Document 4aganajjzZrdd6xpE9XdQ917a

563 CHAPTER 32 1946' Guide ment due to the space, power, or speed limitations. The following laws in which Q = air volume and P = static, velocity or total pressure, apply to all types of fans: 1. Variation in Fan Speed: Constant Air Density--Constant System () Q: () P: (c) Power: Varies as fan speed. Varies as square of fan speed; Varies as cube of fan speed. 2. Variation in Fan Size: Constant Tip Speed--Constant Air Density Constant Fan Proportions--Fixed Point of Rating (a) Q: (b) P: (c) RPM: . (d) Power: Varies as square of wheel diameter. Remains constant. Varies inversely as wheel diameter. Varies as square of wheel diameter. 3. Variation in Fan Size: At Constant RPM--Constant Air Density Constant Fan Proportions--Fixed Point of Rating (a) Qx Varies as cube of wheel diameter. (b) P: Varies as square of wheel diameter, (e) Tip Speed: Variesas square of 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 . fa) Q: (6) P: . (c) RPM: (<Q Power: Varies inversely as square root pf density. Constant. Varies inversely as square root of density. 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: () Pi fc) RPM: \d) Power: Varies inversely as density. Varies inversely as density. Varies inversely as density. Varies inversely as square of density; Examples 1 to 4 illustrate the application of the preceding fan laws. Example l. 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? Speed = 400 X = 500 rpm (SOON 2 400 ) = Power = 4X (p)3 = 7.81 hp.' `n* ' Example 2. ,A certain fan delivers 12,000 cfm at 70 F and normal barometric pressure (density 0.075 lb per cubic foot) at a static pressure of 1 in. of water when operating at Fans 569 400 rpm, and requires 4 hp. . If the air. temperature is iricreased to 200 F (density 0.0602 lb) and the speed of the fan remains the same, what will'be the static pressure and power? eS.tatic pressure %= 1 .^X 0.0602 q = A0.8on0 tn. . ,. Power- 4 X = 3.20 hp Example 3. 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 be the speeds capacity, and power? y Speed = 400 X 0.075 0.0602. 446 rpm Capacity = 12,000 X 0.075 = 13,392 cfm (measured at 200 F) 0.0602 V v:Power = 4 0.075 4.46 hp. 0.0602 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 q ~ rPm Capacity = 12,000 X U.Uou2 ** 14,945 cfm (measured at 200 F) Static pressure = 1 X 0.075 0:0602 1.25 in. Power = 4X (^|)2 = 6.20 hp. Laws of Homologous Fans The laws applying to different sizes of homologous fans are as follows: 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. ' Example 5. Assuming that a fan with a 36 in. 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 = (||)3 X X 12,000 = 23,400 cfm . Static Pressure -- X X 1 -- 1.56 in. Horsepower = (||)6 X (g3 X 4 = 12.2 hp ` FAN EFFICIENCY The efficiency of a fan. may be defined as the ratio of the horsepower.' output to the horsepower input. . . The horsepower output is expressed by the formula: ' .