Appendix D: Useful Formulas

Calculating the Horsepower Requirement of a Load

The mechanical load required by the driven equipment is known as the Brake Horsepower (BHP). The BHP value can be calculated by the following:

BHP =
T x N
5,250
(required HP)

Where:
HP = horsepower supplied by the motor
T = Torque (lb-ft) force x radius
N = base speed of motor (rpm)

Once the machine BHP (speed times torque) requirement is determined, horsepower (HP) can be calculated:

Rated motor HP =
Motor Efficiency (%) / 100
5,250

If the calculated horsepower falls between standard available motor ratings, select the higher available horsepower rating. It is good practice to allow some margin when selecting the motor horsepower.

For many applications, it is possible to calculate the horsepower required without actually measuring the torque required.

Several typical examples:

For Conveyors:

hp (vertical) =
weight (lb) x velocity (FPM)
33,000 x efficiency
hp (horizontal) =
weight (lb) x velocity (FPM) x coefficient of friction
33,000 x efficiency

For Fans and Blowers:

Effect of speed on horsepower

HP = k1 x speed(RPM)³ – horsepower varies as the 3rd power of speed

T = k2 x speed(RPM)² – torque varies as the 2nd power speed

Flow = k3 x speed(RPM) – flow varies directly as the speed

HP =
CFM x pressure (lb/in²)
229 x (eff. of fan)
HP =
CFM x (inches of water gauge total pressure)
6,362 x (eff. of fan)

Total pressure = static pressure + velocity pressure

Velocity pressure = V² x (1/1096.7)² x density

For Pumps

hp =
[GPM x head (ft) x specific gravity]
[3960 x % eff. of pump]

Specific gravity of water = 1.0

1 ft³ per sec = 448 GPM

1 PSI = A head of 2.309 ft for water weighing 62.36 lb/ft³ at 62°F

Constant Displacement Pumps

Effect of speed on horsepower (hp) = k x speed (RPM).

Horsepower and capacity vary directly the speed.

Displacement pumps under constant heat require approximately constant torque at all speeds.

Horsepower and capacity vary directly the speed.

Displacement pumps under constant heat require approximately constant torque at all speeds.

Centrifugal Pumps

Effect of speed on input brake horsepower

HP = k1 x speed (RPM)³ - horsepower varies as the 3rd power of speed

T = k2 x speed (RPM)² - torque varies as the 2nd power of speed

Flow = k3 x speed (RPM) - flow varies directly as the speed

Centrifugal Pump Efficiency (Typical)

500 to 1,000 gal./min. = 70% to 75%

1,000 to 1,500 gal./min. = 75% to 80%

Larger than 1,500 gal./min. = 80% to 85%

Displacement pumps may vary between 50% to 80% efficiency, depending on size of pumps.

Horsepower Required

HP =
[torque(lb-ft) x speed (RPM)]
5,250

HP = torque (lb-in) x speed (RPM)63,000

Torque (lb-ft) =
[HP x 5,250]
speed (RPM)

Ohms Law

Amperes =
volts
ohms
Ohms =
volts
amperes

Volts = amperes x ohms

Power in DC Circuits

Horsepower =
volts x amperes
746

Watts = volts x amperes

Kilowatts =
volts x amperes
1,000
 
Kilowatts x hours =
volts x amperes x hours
1,000

Power in AC Circuits

Kilovolt-Amperes (kVA)

kVA (single-phase) =
volts (line to line) x amperes (line to line)
1,000
kVA (three-phase) =
volts (line to line) x amperes (line to line) x 1.73
1,000

Kilowatts (kW)

kW (single-phase) =
volts (line to line) x amperes (line to line) x power factor
1,000
kW (three-phase) =
volts (line to line) x amperes (line to line) x power factor x 1.73
1,000
Power factor (PF) =
kW
kVA

Three-Phase AC Circuits

hp =
volts(line to line) x amperes(line to line) x1.73 x EFF x PF
746
Motor amps =
hp x 746
volts(line to line) x (1.73) x EFF x PF
Motor amps =
kVA x 1,000
1.73 x volts (line to line)
Motor amps =
kW x 1,000
1.73 x volts(line to line) x PF
Power factor =
kW x 1,000
volts(line to line) x amperes(line to line) x 1.73
Kilowatt-hours =
volts(line to line) x amperes (line to line)x hours x 1.73 x PF
1,000

Power (watts) = volts(line to line) x amperes(line to line) x 1.73 x PF

PF = displacement power factor = cosine Angle =
kW
kVA
Figure 23: Power Triangle

Figure 23: Power Triangle

Figure 23: Power Triangle - Illustrating Relationships Between

  1. Active (kW) and Apparent Power (kVa)
  2. Ration of Active Vs Apparent Power is the Power Factor (kW/kVa)
  3. Inductive Vs Capactive load (kVar)
  4. Inductive (leading) Vs Capacitive (lagging)

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