Notes From Chapter 7, Thinking Like an Engineer

Unit Conversion and Dimension Analysis

A Dimension is a physical idea that is measurable, it is a word description with no numbers, Whereas a Unit quantifies a dimension using a number to describe the quantity.  For example... Length is a Dimension, and the Units for length include a mile, foot, meter, light-year, and fathom.

The SI System is based of off multiples of 10. Using an SI Prefix can help eliminate using scientific notation and a large amount of zeros in a number. For example you can take 500,000 meters and make it 500 kilometers.

The 7 fundamental dimensions and base units:

1. Length (L) - Meter (m)
2. Mass (M) - Kilogram (kg)
3. Time - Second (s)
4. Temperature - Kelvin (K)
5. Amount of Substance - Mole (mol)
6. Light Intensity - Candela (cd)
7. Electric Current - Ampere (A)

The Official SI Rules are very important to know. They are:

• If a unit abbreviation appears as a capital letter, it has been named after a person; all other abbreviations appear as lowercase letters.
• Symbols of units are not shown as plural.
• Symbols are not shown with periods unless they appear at the end of a sentence.
• Symbols are written in upright Roman type (m, k, L) to distinguish them from mathematical variables (m, k, l), which are indicated by italics.
• One space separates the number and symbol, except with the degree symbol referring to an angle.
• Spaces or commas may be used to group digits by threes.
• Symbols for derived units formed by multiple units are joined by a space or the center dot. Care must be taken to avoid confusing SI prefixes with units.
• Symbols for derived units formed by dividing units are joined by a virgule (the "slash" /) or shown with a negative exponent. Care must be taken to appropriately display the entire denominator.
• Do not combine prefixes to form compound prefixes. Use the single correct prefix.

SI stands for Systeme Internationale, or International System. SI is the metric system of measurements. AES stands for American Engineering System and it is in common use by the general public in the United States. USCS stands for United States Customary System and is generally referred to as "English" units. I do prefer AES because it has been the system I have used all of my life.

The Unit Conversion Procedure goes as follows:

1. Write the value and unit to be converted
2. Write the conversion formula between the given unit and the desired unit.
3. Make a fraction, equal to 1, of the conversion formula in step 2, such that the original unit in step 1 is located either in the denominator or the numerator, depending on where it must reside so that the original unit will cancel.
4. Multiply the term from step 1 by the fraction developed in step 3.
5. Cancel units, perform mathematical calculations, and express the answer in "reasonable" terms, not too many decimal places.

Sometimes Multiple Conversion Factors are needed. You can multiply several conversion factors as many times as needed in order to reach desired unit. For example, seeing how many yards is in 123 miles.

(123 mi) (5,280 ft / 1 mi) (1 yd / 3 ft) = 216,000 yd

There are 22 Derived units in the SI System all of which are named after famous engineers who are dead now. The graph shows some of the Derived Units and I have underlined the 5 common units.

A Note of caution is that a letter might represent more than one discipline. Such as Pressure (P) and Power (P). Just be sure to know the nomenclature and what Units are being used in the problem.

A Dimensionless Unit is a unit that has no physical dimension applicable. For example a radian has a value of units but no dimension.

1 radian [rad] = S/r