Document ykNewQYM5ybJ2Bx6qjLz8oQVX

Heating Ventilating Air Conditioning Guide 1939 laws apply to installations comprising any type of fan, any given pin;n system and constant air density, and are as follows: 1. The air capacity varies directly as the fan speed. 2. The pressure (static, velocity, and total) varies as the square of the fan speed. 3. The power demand varies as the cube of the fan speed. 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? Speed = 400 X = 500 rpm (500\2 J = 1.56 in. Power = 4 X (^)* = 7.81 hp When the density of the air varies the following laws apply: 4. At constant speed and capacity the pressure and power vary directly as tbe density. ' Example 2. A certain fan delivers 12,000 cfm at 70 F and normal barometric pressure (density 0.07492 lb per cubic foot) at a static pressure of 1 in. of water when operating at 400 rpm, and requires 4 hp. If the air temperature is increased to 200 F (density 0.06015 lb) and the speed of the fan remains the same, what will be the static pressure and power? Static pressure = 1 X ^= 0.80 in. 0.07492 Power = 4 X 0.06015 0.07492 = 3.20 hp 5. At constant pressure the speed, capacity and power vary inversely as the square root of the density. 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 be the speed, capacity, and power? JSpeed = 400 X 0J.07492 = 446 rpm ,06015 Capacity = 12,000 X x J-TM.07492 \ o..l06015 = 13,392 cfm (measured at 200 F) V-sPower = 4 X ,07492 = 4.46 hp 0.06015 6. For a constant weight of air: .- (a) The speed, capacity, and pressure vary inversely as the density. (b) The horsepower varies inversely as the square of the density. 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? 0 074Q2 Speed = 400 X =498'rpm 0.07492 Capacity = 12,000 X Q Q6015 = 14,945 cfm (measured at 200 F) 550 Chapter 27. Fans , ^ 0.07492 , . Static pressure - 1 X 0 06015 l-25 m- / 0.07492 \2 Power = 4 X (006015) 20 p 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: ,, , cfm X total pressure in inches of water Air Horsepower1 = ----------------- ------------------------------- ,,. (1) When the static pressure is used in the computation it is assumed that this represents the useful pressure and that the velocity pressure is lost in the piping system and in the air which leaves the system. Since in most installations a higher velocity exists at the fan outlet than at the point of delivery into the atmosphere, some of the velocity pressure at the fen outlet may be utilized by conversion to static pressure within the system, but owing to the uncertainty of friction losses which occur at the places where changes in velocity take place, the amount of velocity pressure which is actually utilized is seldom known, and the static pressure alone may best represent the useful pressure. The efficiency based upon static pressure is known as the static efficiency and may be expressed as follows: ,, . _ . , cfm X static pressure in inches of water Static efficiency1 = ----------- 6356 X Horsepower input----------- (2) Different fans may develop the same capacity against the same static pressure and with the same power input, and therefore operate at the same static efficiency, while maintaining different outlet velocities. Where a high outlet velocity is desirable or can be utilized effectively, the static efficiency fails to be a satisfactory measurement of the performance. In many applications of propeller fans, air is circulated without encountering resistance and no static pressure is developed. The static efficiency is zero and its calculation is meaningless. Because of such situations where the static efficiency fails to indicate the true performance, many engineers prefer to base the calculation of efficiency upon the total or dynamic pressure. This efficiency is variously known as the total, dynamic, or mechanical efficiency, and may be expressed as follows: M,,ec,han.ica,l or _To.ta,l e,,ffic.iency,1 = c--f-m----X--6--t3-o-5-t6-a--l-X-p--r-eH--so-s-r-us-r-ee--p-io-n-w--ie-n-rc--hi:-ne--ps--uo-tf--w--a--t-e--r (3) CHARACTERISTIC CURVES In the operation of a fan at a fixed speed the static and total efficiencies vary with any change in the .resistance which is imposed. With different designs the peak of efficiency occurs when the fans deliver different per- *See Standard Test Code for Centrifugal and Axial Fans, Third Edition of 1938.