Dimensions, Units, and Conversions Introduction to Engineering

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Dimensions, Units, and ConversionsIntroduction
to Engineering

• College of Science and Engineering
• The University of Texas Pan American

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Objectives

• Explain the difference between dimensions and
  units.
• Check for dimensional homogeneity.
• Explain SI unit prefixes.
• Convert between SI and U.S. Customary units.
• Explain the difference between mass and weight.
• Assignment Handout or visit website.

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Difference Between Dimensions and Units

• Why are dimensions and units important?
• Dimensions are used to describe objects and
  actions. The three most basic dimensions are
  length, time, and mass
• Units are used to establish the size or magnitude
  of a dimension. Must be based on some convention
  with standards

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Difference Between Dimensions and Units

• Dimensions are divided into fundamental and
  derived. Fundamental are the most basic or
  elementary dimensions necessary to describe the
  physical state of an object. Derived dimensions
  are defined based upon scientific and engineering
  equations, and are a combination of fundamental
  dimensions.

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Fundamental and Derived Dimensions
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Difference Between Dimensions and Units

• Dimensions are fundamental, unchanging
  characteristics or properties of an object.
• Units on the other hand are arbitrary they can
  be changed by the vote of a governing body.
• History of Units cubit, meridian mile, foot,
  etc

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Dimensional Analysis

• Equations in Science and Engineering must be
  dimensionally homogeneous, in other words, the
  dimensions on each side of the equation should be
  the same when dimensions (not units) are
  substituted for the variables and constants.
• For example, if you are calculating velocity from
  the distance traveled in an elapsed time, the
  dimensions on either side should be equal, i.e.,
• Velocity Distance traveled / Elapsed time
• Distance traveled Length (L)
• Elapsed time Time (T)
• Velocity Length / Time L / T

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Unit Systems

• Systems of units differ in the treatment of mass
  and force.
• In the SI system, mass was chosen as the third
  fundamental dimension and force is a derived
  unit.
• In the English system, force was chosen as the
  third fundamental dimension and mass is a derived
  unit.

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The International System of Units

• SI units are derived into three classes base
  units (seven), derived units, and supplementary
  units (two).

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Base Units
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Derived Units
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Supplementary Units

• Radian is equal to the angle between two radii of
  a circle that cut off a piece of the
  circumference whose length is equal to the length
  of the radius.
• Steradian is equal to the solid angle which cuts
  off, on the surface of a sphere, an area equal to
  the area of a square whose sides are the same
  length as the radius of the sphere.

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The International System of Units

• To avoid very small or very large numbers in the
  SI system of units, unit prefixes have been
  developed based on power of ten.

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Unit Systems

• Fundamental and some important derived dimensions
  for the three common systems of units.

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Unit Systems and ConversionsExact Conversions
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Unit Systems and ConversionsExact Conversions
The internet provides valuable resources that can
be used to obtain a variety of different
conversion factors or completely carry out the
conversions for you. Please refer to the
following website
http//www.onlineconversion.com/
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Unit Systems and ConversionsExample

• The employment of the information given in the
  preceding tables allows for ease of conversion
  between different units.
• For example, if you are traveling at a speed of
  65 miles per hour (mi/hr or mph) and wish to know
  your speed in feet per second (ft/s) and in
  meters per second (m/s) you would have to carry
  out the following conversions

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Mass Weight

• The mass of an object is constant.
• Weight is the force required to lift or support
  an object in a gravitational field or an
  acceleration field.
• Acceleration of gravity changes with location.
• For example, on the Moon, your mass would be the
  same as here on Earth, yet your weight would be
  less due to the lower gravitational acceleration
  present on the Moon.

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Open Forum
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Quiz

• Carry out the following conversions
• 125 days to seconds
• 16 lbm/ft3 to kg/m3
• 75 slug/min to kg/s
• 15 ft3 to gallons

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Quiz Solutions
a)
b)
Notice that the (ft/m) part is cubed because we
cannot cancel out ft3 with just ft, remember, the
dimensions must be the same.
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Quiz Solutions
c)
d)