# 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:

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:

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:**

**For Fans and Blowers:**

Effect of speed on horsepower

HP = k_{1} x speed(RPM)³ – horsepower varies as the 3rd power of speed

T = k_{2} x speed(RPM)² – torque varies as the 2nd power speed

Flow = k_{3} x speed(RPM) – flow varies directly as the speed

Total pressure = static pressure + velocity pressure

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

**For Pumps**

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 = k_{1} x speed (RPM)³ - horsepower varies as the 3rd power of speed

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

Flow = k_{3} 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-in) x speed (RPM)63,000

**Ohms Law**

Volts = amperes x ohms

**Power in DC Circuits**

Watts = volts x amperes

**Power in AC Circuits**

**Kilovolt-Amperes (kVA)**

**Kilowatts (kW)**

**Three-Phase AC Circuits**

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

**Figure 23: Power Triangle - Illustrating Relationships Between**

- Active (kW) and Apparent Power (kVa)
- Ration of Active Vs Apparent Power is the Power Factor (kW/kVa)
- Inductive Vs Capactive load (kVar)
- Inductive (leading) Vs Capacitive (lagging)

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