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**International System of Units**

Unit Conversion Gary Anderson EDTC 3123 Spring 2010

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**Metric System & Unit Conversion**

Real world problem! John needs to change out two battery cells on critical equipment where he works. The battery manual says to torque the 8mm connection bolts to 20 N-m (Newton meters). He has a torque wrench that only measures in foot-lbs. At what value (ft-lbs) should he tighten the connector bolts?

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**Facts about the Metric System:**

Developed by the French chemist Lavoisier in the 18th century to promote the standardization of measurement units commonly used in scientific inquiry and experimentation. In 1960, an international conference was called to standardize the metric system. The International System of Units (SI) was the result! There are seven “fundamental” or “base” units: meter (distance), kilogram (mass), second (time), ampere (electrical current), Kelvin (temperature), mole (quantity), and candela (luminous intensity). There are other “derived” units that are built around the “base units”. An example of this is density which is mass/unit volume. An accurate and consistent system of measurement is the foundation of a healthy economy! Click for more details! METER KILOGRAM SECOND AMPERE KELVIN MOLE CANDELA

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Lavoisier – developed the metric system of units to replace the disparate systems of measures with a unified, natural and universal system. Multiples of metric units are related by powers of ten and named by prefixes. The first fundamental or base units included: metre for length gram for weight litre for capacity. : Hecto – one hundred Kilo – one thousand Mega – one million Or Deci – one tenth Centi – one hundredth Milli – one thousandth

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**Consider the importance of units in your life**

Consider the importance of units in your life. We use units everyday, usually without even realizing it! Imagine the following statements being made without their appropriate units! America’s tallest building, the Sears tower in Chicago is 110 ______ high! The Nile is the world’s longest river. It is 4180 ____________ long. The Amazon River in South America is 6296 ____________ long. The largest recorded “hailstone” landed in Aurora, Nebraska in 2003, and had a circumference of 47.6 _________.

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**BTU Density Hertz Pressure Horsepower Foot-pounds Kilowatt hour**

“Derived Units” Units that are build upon the use of one or more of the fundamental units! Here are only a few! Click on any of these for additional detail. Pressure Foot-pounds Bar Newton-meter watts Density Hertz Horsepower ATM Kilowatt hour Velocity BTU

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**How do we convert from one type of units to another?**

Remember John’s Problem with the torque wrench? John needs to change out two battery cells on critical equipment where he works. The battery manual says to torque the 8mm connection bolts to 20 N-m (Newton meters). He has a torque wrench that only measures in foot-lbs. At what value (ft-lbs) should he tighten the connector bolts? We need to use a conversion factor and some simple math!

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Use an equivalent value to convert units! While this chart doesn’t show the equalities for the derived units of ft-lbs and N-m, it will be useful for many other conversions! Here is the conversion factor for ft-lbs and Newton meters. Both are units for “force”. 1 ft-lb = N-m - or - 1 N-m = ft-lbs

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**Using: 1 ft-lb = 1.3558 N-m or 1 N-m = .73756 ft-lbs**

John’s Torque setting Problem: If we use the equivalent factors for these “derived” units, we can easily convert a value of N-m to ft-lbs or ft-lbs to N-m! Using: 1 ft-lb = N-m or 1 N-m = ft-lbs Set the problem up like this, using the factor-label method which will factor-out unwanted units and leave desired units. Unknown: How many ft-lbs? Known: Nm is needed! Equiv units: 1 ft-lb = Nm or 1 Nm = ft-lbs

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**John’s Torque setting Problem:**

Doesn’t really matter which equivalent factor is used – as long as it has the starting units and the desired units! The Nm units divide out and you are left with whatever units are on the dividend or top side of our equation! In this case “ft-lbs”! Either conversion factor would have worked! Remember to always have your desired units in the dividend portion of the equation – that is what will remain after solving! Here’s the equation steps showing how the different units factor out! Using: 1 ft# = Nm Or – Using: 1 Nm = ft#

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Here are two examples showing multiple steps used in converting a value from one type of units to the type of units we need! 1. How many millimeters (mm) is 2 inches? ⁼ 2. An artificial heart is capable of pumping 17 million pints of blood before failure. If a average heart rate is 72 beats/min and average stroke volume is 70 milliliter (ml) then how many years could we expect this artificial heart to last? or Multiply the factors, while the un-desired units cancel out!

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This ends our lesson on SI units and the Unit-Factor method of conversion. Below are additional resources for further exploration into this important topic!

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**Pressure: The amount of force acting upon a surface.**

The SI unit for pressure is the pascal (Pa), which is equal to one Newton per square meter. Expressed as N/m²

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Horsepower A unit of measurement of power, it is related to several common units used to quantify power such as watts, ft-lbs/min, and BTU/hr. It is most simply understood by the following basic relationship! Power = work / time or the ability to do a specific amount of work per a given time frame! While not formally recognized as an SI unit, it is widely used. Below are some equivalencies for different applications. 1 HP(mech) = 550 ft-lbs/sec 1 HP (mech) = 33,000 ft-lbs/min 1 HP(electrical) = 746 Watts 1 HP(steam) = 33,475 BTU/hr

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Foot Pounds (ft-lbs) The energy expended when one pound of force acts through a distance of one foot – along the direction of the force! Equivalent factors: 1 ft-lb = joules 1 ft-lb = calories 1 ft-lb = Newton-meters

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Velocity The rate of change or a position. Requires the use of both speed and direction to define velocity. In SI units it is measured in meters per second . (m/s) or ms-1

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**BTU – British Thermal Unit!**

The amount of heat required to raise the temperature of one pound of water by 1 degree from 60 to 61 deg F at a constant pressure of 1 atmosphere. Equivalent values 1 BTU = Kilojoules 1 BTU = 253 calories 1 BTU = approx 780 ft lbs (force)

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Watts The watt is a derived unit of power in the International System of Units (SI). It is names after 18th century Scottish engineer James Watt. Its unit symbol is “W”. One watt of energy is equal to 1 joule of energy per second. Note that watts represent a “rate” at which work is done! Equivalencies: 1 watt = 1 J s-1 or 1 kg m2 s-3 or 1 Nm s-1 for mechanical energy. 1 watt = 1 volt x 1 amp for electrical energy.

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**A unit of torque (rotational energy) in the SI system.**

Newton-meter A unit of torque (rotational energy) in the SI system. Equivalent factors: 1 N-m = 1 joule 1 N-m = ft lbs force

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Hertz (frequency) Hertz is the SI unit of “frequency” and is defined as the number of “cycles per second” of a periodic phenomenon. It common usage is in describing sinusoidal waveforms such as AC electrical current and radio/audio applications. Equivalent factors: 1 Hz = 1 cycle/second 60 Hz = 60 cycles/second Period of a waveform = 1/hz (length of time of 1 wave)

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Bar A bar is a unit of pressure roughly equal to the atmospheric pressure on Earth at sea level. Equivalent factors: 1 bar = 100 kPa (kilopascals) 1 bar = 1x106 dynes per sq centimeter 1 bar = atm (atmosphere) 1 bar = psi

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Kilowatt-hour The kilowatt-hour, symbol kW-h, is a unit of energy equal to 1000 watt rate per hour! Example: A heater rated at 1000 watts (1 kilowatt), operating for one hour uses one kilowatt hour of energy – which is equal to 3,600 kilojoules! Equivalency factors: 1 Watt-hour = 3,600 kilojoules of energy 1 Watt-hour = calories 1 kWh = 3.6 megajoules

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ATM – atmosphere ATM is the symbol formerly used as the unit for standard pressure, now defined in terms of the Pascal (Pa) by the international system (SI). In most practical applications it has been replaced by the “bar”, which is equal to 100,000 Pa. Equivalent factors: 1 atm = 101,325 Pa 1 atm = psi 1 atm = bar 1 atm = 760 torr

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**(kg/m3) or (g/cc) or (g/cm3)**

Density Density is defined as a substance’s mass per volume. The SI unit for density is kilograms per cubic metre. (kg/m3) or (g/cc) or (g/cm3)

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Metre or meter is the basic unit of length in the International System of Units (SI). It was once defined as the length representing one ten-millionth of the distance from the Equator to the North Pole along the Paris meridian. It is currently defined as the distance that light will travel in space during a time period of x 10-9 seconds. This length is equivalent to inches.

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**1 kilogram = 1000 grams = 2.2046 pounds**

Kilogram: the base unit of mass in the International System of Units. It is the only SI unit that includes a SI prefix as part of its name and is closely related to be equal to the mass of 1 litre of water. The SI system now defines a kilogram to be equal to the mass of the IPK, a platinum alloy standard which is stored at the International Bureau of Weights and Measures in a vault located near Paris! 1 kilogram = 1000 grams = pounds

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**Second: the SI recognized base unit of time!**

The second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the “caesium 133 atom”. 1 sec = 1/60 minute = 1/3600 hour = 1/86,400 day

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Ampere: the SI unit that represents electrical current, named after Andre-Marie Ampere, a French mathematician and physicist. It is often simply referred to as the “amp”. It is the measure of the amount of electric charge passing a point in a given unit of time. Approximately x electrons passing a specific point in a 1 second time period is equal to 1 ampere. Closely related is the “coulomb”: defined as the quantity of electricity (charge) carried in 1 second by a current of 1 amp!

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Kelvin: The kelvin (K) is a unit of temperature and one of the base SI units. It is a absolute temperature scale referenced to absolute zero! Therefore the absence of all thermal energy is measured zero kelvins (0 K) and is not referenced by degrees. K = Celsius K = (Fahrenheit ) x (5/9)

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Mole: The symbol for this unit is “mol” and it is the SI fundamental unit for the amount of substance. It is the amount of substance contained as “elementary entities” such as atoms, molecules, ions, or electrons, as there are atoms in 12 grams of carbon12 . Thus a mole will have x atoms or molecules of whatever pure substance being measured. This unit is widely used in chemistry.

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**1 candela (cd) of intensity!**

Candela: The candela, symbol “cd” is the SI unit of luminous intensity or the power emitted by a light source. In times past it was referred to as “candle” because it was the light intensity output from one common candle. Presently it is defined as the radiant intensity of 1/683 watt per steradian. 1 candela (cd) of intensity!

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