Units and Dimensional Analysis
Dimensional Analysis is an key engineering technique for insuring that units used in an equation are appropriate and consistent for a given problem. Some important points regarding dimenstional analysis are:
- Dimensional analysis is the process of determining if units used in an equation are consistent and appropriate.
- The International System of Units (SI) specifies a set of seven base units from which all other units of measurement are formed. Derived units are based on those seven base units.
- Dimensional analysis may involve using conversion factors, which are ratios of related physical quantities expressed in the desired units.
- Unit analysis help detemine appropriate conversion factors when using different units to describe an entity of phenomena.
Base and Derived Units
For most quantities, a unit is absolutely necessary to communicate values of that physical quantity. Imagine you need to maintain a certain amount of water to grow a crop. How would you indicate the required quantity without specifying some unit (of volume, in this case?
However, not all quantities require a unit of their own. Using physical laws, units of quantities can often be expressed as combinations of units of other quantities. Only a small set of "core" units is required. These units are called base units, and other units are derived units. Derived units are a matter of convenience, as they can be expressed in terms of basic units.
Different systems of units are based on different choices of base units. The most widely used system of units is the International System of Units, or SI. We will use SI units throughout this book. There are seven SI base units, and all other SI units can be derived from these base units.
The seven base SI units are:
- Length: m (meter)
- Mass: kg (kilogram)
- Time: s (second)
- Electric Current: A (Ampere)
- Thermodynamic Temperature: K (degrees Kelvin)
- Amount of Substance: mol ( mole )
- Luminous Intensity: cd (candela)
Derived units are based on units from the SI system of units. For example, volume is a derived unit because volume is based on length. To calculate the volume of something, you multiply the width x length x height, all in meters. Therefore, the derived unit for volume is m3. Here is a list of some commonly derived units:
- Area: m2
- Volume: m3
- Velocity: m/s
- Acceleration: m/s2
- Density: g/mL or g/cm3
- Force: kg⋅m/s2,OR the Newton (N)
- Energy: N⋅m, OR the Joule (J)
Common Conversion Factors
Wikipedia provides a useful summary of conversion factors for many units at: https://en.wikipedia.org/wiki/Conversion_of_units.
An online unit conversion factor calculator is available at: https://www.unitconverters.net/.
Additional Information:
Some useful links addressing dimensional analysis are provided below.
Greg Schwanbecks "How to Convert Units - Unit Conversion Made Easy" video on YouTube: http://www.youtube.com/watch?v=XKCZn5MLKvk.