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## Engineering 10

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Units &Conversions

Bruce Mayer, PE

Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

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

- 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...

http://www.bipm.org/en/si/

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

http://www.bipm.org/en/si/

¿¿ 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

- 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

Length or Distance (meter)

1 meter

Laser

1/299792458 s

photon

Meter Defined- “The path traveled by light in vacuum during a time interval of 1/299792458 of a second.”

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

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

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)

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

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.

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

555nmcolor

- The are 4 (12.57) Steradians in a Sphere
- 1 Str = 7.96% of the Sphere Surface

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 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

- The Seven Base Units May be Algebraically Combined to Produce “Derived Units”
- e.g.:

- Several DerivedUnits have SpecialUsefulness and arethus Given their OWN Names

Derived Units Family Tree

No Special Names

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
- IPS, FPM, FPH
- Inch-Pound-Sec, Foot-Lb-Min, Ft-Lb-Hour

Base Unit

length

mass

force

time

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) UseSome Are the SAME SI

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

- 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

- 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.

- 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

- 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

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

- 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

- 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 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 Column

- Convert out the N & m

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

- Many AutoMobile Tires have a Maximum Pressure Rating of About 44 psig.
- Convert 44 psi to kiloPascals (kPa)

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 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

- 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

How toSpend theCalories

¿¿ Class Question ??

- Let’s Make List of “METRIC” Type Units

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