant Fan Speed (a) Q: Constant. (6) P: Varies as density. (c) Power: Varies as density. 5. Variation in Air Density: . Constant Pressure--Constant System ' ' Fixed Fan Size--Variable Fan Speed -'(a) QVaries'inversely as squareroot of density: (b) P: Constant. ., (c) RPM: Varies inversely as square root of density : (d) Power: Varies inversely as square root of density. ' ' ', ': '; ... 6. Variation in Air Density: 1 Constant Weight of Air--Constant System Fixed Fan Size--Variable Fan Speed .. ,(o) Q:. Varies inversely as density; (6) P: Varies inversely as density. '()' RPM: Varies inversely as density. ' (d) Power: Varies inversely as square Of density.' ` ; ; < ' - Examples 1 to 4 illustrate the application of the preceding fan laws. Example 1: A certain fan delivers 12,000 cfm at a static pressure of 1 in. of water when operating at a speed of 400 rpm and requires an input of 4 hp. If in the same installation 15,000 cfm are desired, what will be the speed, static pressure, and power? 15,000 Speed 400 X ,, = 500 rpm 12,000 /500V_ Static pressure = 1 K 1.56 in. \400/ " /500Y '' pwer = 4 X j = 751 hp Example B: A certain fan delivers 12,000 cfm at 70 F and normal barometric pres sure (density 0.075 lb per cubic foot) at a static pressure of 1 in. of water when operat ing at 400 rpm, and requires 4 hp. If the air temperature is increased to 200 F (den sity 0.0602 lb) and the speed of the fan remains the same, what will be the static pressure and power? , 0.0602 ,, ^. Static pressure 1 X 0,,.075 = 0.80 in. 0.0602 Power = 4 X = 3.20 hp Example S: If the speed of the fan of Example B is increased so as to produce a static pressure of 1 in. of water at the 200 F temperature, what will be the speed, capacity, and power? Fans:- 709 - Speed = 400 X a/ = 446 rpm ' 0:0602; - . - " Capacity .= 12,000 X 0:075 =' 13,392 cfm (measured at 200 F) 0.0602 ' Power = 4 X ji /-5^5. = 4.46 hp 0.0602 , Example If the speed of the fan of the previous examples is increased so as to deliver the same weight of air at 200.F as at 70 F, what will be the.speed, capacity, static pressure, and power? ;; . 0.075 Speed = 400 X 0.0602 = 498 rpm 0.075 . Capacity = 12,000 X.^^^ = 14,945cfm (measured at 200 F) ; h ,,. . , 0.075 : Static pressure = 1 X^^ = 1-25 in........ : /0.075 V Power = 4 X ( r-r--: ) =650hp . V90602/ ... : ,. -r,' . . The fan laws stated may be combined to give other Overall values: One useful combination is the product of laws ! and 3'wluch gives the following relations: ' ' .. Capacity varies as the ratio of Bize cubed, times the ratio of the rpm. ' ' Pressure varies as the ratio of size squared, times the ratio of the rpm squared. Horsepower varies as the ratio of the size to fifth power, times the ratio of the rpm cubed. . Example 5: Assuming-that a fan with a 36 in. diameter blast wheel-will deliver 12,000 cfm at' 70 F at 1 in. static1 pressure, requiring 4.0 brake hp when operating at 400 rpm, what is the capacity, pressure and horsepower of a homologous fan having a 45 m. wheel at the same speed? . (I)'*Capacity /400\ \m) x 12,000 = 23,400 cfm Static pressure = /45\* (- ) X (/4--00\1* x1 = 156 in. (45\S &) xUJx4/4OOV 1 = l-22hp FAN PERFORMANCE CURVES Fan performance curves are the graphical, presentation (for constant speed and air density) of the relation of total pressure, static pressure, power input, and mechanical and static, efficiency, to actual volume, for the .de sired range_.of'volumes. Figs. 2, 3 and 4 illustrate performance (some times called ' characteristic) curves of various types of fans. Centrifugol fans6 may be roughly divided into three classes: (1) those with the.tip of the blades curved forward in the direction of rotation;, (2) those with straight radial blades; and (3) those with the tip of the blades in-