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Useful Formulas

Motor Application Formulas

Output
 

Horsepower =

Torque (lb. ft.) x RPM
5250

Kilowatts =

Torque (Nm) x RPM
9550

Torque (lb. ft.) =

Horsepower x 5250
RPM
Torque (Nm) = Kilowatts x 9550
RPM

Speed - AC Machinery

Synchronous RPM = 120 x Frequency (Hz)
Number of Poles
Percent Slip = Synchronous RPM = Full-Load RPM
Synchronous RPM
x100

Time for Motor to Reach Operating Speed (in Seconds)

Seconds = Wk2 (lb. ft.2) x Speed Change (RPM)
308 x Avg. Accelerating Torque (lb. ft.)
Wk2 = Inertia of Rotor + Inertia of Load x Load RPM2
Motor RPM2
Average Accelerating Torque = [(FLT + BDT)/2] + BDT + LRT
3
Where:

BDT = Breakdown Torque
FLT = Full-Load Torque
LRT = Locked-Rotor Torque

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Shaft Stress

Shaft Stress (psi) =

HP x 321.000
RPM x D3

Shaft Stress (kg/mm2) =

KW x 4.96 x 106
RPM x D3

Where:



D = Shaft Diameter (in or mm)
HP = Motor Output
KW = Motor Output
psi = Pounds Per Square Inch
RPM = Revolutions Per Minute

Centrifugal Applications

Affinity Laws

Fans and Blowers
Flow1
Flow2
= RPM1
RPM2
HP =

CFM x PSF
33000 x Efficiency of Fan

Pres1
Pres2
= (RPM1 )2
(RPM 2) 2
HP =

CFM x PIW
6343 x Efficiency of Fan

HP1
HP2
= (RPM1 )3
(RPM 2) 3
HP =

CFM x PSI
229 x Efficiency of Fan

Where:


Pres = Pressure
RPM = Revolutions Per Minute

CFM = Cubic Feet Per Minute
PIW = Inches of Water Gauge
PSF = Pound Per Square Foot
PSI = Pounds Per Square Inch

Pumps

HP =

GPM x FT x Specific Gravity
3960 x Efficiency of Pump

Volume of Liquid in a Tank

Gallons = 5.875 x D2 x H

1 gallon (US) of water weighs 8.35 lb.

Specific gravity of water = 1.0

HP =

GPM x PSI x Specific Gravity
1713 x Efficiency of Pump

Where:

FT = Head in feet*
GPM = Gallons per minute
PSI = Pounds per square inch
*Head in feet = 2.31 x pounds per square inch gravity.

Where:

D = Tank diameter (ft)
H = Height of liquid (ft)

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