Fan Law

The equations have been expressed as proportionals however, they can be used by simply ratioing an old to a new value. To add credibility to fan law adaptation, recall the flow coefficient, Equation 5.19, The term Qj/N is used which shows a direct proportion between volume Qj and speed N. Equation 5.12 indicates the head, Hp, to be a function of the tip speed, squared. The tip speed is, in turn, a direct function of speed making head proportional to speed. Finally, the power, Wp, is a function of head multiplied by flow, from which the deduction of power, proper tional to the speed cubed, may be made. 

With the introduction of the new instruments, speed is basically taken for granted. It is a very important parameter for reciprocating compressors, however, because speed is one of the factors in generating displaced volume. For the axial and the centrifugal compressor, speed offers a multiple influence. In the fan laws stated in Chapter 5, speed was the common parameter in both capacity and head. In fact, since head is proportional to speed squared, it becomes quite important that the speed be accurate. 

One of the most important parameters to measure is speed, yet it is often overlooked. The fan law in Chapter 5 states that for a centrifugal compressor, the head is proportional to speed squared. For an axial, the sensitivity to speed is as great or greater. Capacity is directly proportional to speed on all compressors, both the positive displacement and the... 

Large towers often have the motor mounted horizontally connected to a right angle gear drive. The motor can be closely coupled- in the air stream- or connected with a drive shaft with the motor outside the air stream. Maintenance personnel typically prefer the external TEFC motor- when available- for its easier access. Cooling tower fans- like all fans- operate in accordance with the fan laws one of which states that the horsepower required to drive a fan increases to the cube of fan speed. 

The appropriate drive ratio is selected for each motor so that it is fully loaded when in operation- a distinct advantage over two speed, variable torque motors where the available horsepower is proportional to the square of fan speed while the required fan horsepower varies as to the cube of fan speed (from the fan law). As an example, a fan motor that can produce 40 hp at high speed can produce 10 hp at low speed while a fan that requires 40 hp at high speed only requires 5 hp at half speed. As a result, 1800/900 rpm motors are always 100 % oversized at low speed. And, since the motor usually operates at low speed most of the time, the... 

Fan laws The equations that describe the relationship between fan flow rate, pressure, density, power, size, rotation speed, and noise levels. 

No. stages from (6) must develop head from (5) or determine average head/stage = Hp/no. stages = head/stage, ft-lb/lb or ft, per stage From the Fan Laws, H N. ... 

Fan laws apply to blowers, exhausters, centrifugal, and axial flow fans. The relations are satisfactory for engineering... 

Examination of Table 12-16 shows that Fan Law 1, for example, can be written for geometrically similar fans ... 

Eor all the fan laws Tqpa = and (point of ratinglg = (point of rating) ... 

In considering Ian performance, it is incorrect to calculate a change for one characteristic and ignore the others in the Fan Law Group, because it takes all three characteristics to properly define the operational point of the fan. 

Note that this gives conditions of the same point of rating for the two fans, and this is the only manner in which fan laws apply to two different units. 

Note that the wheel diameter of 20.6 in. is probably not found in manufacturers standard units. Therefore, select a standard wheel diameter that is closest to the 20.6 in. and then recalculate by Fan Law 1 the change of that wheel s performance to the desired or necessary conditions just calculated. This can be accomplished by changing speed. Most manufacturers have a standard wheel of 20 in. with the next size being 22.25 in. 

The drive losses are generally based on the use of the V-helt drives, because the use of these types of drives is quite popular see losses from Figure 12-139. The mechanical losses in the drive train, must be considered separately, because they cannot be predicted by Fan Laws. 

The multirating tables of the fan manufacturers are convenient for selecting any of the many types of fans. Figure 12-147 is one portion of such a table. Usually cfm values can be found close enough to requirements to be acceptable. Direct interpolation in the table for volume, rpm, and bhp is acceptable for narrow ranges otherwise the Fan Laws must be used. 

Using actual cfm at intake conditions to fan and equivalent static pressure (2), read manufecturers rating tables for bhp and rpm. Note that if exact cfm or pressure value is not listed in tables, it may be reached by (a) interpolation as previously described for approximation or (b) by using fan laws to correct one set of table values. 

Performance at 1,400 ft elevation and 400°F inlet air temperature will be as follows (approximately, this can be improved by applying the Fan Laws to data read from table)... 

Because manufecturers tables are based on standard 0.075 Ib/fd air, this density difference must be recognized. According to Fan Law No. 6, if the rpm (speed) and cfm (capacity) are constant, the pressure and hp vary direcdy as the reladve density. 

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