This key shows the symbols used in the following formulae:

V = Volume in cubic feet per minute (CFM)
P = Pressure in pounds per square inch (PSI) or inches of mercury gage (inches Hg)
N = Speed in revolutions per minute (RPM)
D = Density in pounds per cubic foot (lbs./cu. ft.)
SG = Specific gravity (ratio of density of gas to density of air)
H = Height of air or gas column (ft.)

"Standard Air" is air at 68 degrees F. (absolute temperature 528 degrees F.) and 29.92" Hg. (barometric pressure at sea level).  The density of such air is 0.075 lbs./cu. ft. and the specific volume is 13.33 cu. ft./lb.  Specific Volume = 1/Density.  The specific gravity is 1.0.

1 -   Variation of Blower Speed

As the speed of a centrifugal blower changes, it will influence the volume, pressure, and horsepower input.

1.1  The volume changes in direct ratio to the speed

Suppose a blower is operating at 4000 rpm and delivering 1000 cfm.  If the speed is reduced to 3000 cfm, what is the new volume?

V1 = Original Volume, V2 = New Volume, N1 = Original Speed, and N2 = New Speed.

V2 = V1 x N2/N1 = 1000 x 3000/4000 = 750 cfm.

1.2  The pressure changes as the square of the speed ratio

Suppose a blower is operating at a speed of 4000 rpm and delivering air at 5.0 pounds of pressure.  If the speed is reduced to 3000 rpm, what is the new pressure?

P1 = Original Pressure, P2 = New Pressure, N1 = Original Speed, and N2 = New Speed.

P2 = P1 x (N2/N1)² = 5 x (3000/4000)² = 2.81 pounds.

1.3  The horsepower changes as the cube of the speed ratio

Suppose a blower is operating at a speed of 4000 rpm and requiring 50 horsepower.  If the speed is reduced to 3000 rpm, what is the new required horsepower?

HP1 = Original Horsepower, HP2 = New Horsepower, N1 = Original Speed, and N2 = New Speed.

HP2 = HP1 x (N2/N1)³ = 50 x (3000/4000)³ = 21.1 horsepower.

2 -   Relation of Inlet Density to Outlet Pressure

The outlet pressure of a blower depends on the condition of the air or gas at the inlet.  The inlet condition is influenced by:

a - Specific Gravity
b - Altitude
c - Inlet Air Temperature

2.1  Pressure varies in direct proportion to the density

Suppose a 3 lb. (standard air) blower is to be used to handle gas having a specific gravity of 0.5.  What pressure does the blower create when handling the gas?

Pa = Air Pressure, Pg = Gas Pressure, and SG = Specific Gravity

Pg = Pa x SG = 3 x .5 = 1.5 pounds.

Suppose we are required to handle a gas having a specific gravity of 0.5 at 1.5 lb. pressure.  We can determine the standard air pressure blower as follows:

Pa = Pg/SG = 1.5/.5 = 3 pounds.

2.2  The air density varies in inverse proportion to the absolute temperature (absolute temperature
       is obtained by adding 460 degrees F. to the Fahrenheit reading).

Suppose a blower is to handle 200 degree F. air at 3 PSI pressure.  What pressure (standard air) blower is required?

P1 = Pressure Hot Air, P2 = Pressure Standard Air, AT1 = Absolute Temperature Hot Air, and AT2 = Absolute Temperature Standard Air.

P2 = P1 x AT1/AT2 = 3 x 660/528 = 3.75 pounds

Suppose a blower is capable of delivering 3 PSI pressure with standard air.  What pressure will it develop handling 200 degree F. air?

P1 = P2 x AT2/AT1 = 3 x 528/660 = 2.4 pounds.

3 -   Relation of Inlet Density to Horsepower

The horsepower varies approximately in direct proportion to the specific gravity (ratio of density of gas to density of air).

Suppose a standard air blower requires a 10 HP motor.  What horsepower is required when this blower is to handle a gas whose specific gravity is 0.5?

HP = 10 x .05 = 5 Horsepower

4 -   Relation of Density to Inlet Volume

When a blower is to operate at a high altitude, it is frequently specified that the blower be capable of handling a given volume of "standard air".  It is then necessary to determine the equivalent volume of air at the higher altitude.

Suppose a blower is to operate at 2500' altitude and is to handle 1000 CFM of standard air.  What is the CFM of air the blower must handle at 2500' altitude?
 
 

V1 = Volume of Standard Air, V2 = Volume of Thinner Air, Hg1 = Barometric Pressure at Sea Level, and Hg2 = Barometric Pressure at 2500' (27.31).

V2 = V1 x Hg1/Hg2 = 1000 x 29.92/27.31 = 1096 cfm
 

E-Mail:  esco@valornet.com

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Updated August 2004