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Engineering 10. Units & Conversions. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Units Introduction. People measure quantities through comparisons with standards. Every measured quantity has an associated “unit” Which is the name of the Standard.

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Engineering 10

Units &Conversions

Bruce Mayer, PE

Licensed Electrical & Mechanical

units introduction
Units Introduction
  • People measure quantities through comparisons with standards.
  • Every measured quantity has an associated “unit” Which is the name of the Standard.
  • Need to define sensible and practical "units" and "standards" that scientists & engineers everywhere can agree upon
  • Even though there exist an almost infinite number of different physical quantities, we need no more than a handful of “base” standards.
si system of units
SI System of Units
  • Système International d'Unités (International System of Units)
  • A CompletelyConsistentSet of BasicUnits
    • Requires NO Conversion factors
      • e.g., 5280 ft = 1 mile
    • Defined by UNCHANGING Physical Phenomena
      • Except for one...

si system history
SI System History
  • In 1960 The 11th General Conference on Weights and Measures (GCWM) adopted the name SI System, for the recommended practical system of units of measurement.
  • The 1960 GCWM Specified Seven well-defined “Base” units which, by convention, are regarded as DIMENSIONALLY INDEPENDENT

class question
¿¿ Class Question ??
  • Which of you Have Heard of the unit:
  • METER (m)
  • KILOGRAM (kg)
  • SECOND (s)
  • AMPERE or AMP (A)
  • KELVIN (K)
  • MOLE (mol)
  • CANDELA (cd)
si base units
SI Base Units
  • From this List Observe
    • Very common Units
      • Mass (kg)
      • Length (m)
      • Time (s)
    • Some Not so Common Units
      • Current (A)
      • Temperature (K)
    • Some Uncommon Units
      • Substance amt (mol)
      • Luminous Int (cd)
  • All but the kg are defined by Physical Phenomena
    • Examine the Defs
meter defined
Length or Distance (meter)

1 meter


1/299792458 s


Meter Defined
  • “The path traveled by light in vacuum during a time interval of 1/299792458 of a second.”
kilogram defined
Mass (kilogram)kilogram Defined
  • a cylinder of PLATINUM-IRIDIUM alloy maintained under vacuum conditions by the International Bureau of Weights and Measures in Paris

If The ProtoType Were Cubic, its Edge Length would be About 36.2 mm (1.42”); quite small

second defined
Time (Second)Second Defined
  • 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 cesium 133 atom
    • This is the Definition of an “Atomic” Clock
      • more than 200 atomic clocks are located in metrology institutes and observatories in more than 30 countries around the world
amp defined
Electric Current (Ampere)Amp Defined
  • That constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in a vacuum, would produce between these conductors a force equal to 2 x 10−7Newton per metre of length.
    • What’s a Newton?→ 1kg-m/(s2)
kelvin temperature defined
Thermo-dynamic temperature (Kelvin)Kelvin (Temperature) Defined
  • The unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
  • 273.16K = 0.0098 °C
  • Room Temperature (72 °F) is about 295.5 Kelvins
  • NO “Degree” Sign Used with the Kelvin Unit
mole amt of substance defined
Amount of Substance (mole)mole (amt of Substance) Defined
  • The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilograms of carbon 12.
  • 1 mole = 6.023x1023entities
    • entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
luminous intensity defined
Light Brightness (candela)Luminous Intensity Defined
  • The luminous intensity, in a given direction, of a source that emits monochromatic radiation (one-color light) of frequency 540 x 1012 Hertz (555 nm) and that has a radiant intensity in that direction of 1/683 watt per steradian


  • The are 4 (12.57) Steradians in a Sphere
    • 1 Str = 7.96% of the Sphere Surface
units have evolved
Units Have Evolved
  • Candela Predecessor based on a Flame
    • Hence the Name
  • Temperature Based on Freezing points
    • Water
    • Platinum
  • Second Based on the Sidereal (standard) day
units have evolved1
Units Have Evolved
  • History of the Meter (or Metre)
    • One ten millionth of the distance from the North pole to the equator. 
    • The distance between two fine lines engraved near the ends of a platinum-iridium bar 
    • 1 650 763.73 wavelengths of a particular orange-red light emitted by atoms of krypton-86 (86Kr).
    • The length of the path traveled by light in a vacuum during a time interval of 1/299 792 458 of a second.
si derived units
SI Derived Units
  • The Seven Base Units May be Algebraically Combined to Produce “Derived Units”
    • e.g.:
  • Several DerivedUnits have SpecialUsefulness and arethus Given their OWN Names
old and tired unit sets
Old (and Tired) Unit Sets
  • MKS
    • Stands for Meter-Kilogram-Second as the Most Common Units
      • Predecessor to The SI System
  • CGS
    • Means Centimeter-Gram-Second
      • Still Widely Used
    • Inch-Pound-Sec, Foot-Lb-Min, Ft-Lb-Hour
american engineering system aes still in declining use

Fundamental Dimension

Base Unit





electric charge [Q]

absolute temperature

luminous intensity

amount of substance

foot (ft)

pound (lbm)

pound (lbf)

second (sec)

coulomb (C)

degree Rankine (oR)

candela (cd)

mole (mol)

American Engineering System, AES – Still in (declining) Use

Some Are the SAME SI

conservation of units
Conservation of Units
  • Principle of conservation of units:
    • Units on the LEFT side of an equation MUST be the SAME as those on the RIGHT side of an Equation
  • Then Have Dimensional Homogeneity
    • Needed to Prevent “Apples & Oranges” Confusion
      • e.g., I Buy 100 ft of Wire at One Store and 50 m at another; how much total Wire do I have? (It’s NOT “150”)
unit conversion by chain link
Unit Conversion by Chain-Link
  • To Determine the Amount of Wire I have I Need to Convert to Consistent (Homogeneous) Units
  • Start by Thinking About the Definition of “1”
    • AnyThing divided by ITSELF = “1”
    • Now Consider a “minute”
  • Read as “60 Seconds per minute”
chain link unit conversion
Chain-Link Unit Conversion
  • Units can also be Multiplied and Divided in a manner similar to Numbers
    • This how we get, say, “Square Feet”
      • e.g.; Consider an 8ft x 10ft Engineer’s Cubicle in Dilbert-Land. How Much WorkSpace Does the Engineer Have?
  • Now Back to the Wire
    • Want to Know how many FEET of Wire I have in Total
chain link unit conversion cont
Chain-Link Unit Conversion cont.
  • Check in Table 16.8 and Find “3.2808 ft = 1meter (“3.2808 ft per meter”)
    • Multiply the 50m by this special Value of 1
  • Can “Cancel” The Units by Division
  • So then the Total Wire = 264 ft
chain link examples
Chain Link Examples
  • A World-Class Sprinter can Run 100m in 10s.
    • How Fast is this in MPH?
  • Gasoline In Seoul Costs 1840 Korean-Won (W) for one Liter of Regular Unleaded
    • How Much is this in $ per Gallon
      • Find Currency Exchange Rate → $1 = 1150 W
several forms of 1
Several Forms of “1”
  • Unit Conversion Factors
  • ANYTHING Divided by ItSelf = 1 
units exponent properties
Units – Exponent Properties

This summary assumes that no denominators are 0 and that 00 is not considered. For any integers m and n

raising units to powers
Raising units to POWERS
  • Start again with 1
  • Can do the SAME Thing with Units.
  • And 123 = 1728 so
  • Thus have 1728 “cubic inches” per “Cubic Foot”
  • What’s a “Cubic Yard” in “Cubic Feet”?
  • So have 27 cubic-ft per cubic-yd
    • NOT “9”
7 inches water column
7 inches, Water Column
  • Ms. Ezersky noted that Natural Gas is delivered by PG&E to homes at a pressure of 4-7 “inches of Water Column”
  • This is a unit of pressure, Just Like Pascals or psig
  • A U-Tube Manometer can Measure Pressure Differences in Inches of Water Column
7 inches water column1
7 inches, Water Column
  • To Calc the “in-WC” pressure we need to know some Engineering Physics
  • From ENGR36
    • Where
      • ≡ Liquid SPECIFIC WEIGHT
      • h ≡ Liquid Column Height
  • For Liquid Water at Room Temperature and Pressure
  • Now find 7 in-WC in psig

Natural Gas @ 9.5 inWC

7 inches water column2
7 inches, Water Column
  • Convert out the N & m
white board examples cont
White Board Examples cont.
  • The USA FDA recommends that Adults consume 2200 Calories per Day
    • What then is the “Power Rating” of a Grown Human Being?
      • Note that there are TWO types of “Calories”
        • The Amount of Heat Required to Raise the Temperature of 1 GRAM of water by 1 °C (or 1 Kelvin)
          • Often Called the Gram-CAL; This is what is in the Text
        • The Amount of Heat Required to Raise the Temperature of 1 KILOgram of water by 1 °C
          • Often Called the kgCAL or kiloCal; This is what you read on the side of Food Packaging
tire pressure
Tire Pressure
  • Many AutoMobile Tires have a Maximum Pressure Rating of About 44 psig.
  • Convert 44 psi to kiloPascals (kPa)
ton of refrigeration
Ton of Refrigeration
  • During his Presentation Mr. Ian McClaren of SouthLandIndustries described the “Ice Storage” Cooling System Behind Bldg-1800.
  • He Noted that the Cooling Power of this system was Rated in “Tons”
  • What is a “Ton” of Cooling Power
ton of refrigeration1
Ton of Refrigeration
  • A TON of the refrigeration is defined, roughly, as the COOLING effect of melting 2000 lbs of water ICE over a 24 HOUR Period
    • From PHYS4C (or ASHRAE HandBook) find that the “Latent Heat of Fusion” for ice is 333.55 kJ/kg
  • On WhtBoard Convert a “Ton of Refrigeration” to
    • kW and Btu/hr
white board examples
White Board Examples
  • A 2003 Chevy z06 corvette
    • Has a 5.7 Liter V8 Engine
      • What is the Engine Displacement in cubic-inches?
    • Develops 410 HP
      • What is the Power in Watts?
  • A the Maximum recommended pressure for many 65R15 tires is 44 psi (lbs per sq-inch; NOT lbs)
    • What is this Max Pressure in kPa?
all done for today
All Done for Today

How toSpend theCalories

class question1
¿¿ Class Question ??
  • Let’s Make List of “METRIC” Type Units