Document N2Oo3VM2K7gmwkKz9GQ1kKZLD

760 CHAPTER 33 1955 Guide 3; Variation in Fan Size: At Constant RPM--Constant Air Density Constant Fan Proportions--Fixed Point of Rating (d) Q: Varies as cube of wheel diameter. (6) Pi 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 (o) 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 () Q: Varies inversely as square root of density. () 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: Constant Weight of Air--Constant System Fixed Fan Size--Variable Fan Speed () Q: Varies inversely as density. () P: Varies inversely as density. (c) RPM: Varies inversely as density. (id) 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 Static pressure lx(/50w0V =1'56i Power = 4 = 7.81 hp Example : 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 0.0602 Power = 4 X 0.075 3.20 hp Example S: If the speed of the fan of Example S 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 761 / 0.075 Speed = 400 X V 0.0602 = 446 rpm VCapacity = 12,000 X f 0.075 = 13.392 cfm (measured at 200 F) 0.0602 Power = 4 X 0.075 .=: 4.46 hp 0.0602 Example 4If the speed of the fan of the previous examples is increased so as te deliver the same weight of air at 200 F as at 7.0 F, what will be the speed, capacity, static pressure, and power? ,... 0.075 Speed = 400 X = 498 rpm . ... .. ................... 0.075 -; Capacity = 12,000 X = 14,945 cfm (measured at 200 F) ,,. 0.075 Static pressure = 1 X-----r-- = 1.25 in. 0.0602 _POWer = 4. X{[o0.0^752Vj=6-20hp The fan laws stated may be combined to give other overall 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. inSvf?7f^C ^ssumin? that a fan with a 36 in. diameter blast wheel will deliver A^jUuO cfm at 70 F at 1 in. static pressure, requiring 4.0 brake hp when operating at 4Uu rpm, what is the capacity, pressure and horsepower of a homologous fan having a 45 in. wheel at- the same speed? Capacity = /45\* ( -J X /f4--00\1 X 12,000 = 23,400 cfm Static pressure = X X 1 = 1-56 in. (g)` gg)*Horsepower = X X 4= 12.2 hp FAN PERFORMANCE CURVES Fan performance curves are the graphical presentation (for constant ?peed and air density) of the relation of total pressure, static pressure, power H'Pdt, and mechanical and static efficiency, to actual volume, for the de sired range of volumes. Figs. 2, 3 and 4 illustrate performance (somemies called characteristic) curves of various types of fans. Centrifugal fans6 may be roughly divided into three classes: (1) those with the tip of the blades curved forward in the direction of rotation; (2) nose with straight radial blades; and (3) those with the tip of the blades in-