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Fan Laws

Formulae for Fan Applications
Mechanical Efficiency, ME = (CFM x TP) / (6356 x BHP) x 100
Static Efficiency, SE = (CFM x SP) / (6356 x BHP) x 100
Total Pressure, TP = SP + VP
Velocity, V = CFM / Area in sq. ft.
Velocity Pressure, VP = (V / 1096.7)2 x density in lbs/ft3
If the density is 0.075 lbs/ft3, the equation for VP reduces to:- = (V / 4005)2
System Curve Equation.  The following formula is used to find other points on the system line where SP1 and CFM1 are known. Most systems follow this relationship, but not all. = SP2 = SP1 x (CFM2 / CFM1)2

How To Use The Fan Laws For Performance Changes

There are two reasons why a fan's performance may need to be changed.  Here are two examples:-

bulletThe system or area requires additional airflow (CFM).
bulletThe actual system static pressure (SP) is different from the design value.

When these situations occur, it is important to understand how they can affect the fan's performance.

The affect on the fan's performance can be shown by using the Fan Laws shown below.

Fan Law Equations
CFM2 = (RPM2 / RPM1) x CFM1
SP2 = (RPM2 / RPM1)2 x SP1
BHP2 = (RPM2 / RPM1)3 x BHP1
Subscript 1 describes the existing conditions.   Subscript 2 describes the new conditions.

Example

  1. Assume a customer requires a fan to operate at 33,120 CFM at 2.5" SP at standard air density.  Per the specification, a BC backward inclined fan is required.
  2. Based on the above information, from Twin City Fan & Blower's Bulletin 300, a 490 BC SWSI, CL. II fan is selected.  This fan will operate at 620 RPM and 20.01 BHP to meet the required performance.
  3. After installing the fan, the Plant Manager wants to increase the airflow into the plant to 41,500 CFM.  The fan laws are used to determine how this fan will be affected by the new system requirements.
  4. The known values are:-
    bulletCFM1 - 33,120 CFM
    bulletCFM2 - 41,500 CFM
    bulletBHP1 - 20.01 BHP
    bulletSP1 - 2.5" SP
    bulletRPM1 - 620 RPM
  5. The unknown values are:-
    bulletRPM2
    bulletSP2
    bulletBHP2
  6. Using the Fan Law equations, the unknown values (RPM2, SP2 & BHP2) are calculated as follows:-
RPM2 = 41,500 / 33,120 x 620 = 777 RPM
SP2 = (777 / 620)2 x 2.5" = 3.93" SP
BHP2 = (777 / 620)3 x 20.01 = 39.39 BHP
  1. What does this information tell us?
    bulletIn order to use the same fan for an airflow of 41,500 CFM, the RPM needs to be increased to 777 RPM.
    bulletThe new performance increases the fan's horsepower requirement from 25 HP to 50 HP.  If the fan is sped up to 777 RPM, the motor must be re-sized.

IMPORTANT NOTE.    The new RPM should be checked to make sure it does not exceed the maximum allowable RPM for the fan that is installed.   If this information is not provided in the catalogue or you would like the application reviewed, please contact EFI Systems Group.

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Last modified: July 21, 2003