CONCEPTS, FORMULAS AND UNITS OF MEASUREMENT

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Engineering-Book ENGINEERING FUNDAMENTALS AND HOW IT WORKS

September 2014

Expertise in Process Engineering Optimization Solutions & Industrial Engineering Projects Management 

Supply Chain Manufacturing & DC Facilities Logistics Operations Planning Management

Glossary

HVAC (heating, ventilation, and air conditioning) The goal of HVAC design is to balance indoor environmental comfort with other factors such as installation cost, ease of maintenance, and energy efficiency

air changes per hour The number of times per hour that the volume of a specific room or building is supplied or removed from that space by mechanical and natural ventilation

air conditioner An appliance, system, or mechanism designed to dehumidify and extract heat from an area. Usually this term is reserved for smaller self contained units such as a residential system.

air handling unit A central unit consisting of a blower, heating and cooling elements, filter racks or chamber, dampers, humidifier, and other central equipment in direct contact with the airflow. This does not include the ductwork through the building

British thermal unit (BTU) Any of several units of energy (heat) in the HVAC industry, each slightly more than 1 kJ. One BTU is the energy required to raise one pound of water one degree Fahrenheit

Glossary

The power of HVAC systems (the rate of cooling and dehumidifying or heating) is sometimes expressed in BTU/hour instead of watts The unit watt, is defined as one joule per second, and measures the rate of energy conversion or transfer

Chiller A device that removes heat from a liquid via a vapor-compression or absorption refrigeration cycle

This cooled liquid flows through pipes in a building and passes through coils in air handlers, fan-coil units, or other systems, cooling and usually dehumidifying the air in the building.

Chillers are of two types; air-cooled or water-cooled. Air-cooled chillers are usually outside and consist of condenser coils cooled by fan-driven air.

Water-cooled chillers are usually inside a building, and heat from these chillers is carried by re-circulating water to a heat sink such as an outdoor cooling tower

Glossary

Coil Equipment that performs heat transfer to air when mounted inside an air handling unit or ductwork. It is heated or cooled by electrical means or by circulating liquid or steam within it.

Condenser A component in the basic refrigeration cycle that ejects or removes heat from the system.

The condenser is the hot side of an air conditioner or heat pump. Condensers are heat exchangers, and can transfer heat to air or to an intermediate fluid (such as water or an aqueous solution of ethylene glycol) to carry heat to a distant sink, such as ground (earth sink), a body of water, or air (as with cooling towers)

Evaporator A component in the basic refrigeration cycle that absorbs or adds heat to the system. Evaporators can be used to absorb heat from air or from a liquid. The evaporator is the cold side of an air conditioner or heat pump

Glossary

Enthalpy For a given sample of air, a measure of the total heat content (the sum of the heat energy of the dry air and heat energy of the water vapor within it). It is typically used to determine the amount of fresh outside air that can be added to re-circulated air for the lowest cooling cost.

Economizer An HVAC component that uses outside air, under suitable climate conditions, to reduce required mechanical cooling. When the outside air’s enthalpy is less than the required supply air during a call for cooling, an economizer allows a building’s mechanical ventilation system to use up to the maximum amount of outside air

Damper A plate or gate placed in a duct to control air flow by increasing friction in the duct

fan coil unit A small terminal unit that is often composed of only a blower and a heating and/or cooling coil, as is often used in hotels, condominiums, or apartments

Flow A transfer of fluid volume per unit time

Glossary

fresh air intake An opening through which outside air is drawn into the building. This may be to replace air in the building that has been exhausted by the ventilation system, or to provide fresh air for combustion of fuel

Grille A facing across a duct opening, often rectangular in shape, containing multiple parallel slots through which air may be delivered or withdrawn from a ventilated space. The grille directs the air flow in a particular direction and prevents the passage of large items

heat gain / heat load / heat lossTerms for the amount of cooling (heat gain) or heating (heat loss) needed to maintain desired temperatures and humidity's in controlled air

Regardless of how well-insulated and sealed a building is, buildings gain heat from sunlight, conduction through the walls, and internal heat sources such as people and electrical equipment

Buildings lose heat through conduction during cold weather. Engineers use heat load calculations to determine the HVAC needs of the space being cooled or heated

Glossary

intermediate fluid A liquid or gas used to transfer heat between two heat exchangers.

An intermediate fluid is used when the hot and cold fluids are too bulky (such as air) or difficult to handle (such as halocarbon refrigerant) to directly transfer the heat

makeup air unit An air handler that conditions 100% outside air. Typically used in industrial or commercial settings, or in "once-through" (blower sections that only blow air one-way into the building), "low flow" (air handling systems that blow air at a low flow rate), or "primary-secondary" (air handling systems that have an air handler or rooftop unit connected to an add-on makeup unit or hood) commercial HVAC systems

Psychometric The study of the behavior of air-water vapor mixtures. Water vapor plays an important role in energy transfer and human comfort in HVAC design

Radiation The transfer of heat directly from one surface to another (without heating the intermediate air acting as a transfer mechanism).

Superheat The number of degrees a vapor is above its boiling point at a specific pressure

Glossary

8 –

Sub-cooling The condition where liquid refrigerant is colder than the minimum temperature required to keep it from boiling which would change it from a liquid to a gas phase.

Sub-cooling is the difference between its saturation temperature and the actual liquid refrigerant temperature

terminal unit A small component that contains a heating coil, cooling coil, automatic damper, or some combination of the three. Used to control the temperature of a single room

variable air volume An HVAC system that has a stable supply-air temperature, and varies the air flow rate to meet the temperature requirements

Compared to constant air volume systems, these systems conserve energy through lower fan speeds during times of lower temperature control demand

Most new commercial buildings have VAV systems. VAVs may be bypass type or pressure dependent. Pressure dependent type VAVs save energy while both types help in maintaining temperature of the zone that it feeds

Glossary

9 –

In thermodynamics, entropy (usual symbol S) is a measure of the number of specific ways in which a thermodynamic system may be arranged, often taken to be a measure of disorder, or a measure of progressing towards thermodynamic equilibrium

The entropy of an isolated system never decreases, because isolated systems spontaneously evolve towards thermodynamic equilibrium, the maximum entropy

Systems which are not isolated may decrease in entropy

Since entropy is a state function, the change in the entropy of a system is the same whether a process going from one defined state to another is reversible or irreversible, but irreversible processes increase the entropy of the environment

The change in entropy (ΔS) was originally defined for a thermodynamically reversible process

which is found from the uniform thermodynamic temperature (T) of a closed system dividing an incremental reversible transfer of heat into that system (dQ).

Glossary

10 –

Enthalpy is a defined thermodynamic potential, designated by the letter "H", that consists of the internal energy of the system (U) plus the product of pressure (P) and volume (V) of the system

The unit of measurement for enthalpy is the joule, but other historical, conventional units are still in use, such as the British thermal unit and the calorie.

The total enthalpy, H, of a system cannot be measured directly

The same situation exists in classical mechanics: only a change or difference in energy carries physical meaning

Enthalpy itself is a thermodynamic potential, so in order to measure the enthalpy of a system, we must refer to a defined reference point; therefore what we measure is the change in enthalpy, ΔH

The change ΔH is positive in endothermic reactions, and negative in heat-releasing exothermic processes.

ΔH of a system is equal to the sum of non-mechanical work done on it and the heat supplied to it

Glossary

11 –

One of the fundamental thermodynamic equations is the description of thermodynamic work in analogy to mechanical work, or weight lifted through an elevation against gravity

Power, is the elevation of a weight to a certain height. The product of the weight multiplied by the height to which it is raised.” With the inclusion of a unit of time

The state of a thermodynamic system is specified by a number of extensive quantities, the most familiar of which are volume, internal energy, and the amount of each constituent particle (particle numbers).

Extensive parameters are properties of the entire system, as contrasted with intensive parameters which can be defined at a single point, such as temperature and pressure

The extensive parameters (except entropy) are generally conserved in some way as long as the system is "insulated" to changes to that parameter from the outside

Glossary

12 –

The concept which governs the path that a thermodynamic system traces in state space as it goes from one equilibrium state to another is that of entropy. The entropy is first viewed as an extensive function of all of the extensive thermodynamic parameters

If we have a thermodynamic system in equilibrium, and we release some of the extensive constraints on the system, there are many equilibrium states that it could move to consistent with the conservation of energy, volume, etc.

In the case of energy, the statement of the conservation of energy is known as the first law of thermodynamics, where is the infinitesimal increase in internal energy of the system. Is the infinitesimal heat flow into the system and is the infinitesimal work done by the system

In physical chemistry, positive work is conventionally considered work done on the system rather than by the system, and the law is expressed as

.

Glossary

13 –

The second law of thermodynamics specifies that the equilibrium state that it moves to is in fact the one with the greatest entropy. Once we know the entropy as a function of the extensive variables of the system, we will be able to predict the final equilibrium state.

The zeroth law says that systems that are in thermodynamic equilibrium with each other have the same temperature. The law was actually the last of the laws to be formulated

The entropy of an isolated system never decreases for an isolated system

A process within a given isolated system is said to be reversible if throughout the process the entropy never increases (i.e. the entropy remains unchanged).

The third law of thermodynamics states that at the absolute zero of temperature, the entropy is zero for a perfect crystalline structure when

consider a system composed of a number of k  different types of particles and has the volume as its only external variable. The fundamental thermodynamic relation may then be expressed in terms of the internal energy as

The thermodynamic space has k+2  dimensionsThe differential quantities (U, S, V, Ni)  are all extensive

quantities

Glossary

14 –

Power in mechanical systems is the combination of forces and movement. In particular, power is the product of a force on an object and the object's velocity, or the product of a torque on a shaft and the shaft's angular velocity measured in radians per second

In fluid power systems such as hydraulic actuators, power is given by

where p is pressure in pascals, or N/m2 and Q is volumetric flow rate in m3/s in SI units

The instantaneous electrical power P delivered to a component is given by

P(t) is the instantaneous power, measured in watts (joules per second)V(t) is the potential difference (or voltage drop) across the component, measured in voltsI(t) is the current through it, measured in amperes

If the component is a resistor with time-invariant voltage to current ratio, then

is the resistance, measured in ohms

Glossary

15 –

Electric power, like mechanical power, is the rate of doing work, measured in watts, and represented by the letter P.

The term wattage is used colloquially to mean "electric power in watts."

The electric power in watts produced by an electric current I consisting of a charge of Q coulombs every t seconds passing through an electric potential (voltage) difference of V is

Q is electric charge in coulombst is time in secondsI is electric current in amperesV is electric potential or voltage in volts

In the case of resistive (Ohmic, or linear) loads, Joule's law can be combined with Ohm's law (V = I·R) to produce alternative expressions for the dissipated power

where R is the electrical resistance.

Glossary

16 –

In alternating current circuits, energy storage elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow

The portion of power flow that, averaged over a complete cycle of the AC waveform, results in net transfer of energy in one direction is known as real power (also referred to as active power)

That portion of power flow due to stored energy, that returns to the source in each cycle, is known as reactive power

The real power P in watts consumed by a device is given by

Vp is the peak voltage in volts

Ip is the peak current in amperes

Vrms is the root-mean-square voltage in volts

Irms is the root-mean-square current in amperes

θ is the phase angle between the current and voltage sine waves

The ratio of real power to apparent power is a number between 0 and 1

Glossary

17 –

Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces

The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology

It is also widely known as Newtonian mechanics

Isaac Newton proposed three laws of motion: the law of inertia, his second law of acceleration (mentioned above), and the law of action and reaction; and hence laid the foundations for classical mechanics

Newton also enunciated the principles of conservation of momentum and angular momentum. In mechanics, Newton was also the first to provide the first correct scientific and mathematical formulation of gravity in Newton's law of universal gravitation.

He demonstrated that these laws apply to everyday objects as well as to celestial objects.

In particular, Newton obtained a theoretical explanation of Kepler's laws of motion of the planets.

Glossary

18 –

The velocity, or the rate of change of position with time, is defined as the derivative of the position with respect to time:

.

The acceleration, or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time):

Some physicists interpret Newton's second law of motion as a definition of force and mass

The quantity mv is called the (canonical) momentum. The net force on a particle is thus equal to the rate of change of the momentum of the particle with time

If a constant force F is applied to a particle that achieves a displacement Δr, the work done by the force is defined as the scalar product of the force and displacement vectors

Glossary

19 –

The kinetic energy Ek of a particle of mass m travelling at speed v is given by

In special relativity, the momentum of a particle is given by

where m is the particle's rest mass, v its velocity, and c is the speed of light.If v is very small compared to c, v2/c2 is approximately zero, and so

Thus the Newtonian equation p = mv is an approximation of the relativistic equation for bodies moving with low speeds compared to the speed of light•Statics, the study of equilibrium and its relation to forces

•Dynamics, the study of motion and its relation to forces•Kinematics, dealing with the implications of observed motions without regard for circumstances causing them

Glossary

20 –

Derived kinematic quantities Derived dynamic quantities

Velocity

Acceleration

Jerk

Angular velocity

Angular Acceleration

Momentum

Force

Impulse

Angular momentum about a position point

r0, Most of the time we can set r0 = 0 if particles are orbiting about axes intersecting at a common point

Torque

Angular impulse

Mechanical work

Glossary

21 – Title of the document or activity name – Month XX, 2012 – Insert tab > Header/Footer

Momentum is the "amount of translation"

For a rotating rigid body:

Angular momentum is the "amount of rotation":

Torque τ is also called moment of a force, because it is the rotational analogue to force

Resultant force acts on a system at the center of mass, equal to the rate of change of momentum

Impulse is the change in momentum

Angular impulse is the change in angular momentum

For constant force F:

For constant torque τ:

The work done W by an external agent which exerts a force F (at r) and torque τ on an object along a curved path C is

Kinetic energy

Glossary

22 –

A hoist is a device used for lifting or lowering a load by means of a drum or lift-wheel around which rope or chain wraps

"Chain hoist" also describes a hoist using a differential pulley

A compound pulley with two different radii and teeth engage an endless chain,

Allowing the exerted force to be multiplied according to the ratio of the radii.

Glossary

23 –

Consider the set of pulleys that form the moving block and the parts of the rope that support this block

If there are p of these parts of the rope supporting the load W, then a force balance on the moving block shows that the tension in each of the parts of the rope must be W/p

This means the input force on the rope is T=W/p. Thus, the block and tackle reduces the input force by the factor p

The mechanical advantage of a pulley system can be analyzed using free body diagrams which balance the tension force in the rope with the force of gravity on the load

In this case, a force balance on a free body that includes the load, W, and n supporting sections of a rope with tension T, yields

the mechanical advantage of the system is equal to the number of sections of rope supporting the load

Glossary

24 –

Differential pulley

is used to manually lift very heavy objects like car engines. It is operated by pulling upon the slack section of a continuous chain that wraps around pulleys. The relative size of two connected pulleys determines the maximum weight that can be lifted by hand.

It consists of two fixed pulleys of unequal radii that are attached to each other and rotate together, a single pulley bearing the load, and an endless rope looped around the pulleys. To avoid slippage, the rope is usually replaced by a chain, and the connected pulleys by sprockets.

Glossary

25 –

The two sections of chain carrying the single pulley exert opposing and unequal torques on the connected pulleys, such that only the difference of these torques has to be compensated manually by pulling the loose part of the chain.

This leads to a mechanical advantage: the force needed to lift a load is only a fraction of the load's weight.

At the same time, the distance the load is lifted is smaller than the length of chain pulled by the same factor.

This factor (the mechanical advantage MA) depends on the relative difference of the radii r and R of the connected. The effect on the forces and distances is quantitatively

The difference in radii can be made very small, making the mechanical advantage of this pulley system very large. In the extreme case of zero difference in radii, MA becomes infinite, thus no force (besides friction) is needed to move the chain, but moving the chain will no longer lift the load, when r is zero, the system becomes with a MA = 2

Glossary

26 –

A belt and pulley system is characterized by two or more pulleys in common to a belt. This allows for mechanical power, torque, and speed to be transmitted across axles. If the pulleys are of differing diameters, a mechanical advantage is realized

A belt drive is analogous to that of a chain drive, however a belt sheave may be smooth (devoid of discrete interlocking members as would be found on a chain sprocket, spur gear, or timing belt) so that the mechanical advantage is approximately given by the ratio of the pitch diameter of the sheaves only, not fixed exactly by the ratio of teeth as with gears and sprockets.

Glossary

27 –

The gear ratio of a gear train, also known as its speed ratio, is the ratio of the angular velocity of the input gear to the angular velocity of the output gear

The gear ratio can be calculated directly from the numbers of teeth on the gears in the gear train

The torque ratio of the gear train, also known as its mechanical advantage, is determined by the gear ratio

The speed ratio and mechanical advantage are defined so they yield the same number in an ideal linkage

Glossary

28 –

A gear train is formed by mounting gears on a frame so that the teeth of the gears engage

Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, providing a smooth transmission of rotation from one gear to the next

Gear teeth are designed so that the number of teeth on a gear is proportional to the radius of its pitch circle, and so that the pitch circles of meshing gears roll on each other without slipping.

The speed ratio for a pair of meshing gears can be computed from ratio of the radii of the pitch circles and the ratio of the number of teeth on each gear

The velocity v of the point of contact on the pitch circles is the same on both gears, and is given by

Glossary

29 –

where input gear A has radius rA and meshes with output gear B of radius rB

where NA is the number of teeth on the input gear and NB on the output gear

The mechanical advantage of a pair of meshing gears for which the input gear has NA

teeth and the output gear has NB teeth is given by MA

This shows that if the output gear GB has more teeth than the input gear GA, then the gear

train amplifies the input torque

And, if the output gear has fewer teeth than the input gear, then the gear train reduces the input torque

If the output gear of a gear train rotates more slowly than the input gear, then the gear train is called a speed reducer

In this case, because the output gear must have more teeth than the input gear, the speed reducer amplifies the input torque.

Glossary

30 –

Speed ratio. Gear teeth are distributed along the circumference of the pitch circle so that the thickness t of each tooth and the space between neighboring teeth are the same

The pitch p of a gear, which is the distance between equivalent points on neighboring teeth along the pitch circle, is equal to twice the thickness of a tooth,

The pitch of a gear GA can be computed from the number of teeth NA and the radius rA of

its pitch circle

In order to mesh smoothly two gears GA and GB must have the same sized teeth and

therefore they must have the same pitch p, which means

This equation shows that the ratio of the circumference, the diameters and the radii of two meshing gears is equal to the ratio of their number of teeth,

The speed ratio of two gears rolling without slipping on their pitch circles is given by,

Glosary

31 –

Calculating powerWatt determined that a horse could turn a mill wheel 144 times in an hour (or 2.4 times a minute). The wheel was 12 feet in radius; therefore, the horse travelled 2.4 × 2π × 12 feet in one minute. Watt judged that the horse could pull with a force of 180 pounds. So:

This was rounded to an even 33,000 ft·lbf/min.

If torque and angular speed are known, the power may be calculated. The relationship when using a coherent system of units (such as SI) is simply 

The constant 5252 is the rounded value of (33,000 ft·lbf/min)/(2π rad/rev).

When torque is in inch pounds:The constant 63,025 is the rounded value of (33,000 ft·lbf/min) × (12 in/ft)/(2π rad/rev).

Glosary

32 –

The following definitions have been widely used:Mechanical horsepowerhp(I) ≡ 33,000 ft-lbf/min = 550 ft·lbf/s ≈ 17,696 lbm·ft2/s3

= 745.69987158227022  WMetric horsepowerhp(M) - also PS, ''cv, hk, pk, ks or ch ≡ 75 kgf·m/s ≡ 735.49875  WElectrical horsepowerhp(E) ≡ 746 WBoiler horsepowerhp(S) ≡ 33,475 BTU/h = 9,812.5 WHydraulic horsepower= flow rate (US gal/min) × pressure (psi) × 7/12,000 = 550 ft·lbf/s = flow rate (US gal/min) × pressure (psi) / 1714 = 745.699 W

Glosary

33 –

Torque converter is generally a type of fluid coupling (but also being able to multiply torque) that is used to transfer rotating power from a prime mover, such as an internal combustion engine or electric motor, to a rotating driven load

The torque converter normally takes the place of a mechanical clutch in a vehicle with an automatic transmission, allowing the load to be separated from the power source

It is usually located between the engine's flexplate and the transmission.

The key characteristic of a torque converter is its ability to multiply torque when there is a substantial difference between input and output rotational speed, thus providing the equivalent of a reduction gear

Glosary

34 –

As with a basic fluid coupling the theoretical torque capacity of a converter is proportional to

where is the mass density of the fluid (kg/m³),

is the impeller speed (rpm), and

is the diameter(m)

A torque converter cannot achieve 100 percent coupling efficiency.

The classic three element torque converter has an efficiency curve that resembles ∩:

zero efficiency at stall, generally increasing efficiency during the acceleration phase and low efficiency in the coupling phase

Typical stall torque multiplication ratios range from 1.8:1 to 2.5:1 for most automotive applications

Specialized converters designed for industrial, rail, or heavy marine power transmission systems are capable of as much as 5.0:1 multiplication

Glosary

35 –

Power

Motor Velocity (rpm)

3450 2000 1000 500

Torque

hp kW (in lbf) (ft lbf) (Nm) (in lbf) (ft lbf) (Nm) (in lbf) (ft lbf) (Nm) (in lbf) (ft lbf) (Nm)

1 0.75 18 1.5 2.1 32 2.6 3.6 63 5.3 7.1 126 10.5 14.2

1.5 1.1 27 2.3 3.1 47 3.9 5.3 95 7.9 10.7 189 15.8 21.4

2 1.5 37 3.0 4.1 63 5.3 7.1 126 10.5 14.2 252 21.0 28.5

3 2.2 55 4.6 6.2 95 7.9 10.7 189 15.8 21.4 378 31.5 42.7

5 3.7 91 7.6 10 158 13.1 18 315 26.3 36 630 52.5 71

7.5 5.6 137 11 15 236 20 27 473 39 53 945 79 107

10 7.5 183 15 21 315 26 36 630 53 71 1260 105 142

15 11 274 23 31 473 39 53 945 79 107 1891 158 214

20 15 365 30 41 630 53 71 1260 105 142 2521 210 285

25 19 457 38 52 788 66 89 1576 131 178 3151 263 356

30 22 548 46 62 945 79 107 1891 158 214 3781 315 427

40 30 731 61 83 1260 105 142 2521 210 285 5042 420 570

50 37 913 76 103 1576 131 178 3151 263 356 6302 525 712

60 45 1096 91 124 1891 158 214 3781 315 427 7563 630 855

70 52 1279 107 145 2206 184 249 4412 368 499 8823 735 997

80 60 1461 122 165 2521 210 285 5042 420 570 10084 840 1140

90 67 1644 137 186 2836 236 321 5672 473 641 11344 945 1282

100 75 1827 152 207 3151 263 356 6302 525 712 12605 1050 1425

125 93 2283 190 258 3939 328 445 7878 657 891 15756 1313 1781

Example - Electrical Motor Torque

Torque from an electrical motor with

100 hp and speed 1000 rpm can be calculated as

T = (100 hp) 63025 / (1000 rpm)     = 6303 (in lbf)

To convert to foot pound-force -

divide the torque by 12.

Glosary

36 –

Electrical Motor Torque EquationTorque can be calculated in Imperial units asT = Php 63025 / n         (1)

where T = torque (in lbf)

Php =  horsepower delivered by the electric motor

n = revolution per minute (rpm)

Alternatively Tft = Php 5252 / n         (1b)

whereTft = torque (ft lbf)

•1 ft lbf = 1.356 Nm

Torque can be calculated in SI units asT = PW 9.554 / n         (1)

whereT = torque (Nm)PW =  power (watts)

n = revolution per minute (rpm)

Glosary

37 –

Calculating Motor Speed:A squirrel cage induction motor is a constant speed device. It cannot operate for any length of time at speeds below those shown on the nameplate without danger of burning out.To Calculate the speed of a induction motor, apply this formula:Srpm = 120 x F            PSrpm = synchronous revolutions per minute.120   = constantF       = supply frequency (in cycles/sec)P       = number of motor winding polesExample: What is the synchronous of a motor having 4 poles connected to a 60 hz power supply?Srpm = 120 x F            PSrpm = 120 x 60            4Srpm = 7200             4Srpm = 1800 rpm

Glosary

38 –

Calculating Braking Torque:Full-load motor torque is calculated to determine the required braking torque of a motor.

To Determine braking torque of a motor, apply this formula:

T = 5252 x HP    rpmT      = full-load motor torque (in lb-ft)5252 = constant (33,000 divided by 3.14 x 2 = 5252)HP    = motor horsepowerrpm = speed of motor shaft

Example: What is the braking torque of a 60 HP, 240V motor rotating at 1725 rpm?

T = 5252 x HP    rpmT = 5252 x 60     1725T = 315,120     1725T = 182.7 lb-ft

Glosary

39 –

Calculating Work:

Work is applying a force over a distance. Force is any cause that changes the position, motion, direction, or shape of an object. Work is done when a force overcomes a resistance. Resistance is any force that tends to hinder the movement of an object.If an applied force does not cause motion the no work is produced.

To calculate the amount of work produced, apply this formula:W = F x DW = work (in lb-ft)F  = force (in lb)D  = distance (in ft)

Example: How much work is required to carry a 25 lb bag of groceries vertically from street level to the 4th floor of a building 30' above street level?

W = F x DW = 25 x 30W = 750 -lb

Glosary

40 –

Calculating Torque:

Torque is the force that produces rotation. It causes an object to rotate. Torque consist of a force acting on distance. Torque, like work, is measured is pound-feet (lb-ft). However, torque, unlike work, may exist even though no movement occurs.

To calculate torque, apply this formula:

T = F x DT = torque (in lb-ft)F = force (in lb)D = distance (in ft)

Example: What is the torque produced by a 60 lb force pushing on a 3' lever arm?

T = F x DT = 60 x 3T = 180 lb ft

Glosary

41 –

Calculating Full-load Torque:Full-load torque is the torque to produce the rated power at full speed of the motor. The amount of torque a motor produces at rated power and full speed can be found by using a horsepower-to-torque conversion chart. When using the conversion chart, place a straight edge along the two known quantities and read the unknown quantity on the third line.

To calculate motor full-load torque, apply this formula:T = HP x 5252    rpmT = torque (in lb-ft)HP = horsepower5252 = constantrpm = revolutions per minute

Example: What is the FLT (Full-load torque) of a 30HP motor operating at 1725 rpm?T = HP x 5252    rpmT = 30 x 5252     1725T = 157,560     1725T = 91.34 lb-ft

Glosary

42 –

Calculating Horsepower:Electrical power is rated in horsepower or watts. A horsepower is a unit of power equal to 746 watts or 33,0000 lb-ft per minute (550 lb-ft per second). A watt is a unit of measure equal to the power produced by a current of 1 amp across the potential difference of 1 volt. It is 1/746 of 1 horsepower. The watt is the base unit of electrical power. Motor power is rated in horsepower and watts.Horsepower is used to measure the energy produced by an electric motor while doing work. To calculate the horsepower of a motor when current and efficiency, and voltage are known, apply this formula:HP = V x I x Eff        746HP = horsepowerV    = voltageI     = curent (amps)Eff. = efficiencyExample: What is the horsepower of a 230v motor pulling 4 amps and having 82% efficiency?HP = V x I x Eff        746HP = 230 x 4 x .82        746HP = 754.4        746HP = 1 Hp

Eff = efficiency / HP = horsepower / V = volts / A = amps / PF = power factor

Glosary

43 –

Horsepower Formulas

To Find Use FormulaExample

Given Find Solution

HPHP = I X E X Eff.

       746240V, 20A, 85%

Eff.HP

HP = 240V x 20A x 85%

       746HP=5.5

II = HP x 746

     E X Eff x PF10HP, 240V,

90% Eff., 88% PFI

I = 10HP x 746      240V x 90% x

88%I = 39 A

To calculate the horsepower of a motor when the speed and torque are known, apply this formula:

HP = rpm x T(torque)         5252(constant)

Example: What is the horsepower of a 1725 rpm motor with a FLT 3.1 lb-ft?

HP = rpm x T         5252HP = 1725 x 3.1         5252HP = 5347.5         5252HP = 1 hp

Glosary

44 –

Calculating Synchronous Speed:AC motors are considered constant speed motors. This is because the synchronous speed of an induction motor is based on the supply frequency and the number of poles in the motor winding. Motor are designed for 60 hz use have synchronous speeds of 3600, 1800, 1200, 900, 720, 600, 514, and 450 rpm.

To calculate synchronous speed of an induction motor, apply this formula:rpmsyn = 120 x f              Nprpmsyn = synchronous speed (in rpm)f           = supply frequency in (cycles/sec)Np       =  number of motor poles

Example: What is the synchronous speed of a four pole motor operating at 50 hz.?

rpmsyn = 120 x f              Nprpmsyn = 120 x 50              4rpmsyn = 6000              4rpmsyn = 1500 rpm

Glosary

45 –

Torque in lb.ft. =

HP x 5250

rpmHP =

Torque x rpm

5250

rpm =

120 x Frequency

No. of Poles

Rules Of Thumb (Approximation)

At 1800 rpm, a motor develops a 3 lb.ft. per hpAt 1200 rpm, a motor develops a 4.5 lb.ft. per hpAt 575 volts, a 3-phase motor draws 1 amp per hpAt 460 volts, a 3-phase motor draws 1.25 amp per hpAt 230 volts a 3-phase motor draws 2.5 amp per hpAt 230 volts, a single-phase motor draws 5 amp per hpAt 115 volts, a single-phase motor draws 10 amp per hp

Mechanical Formulas

Glosary

46 –

t =

High Inertia Loads

WK2 x rpm308 x T av.

WK2 = inertia in lb.ft.2

t = accelerating time in sec.T = Av. accelerating torque lb.ft..

Temperature ConversionDeg C = (Deg F - 32) x 5/9Deg F = (Deg C x 9/5) + 32

inertia reflected to motor = Load Inertia (Load rpm)Motor rpm

2

ns =120 x f

Pf =

P x ns

120P =

120 x fns

HP =T x n5250

T =5250 HP

nn =

5250 HPT

% Slip =ns - n

ns

x 100

Synchronous Speed, Frequency And Number Of Poles Of AC Motors

Relation Between Horsepower, Torque, And Speed

Motor Slip

Glosary

47 –

Code KVA/HP Code KVA/HP Code KVA/HP Code KVA/HP

A 0-3.14 F 5.0 -5.59 L 9.0-9.99 S 16.0-17.99

B 3.15-3.54 G 5.6 -6.29 M 10.0-11.19 T 18.0-19.99

C 3.55-3.99 H 6.3 -7.09 N 11.2-12.49 U 20.0-22.39

D 4.0 -4.49 I 7.1 -7.99 P 12.5-13.99 V 22.4 & Up

E 4.5 -4.99 K 8.0 -8.99 R 14.0-15.99

Symbols 

I = current in amperesE = voltage in voltsKW = power in kilowattsKVA = apparent power in kilo-volt-amperesHP = output power in horsepowerN = motor speed in revolutions per minute (RPM)Ns = synchronous speed in revolutions per minute (RPM)P = number of polesF = frequency in cycles per second (CPS)T = torque in pound-feetEFF = efficiency as a decimalPF = power factor as a decimal

Glosary

48 –

WK2EQ = WK2

part (Npart) 2

Nprime mover

Equivalent Inertia

In mechanical systems, all rotating parts do not usually operate at the same speed. Thus, we need to determine the "equivalent inertia" of each moving part at a particular speed of the prime moverThe total equivalent WK2 for a system is the sum of the WK2 of each part, referenced to prime mover speed The equation says:

This equation becomes a common denominator on which other calculations can be based. For variable-speed devices, inertia should be calculated first at low speed

Let's look at a simple system which has a prime mover (PM), a reducer and a load

WK2 = 100 lb.ft.2WK2 = 900 lb.ft.2

(as seen at output shaft)WK2 = 27,000 lb.ft.2

PRIME MOVER 3:1 GEAR REDUCER LOAD

The formula states that the system WK2 equivalent is equal to the sum of WK2parts at the prime mover's RPM

Glosary

49 –

or in this case:

WK2EQ = WK2

pm +

WK2Red.

(Red. RPM)

PM RPM2 + WK2

Load (Load RPM)

PM RPM2

Note: reducer RPM = Load RPM

WK2EQ = WK2

pm + WK2Red.

(1)3

2 + WK2Load

(1)3

2

The WK2 equivalent is equal to the WK2 of the prime mover, plus the WK2 of the load. This is equal to the WK2 of the prime mover, plus the WK2 of the reducer times (1/3)2, plus the WK2 of the load times (1/3)2

This relationship of the reducer to the driven load is expressed by the formula given earlier:

WK2EQ = WK2

part (Npart)

Nprime mover

2

In other words, when a part is rotating at a speed (N) different from the prime mover, the WK 2EQ is equal to the WK2 of the

part's speed ratio squared

Glosary

50 –

WK2EQ = 100 lb.ft.2 + 900 lb.ft.2

(1)3

2+ 27,000

lb.ft.2

(1)3

2

WK2EQ = lb.ft.2

pm + 100 lb.ft.2Red + 3,000 lb.ft2

Load

WK2EQ = 3200 lb.ft.2

In the example, the result can be obtained as follows: The WK2 equivalent is equal to:

Finally:

The total WK2 equivalent is that WK2 seen by the prime mover at its speed.

Glosary

51 –

To FindAlternating Current

Single-Phase Three-Phase

Amperes when horsepower is knownHP x 746

E x Eff x pfHP x 746

1.73 x E x Eff x pf

Amperes when kilowatts are knownKw x 1000

E x pfKw x 1000

1.73 x E x pf

Amperes when kva are knownKva x 1000

EKva x 1000

1.73 x E

KilowattsI x E x pf

10001.73 x I x E x pf

1000

KvaI x E1000

1.73 x I x E1000

Horsepower = (Output)I x E x Eff x pf

7461.73 x I x E x Eff x pff

746

Electrical Formulas

I = Amperes; E = Volts; Eff = Efficiency; pf = Power Factor; Kva = Kilovolt-amperes; Kw = Kilowatts

Glosary

52 –

Three Phase: IL =577 x HP x KVA/HP

ESee: KVA/HP Chart

Single Phase: IL =1000 x HP x KVA/HP

E

Locked Rotor Current (IL) From Nameplate Data

EXAMPLE: Motor nameplate indicates 10 HP, 3 Phase, 460 Volts, Code F

IL = 577 x 10 x (5.6 or 6.29)460

IL = 70.25 or 78.9 Amperes (possible range)

IL @ ELINE = IL @ EN/P

x

ELINE

EN/P

Effect Of Line Voltage On Locked Rotor Current (IL) (Approx.)

EXAMPLE: Motor has a locked rotor current (inrush of 100 Amperes (IL) at the rated nameplate voltage (EN/P) of 230 volts. What is IL with 245 volts (ELINE) applied to this motor?

IL @ 245 V. = 100 x 254V/230V IL @ 245V. = 107 Amperes

Glosary

53 –

radius x 2 x rpm x lb. or 2 TM

HP =radius x 2 x rpm x lb.

33,000=

TN5,250

Basic Horsepower CalculationsHorsepower is work done per unit of time. One HP equals 33,000 ft-lb of work per minute. When work is done by a source of torque (T) to produce (M) rotations about an axis, the work done is:

When rotation is at the rate N rpm, the HP delivered is:

For vertical or hoisting motion HP =W x S

33,000 x E

W = total weight in lbs. to be raised by motor

S = hoisting speed in feet per minute

E = overall mechanical efficiency of hoist and gearing. For purposes of estimating

E = .65 for eff. of hoist and connected gear.

Where:

Glosary

54 –

For fans and blowers:

HP =Volume (cfm) x Head (inches of water)

6356 x Mechanical Efficiency of Fan

Note: Air Capacity (cfm) varies directly with fan speed. Developed Pressure varies with square of fan speed.

Hp varies with cube of fan speed.

For purpose of estimating, the eff. of a fan or blower may be assumed to be 0.65.

HP =

Volume (cfm) x Pressure (lb. Per sq. ft.)3300 x Mechanical Efficiency of Fan

HP =Volume (cfm) x Pressure (lb. Per sq. in.)

229 x Mechanical Efficiency of Fan

For pumps: HP =GPM x Pressure in lb. Per sq. in. x Specific Grav.

1713 x Mechanical Efficiency of Pump

HP =GPM x Total Dynamic Head in Feet x

S.G.3960 x Mechanical Efficiency of Pump

where Total Dynamic Head = Static Head + Friction Head

For estimating, pump efficiency may be assumed at 0.70

Glosary

55 –

Accelerating TorqueThe equivalent inertia of an adjustable speed drive indicates the energy required to keep the system running. However, starting or accelerating the system requires extra energy. The torque required to accelerate a body is equal to the WK2 of the body, times the change in RPM, divided by 308 times the interval (in seconds) in which this acceleration takes place:

ACCELERATING TORQUE =

WK2N (in lb.ft.)308t

N = Change in RPM

W = Weight in Lbs.

K = Radius of gyration

t = Time of acceleration (secs.)

WK2 = Equivalent Inertia

308 = Constant of proportionality

Where:

TAcc =WK2N308t

The constant (308) is derived by transferring linear motion to angular motion, and considering acceleration due to gravity. If, for example, we have simply a prime mover and a load with no speed adjustment

Glosary

56 –

Example 1 PRIME LOADER LOAD

WK2 = 200 lb.ft.2 WK2 = 800 lb.ft.2 The WK2EQ is determined as before:

WK2EQ = WK2

pm + WK2Load

WK2EQ = 200 + 800

WK2EQ = 1000 ft.lb.2

If we want to accelerate this load to 1800 RPM in 1 minute, enough information is available to find the amount of torque necessary to accelerate the load. The formula states:

TAcc =WK2

EQN

308tor

1000 x 1800308 x 60

or 1800000

18480

TAcc = 97.4 lb.ft

In other words, 97.4 lb.ft. of torque must be applied to get this load turning at 1800 RPM, in 60 seconds. Note that TAcc is an average value of accelerating torque during the speed change under consideration. If a more accurate calculation is desired, the following example may be helpful.

Example 2 The time that it takes to accelerate an induction motor from one speed to another may be found from the following equation:

t =WR2 x change in rpm

308 x TT = Average value of accelerating torque during the speed change under consideration.

t = Time the motor takes to accelerate from the initial speed to the final speed.

WR2 = Flywheel effect, or moment of inertia, for the driven machinery plus the motor rotor in lb.ft.2 (WR2 of driven machinery must be referred to the motor shaft).

Glosary

57 –

The Application of the above formula will now be considered by means of an example

Figure A shows the speed-torque curves of a squirrel-cage induction motor and a blower which it drives. At any speed of the blower, the difference between the torque which the motor can deliver at its shaft and the torque required by the blower is the torque available for acceleration

Reference to Figure A shows that the accelerating torque may vary greatly with speed. When the speed-torque curves for the motor and blower intersect there is no torque available for acceleration. The motor then drives the blower at constant speed and just delivers the torque required by the load

In order to find the total time required to accelerate the motor and blower, the area between the motor speed-torque curve and the blower speed-torque curve is divided into strips, the ends of which approximate straight lines. Each strip corresponds to a speed increment which takes place within a definite time interval

The solid horizontal lines in Figure A represent the boundaries of strips; the lengths of the broken lines the average accelerating torques for the selected speed intervals. In order to calculate the total acceleration time for the motor and the direct-coupled blower it is necessary to find the time required to accelerate the motor from the beginning of one speed interval to the beginning of the next interval and add up the incremental times for all intervals to arrive at the total acceleration time

If the WR2 of the motor whose speed-torque curve is given in Figure A is 3.26 ft.lb.2 and the WR2 of the blower referred to the motor shaft is 15 ft.lb.2, the total WR2 is 15 + 3.26 = 18.26 ft.lb.2

Glosary

58 –

And the total time of acceleration is:

WR2

308X [

rpm1

T1

+rpm2

T2

+rpm3

T3

+ - - - - - - - - - +

rpm9

T9

]

t =18.2

6308

X [15046

+15048

+30047

+30043.8

+20039.8

+20036.4

+30032.8

+10029.6

+4011

]

t = 2.75 sec.Accelerating Torques

T1 = 46 lb.ft. T4 = 43.8 lb.ft. T7 = 32.8 lb.ft.

T2 = 48 lb.ft. T5 = 39.8 lb.ft. T8 = 29.6 lb.ft.

T3 = 47 lb.ft. T6 = 36.4 lb.ft. T9 = 11 lb.ft.

Curves used to determine time required to accelerate induction motor and blower

Glosary

59 –

In order for a duty cycle to be checked out, the duty cycle information must include the following:

Inertia reflected to the motor shaft.

Torque load on the motor during all portions of the duty cycle including starts, running time, stops or reversals.

Accurate timing of each portion of the cycle.

Information on how each step of the cycle is accomplished. For example, a stop can be by coasting, mechanical braking, DC dynamic braking or plugging. A reversal can be accomplished by plugging, or the motor may be stopped by some means then re-started in the opposite direction.

When the motor is multi-speed, the cycle for each speed must be completely defined, including the method of changing from one speed to another.

Any special mechanical problems, features or limitations

Glosary

60 –

Duty cycle refers to the detailed description of a work cycle that repeats in a specific time period

This cycle may include frequent starts, plugging stops, reversals or stalls

These characteristics are usually involved in batch-type processes and may include tumbling barrels, certain cranes, shovels and draglines, dampers, gate- or plow-positioning drives, drawbridges, freight and personnel elevators, press-type extractors, some feeders,presses of certain types, hoists, indexers, boring machines,cinder block machines, keyseating, kneading, car-pulling, shakers (foundry or car), swaging and washing machines, and certain freight and passenger vehicles

The list is not all-inclusive. The drives for these loads must be capable of absorbing the heat generated during the duty cycles

Adequate thermal capacity would be required in slip couplings, clutches or motors to accelerate or plug-stop these drives or to withstand stalls

It is the product of the slip speed and the torque absorbed by the load per unit of time which generates heat in these drive components

All the events which occur during the duty cycle generate heat which the drive components must dissipate.

Conversion Units

61 –

Conversion Units

62 –

Conversion Units

63 –

Conversion Units

64 –

Conversion Units

65 –

Conversion Units

66 –

1 mile per hour (mph) ≅ 1.46666667 feet per second (fps)1 mile per hour (mph) = 1.609344 kilometers per hour1 knot ≅ 1.150779448 miles per hour1 foot per second ≅ 0.68181818 miles per hour (mph)1 kilometer per hour ≅ 0.62137119 miles per hour (mph)

1 square foot = 144 square inches1 square foot = 929.0304 square centimeters1 square yard = 9 square feet1 square meter ≅ 10.7639104 square feet1 centimeter (cm) = 10 millimeters (mm)1 inch = 2.54 centimeters (cm)1 foot = 0.3048 meters (m)1 foot = 12 inches1 yard = 3 feet1 meter (m) = 100 centimeters (cm)1 meter (m) ≅ 3.280839895 feet1 furlong = 660 feet1 kilometer (km) = 1000 meters (m)1 kilometer (km) ≅ 0.62137119 miles1 mile = 5280 ft1 mile = 1.609344 kilometers (km)1 nautical mile = 1.852 kilometers (km)1 pound (lb) = 0.45359237 kilograms (kg)

Conversion Units

67 –

Some Formulas

Area of Square Side Squared

Area of Circle 3.1415927 x Radius Square

Area of Sphere 4 x 3.1415927 x Radius Squared

Area of Parallelogram Base x Height

Circumference of Circle 2 x 3.1415927 x Radius

Volume of Rectangular Box Length x Width x Height

Volume of Cone 1/3 x 3.1415927 x Radius Squared x Height

Volume of Cylinder 3.1415927 x Radius Squared x Height

Volume of Sphere 4 x 3.1415927 x Radius Cubed ÷ 3

Volume of Cube Side Cubed

a = areac = circumferencev = volumesq = squarecu = cubicr = radiusd = diameterl = lengthw = widthh = heights = sidePi = 3.1415927 (approx)

Conversion Units

68 –

Given Multiply by To Find

Length [L]

Foot (ft) 0.304800 Meter (m)

Inch (in) 25.4000 Millimeter (mm)

Mile (mi) 1.609344 Kilometer (km)

Area [L]2

ft2 0.092903 m2

in2 645.16 mm2

in2 6.45160 cm2

Volume [L]3 & Capacity

in3 16.3871 cm3

ft3 0.028317 m3

ft3 7.4805 Gallon

ft3 28.3168 Liter (l)

Gallon 3.785412 Liter

Conversion Units

69 –

Energy, Work or Heat [M] [L]2 [t]-2

Btu 1.05435 kJ

Btu 0.251996 kcal

Calories (cal) 4.184* Joules (J)

ft-lbf 1.355818 J

ft-lbf 0.138255 kgf-m

hp-hr 2.6845 MJ

KWH 3.600 MJ

m-kgf 9.80665* J

N-m 1. J

Flow Rate [L]3 [t]-1

ft3/min 7.4805 gal/min

ft3/min 0.471934 l/s

gal/min 0.063090 l/s

Conversion Units

70 –

Force or Weight [M] [L] [t]-2

kgf 9.80665* Newton (N)

lbf 4.44822 N

lbf 0.453592 Kgf

Fracture Toughness

ksi sqr(in) 1.098800 MPa sqr(m)

Heat Content

Btu/lbm 0.555556 cal/g

Btu/lbm 2.324444 J/g

Btu/ft3 0.037234 MJ/m3

Heat Flux

Btu/hr-ft2 7.5346 E-5 cal/s-cm2

Btu/hr-ft2 3.1525 W/m2

cal/s-cm2 4.184* W/cm2

Conversion Units

71 –

Mass Density [M] [L]-3

lbm/in3 27.68 g/cm3

lbm/ft3 16.0184 kg/m3

Power [M] [L]2 [t]-3

Btu/hr 0.292875 Watt (W)

ft-lbf/s 1.355818 W

Horsepower (hp) 745.6999 W

Horsepower 550.* ft-lbf/s

Pressure (fluid) [M] [L]-1 [t]-2

Atmosphere (atm) 14.696 lbf/in2

atm 1.01325 E5* Pascal (Pa)

lbf/ft2 47.88026 Pa

lbf/in2 27.6807 in. H20 at 39.2°F

Conversion Units

72 –

Stress [M] [L]-1 [t]-2

kgf/cm2 9.80665 E-2* MPa

ksi 6.89476 MPa

N/mm2 1. MPa

kgf/mm2 1.42231 ksi

Specific Heat

Btu/lbm-°F 1. cal/g-°C

Temperature*

Fahrenheit (°F-32) /1.8 Celsius

Fahrenheit °F+459.67 Rankine

Celsius °C+273.16 Kelvin

Rankine R/1.8 Kelvin

Conversion Units

73 –

Stress [M] [L]-1 [t]-2

kgf/cm2 9.80665 E-2* MPa

ksi 6.89476 MPa

N/mm2 1. MPa

kgf/mm2 1.42231 ksi

Specific Heat

Btu/lbm-°F 1. cal/g-°C

Temperature*

Fahrenheit (°F-32) /1.8 Celsius

Fahrenheit °F+459.67 Rankine

Celsius °C+273.16 Kelvin

Rankine R/1.8 Kelvin

Thermal Conductivity

Btu-ft/hr-ft2-°F 14.8816 cal-cm/hr-cm2-°C

Conversion Units

74 –

pound TO g Multiply pound by 453.5924

pound TO joule/cm Multiply pound by 0.04448

pound TO joule/m (newton) Multiply pound by 4.448

pound TO kg Multiply pound by 0.4536

pound/ft TO kg/m Multiply pound/ft by 1.488

pound/in TO gm/cm Multiply pound/in by 178.6

pound/sq ft TO kg/sq m Multiply pound/sq ft by

4.882

pound/sq ft TO pound/sq in Multiply pound/sq ft by

6.94E-03

pound/sq in TO kg/sq m Multiply pound/sq in by

703.1

pound/sq in TO pound/sq ft Multiply pound/sq in by

144

radian/sec TO degree/sec Multiply radian/sec by

57.29578

radian/sec TO revolution/min Multiply radian/sec by

9.549

radian/sec TO revolution/sec Multiply radian/sec by

0.1592

Conversion Units

75 –

revolution TO degree Multiply revolution by

360

revolution/min TO degree/sec Multiply revolution/min by

6

revolution/min TO radian/sec Multiply revolution/min by

0.1047

revolution/min TO revolution/sec Multiply revolution/min by

0.01667

sq cm TO sq ft Multiply sq cm by 1.08E-03

sq cm TO sq in Multiply sq cm by 0.155

sq cm TO sq m Multiply sq cm by 0.0001

sq cm TO sq mile Multiply sq cm by 3.86E-11

sq cm TO sq mm Multiply sq cm by 100

sq cm TO sq yard Multiply sq cm by 1.20E-04

sq ft TO acre Multiply sq ft by 2.30E-05

sq ft TO sq cm Multiply sq ft by 929

Conversion Units

76 –

sq ft TO sq in Multiply sq ft by 144

sq ft TO sq m Multiply sq ft by 0.0929

sq ft TO sq mm Multiply sq ft by 9.29E+04

sq in TO sq cm Multiply sq in by 6.452

sq in TO sq ft Multiply sq in by 6.94E-03

sq in TO sq mm Multiply sq in by 645.2

ton (metric) TO kg Multiply ton (metric) by

1000

ton (metric) TO pound Multiply ton (metric) by

2205

watt TO Btu/hr Multiply watt by 3.4129

watt TO Btu/min Multiply watt by 0.05688

watt TO ft-pound/min Multiply watt by 44.27

watt TO ft-pound/sec Multiply watt by 0.7378

watt TO hp Multiply watt by 1.34E-03

watt-hr TO Btu Multiply watt-hr by 3.413

watt-hr TO ft-pound Multiply watt-hr by 2656

watt-hr TO hp-hr Multiply watt-hr by 1.34E-03

watt-hr TO kg-m Multiply watt-hr by 367.2

watt-hr TO kilowatt-hr Multiply watt-hr by 0.001

Conversion Units

77 –

To Convert From To Convert To Multiply By

lbf/in2 (psi) pascal (Pa) 6894.757

pascal (Pa) lbf/in2 (psi) 1.4504E-4

g/cm3 lb/ft3 62.427974

lb/ft3 kg/m3 16.01846

lb/in3 kg/m3 27,679.90

lb/ft3 g/cm3 0.01601846

volts/mil kV/mm 0.039370

mil (0.001 inch) cm 2.54E-3

cm mil 393.70

MPa(m1/2) psi(in1/2) 910.06

Conversion Units

78 –

J/(g-°C) BTU/(lb-°F) 0.239006

BTU/(lb-°F) J/(g-°C) 4.184000

joule (J) cal (thermochemical) 0.2390057

cal (thermochemical) joule (J) 4.184000

joule (J) BTU (thermochemical) 9.4845E-4

BTU (thermochemical) joule 1054.350

µm/(m-°C) µin/(in-°F) 0.55556

µin/(in-°F) µm/(m-°C) 1.80

cm3/Kg in3/lb 0.027680

in3/lb cm3/kg 36.127

W/(m K) BTU in /(hr ft2  F) 6.9334713

BTU in /(hr ft2  F) W/(m K) 0.1441314

(J m)/(min m2  C) W/(m-K) 0.016667

W/(m-K) (J m)/(min m2  C) 60

Conversion Units

79 –

Millimeters x 0.0394 = Inches

Centimeters x 0.3937 = Inches

Inches x 25.4 = Millimeters

Inches x 2.54 = Centimeters

Feet x 30.48 = Centimeters

Meters x 3.281 = Feet

Square Inches x 6.45 =Square Centimeters

Square Centimeters

x 155 = Square Inches

Square Meters x 10.76 = Square Feet

Cubic Centimeters

x .0610 = Cubic Inches

Cubic Feet x 1728 = Cubic Inches

Cubic Feet x 28.32 = Liters

Cubic Inches x 0.004329 = Gallons

Conversion Units

80 –

Gallons of Water

x 8.35 =Pounds of Water

Pounds of Water

x 27.65 = Cubic Inches

Gallons x 231 = Cubic Inches

Pounds x .45359 = Kilograms

Kilograms x 2.2046 = Pounds

Grams x 15.43 = Grains

Watts x 0.001341 = Horsepower

Amps x Volts = Watts

Atmospheres x 14.7 =Lbs per square inch

Horsepower x .7457 = Kilowatts

British Thermal Units

x 3.927 x 10-4 =Horsepower-hours

British Thermal Units

x 2.928 x 10-4 = Kilowatt-hours

Thank You

L | C | LOGISTICS

PLANT MANUFACTURING AND BUILDING FACILITIES EQUIPMENTEngineering-Book

ENGINEERING FUNDAMENTALS AND HOW IT WORKS

CONCEPTS, FORMULAS AND UNITS OF MEASUREMENT