Document 7Omd0m2YL8rLg7RwaJep91pkE

678 CHAPTER 32 1950 Guide : . 31 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. 4. Variation in Air Density: Constant Volume--Constant System Fixed Fan Size--Constant Fan Speed () Q: Constant. () 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) Q: Varies inversely as square root of density. (bj P: Constant. (e) RPM: Varies inversely as square root of density. (d) Power: Varies inversely as'square root of density. ' 6. Variation in Air Density: Constant Weight of Air--Constant System ' Fixed Fan Size---Variable Fan Speed ` () Q- ; Varies inversely as density.: () P: ' Varies inversely as densityl (c),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 cfmare desired, what will be the speed, static pressure, and power? 15,000 " ' : Speed = 400 X = 500 rpm rsoo y - 1-56 in. Static pressure: = 1 X (400 (5w00\)* -7Sl hp r. Example 2. 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 ------ = 0.80 in. 0.075 U.U6UZ Power 4X -- - =* 3.20 hp 0.075 -' - Example S. If the speed of the fan of Example 2 is increased so as. to produce, a static pressure of 1 in. of water at the 200 F'temperature, what will beTthe speed, capacity, and power? Fans- 0 /``l 679 / Speed- 400 X i/2TM! = 446 rpm ' y 0.0602 .' ! / Capacity = 12,000.X 4 / --^- = 13,392 cfm (measured at 200 F) y 0.0602 . Power = 4X4/'^0.075 y o0..0o602 . 4.46. hp ; Example. 4- 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?- Speed = 400 X = 498 rpm . 0.075 , Capacity = 12,000 X = 14,945 cfm (measured at 200 F) : 0.075 Static pressure 1 X -------- 1.25 in. 0.0602 Power 6.20 hp The fan laws stated may be combined to give other oyerall values. One useful combination is the product of laws, 1 and 3 which gives the following relations:' Capacity varies as the ratio of size 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. i . -. Example 5. Assuming that afanwitha36in. diameter blast wheel, will deliver 12,000 cfm at 70 F at 1 in. static 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 in. wheel at the same speed? . Capacity = / 45V X(4^00 | X 12,000 = 23,400 cfm ' : ' . - Static.Pressure = /45V I--I X (sy*1 = 1.56 in. (45V /400V 36/ X \400/ X 4 = 12 2 hp'; --- 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 desired range of volumes. Figs. 2, 3 and 4 illustrate performance (some times called characteristic) curves of various.'types of fans. . .' -i Centrifugal fans` 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-