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Section 1-13 Conversion

The conversion of quantities in a specific unit into its respective quantiy for another unit is necessary in order to properly evaluate relationships. This is a straight-forward process with individual conversions and the procedure is consistent once understood.

Units defined for parameters involved with natural processes, when relationships are understood, allow for the calculation of other parameters in combination. For example, Newtons law describing inertial forces, Force = mass * Acceleration, is understood when evaluated using specific units. In order to accelerate a mass of 2 kilograms at 3 meters per second per second (m / s^2) a force of 2 * 3 = 6 "newtons" is required. A "newton" is equivalent to a "kg * m / s^2". The measure of mass (kilogram, kg, in this example), distance (meter, m) and time (second, s) in this example demonstrates that the resulting force, (newton) can be calculated by evaluating the expression directly.

Unfortunately, many common units cannot be evaluated directly in this manner. The most common example of this is found when the quantities are expressed using units that do not directly relate. If the previous example is evaluated using pounds-mass (lbm), for the mass, feet (ft), for the distance and minutes (min) for the time, the expression will not yield correct results for the force unless the quantities are expressed in units from the same "unit system". If the quantities are converted into a consisten system, then evaluated, they will yield proper results which are correct.

Re-evaluating the original example using the same quantities requiries that the 2 kg mass be expressed in lbm correctly. A 2 kg mass is the same as a mass of 4.409 lbm. In like manner, an acceleration of 3 m/s^2 is the same as an acceleration of 35433 ft/min^2. The force relating to this is 156224.097 lbm*ft/min^2 = 1.349 pounds-force (lbf) = 6.0 n as shown above.

Unit Converter

Unit Converter Website at http://analysisChamp.com/EEx/ExpEvalCV.asp

These relationships can be properly evaluated using units that are from consistent systems. The System International (SI) is an example of such a system. It allows for calculations to be performed with results that directly relate to known quantities. The expression evaluated using kg, m and s units was consistent with SI and yields force in units of newtons, n. The same quantities, expressed in British Units (lbm, ft, min), yielded the same force, 156224.097 lbm*ft/min^2 which is also 6.0 newtons but appears wrong because the units are non-customary. The British system expresses force in pounds-force (lbf) which relate to pounds-mass (lbm). This relationship is the source of much confusion when evaluating relationships with the British system.

The unit converter and expression evaluator website provided above properly converts quantities into the SI system, evaluates the relationships, and converts the result into the desired units. Demonstrating the previous example:

Conversion Example Screenshot

The expression, "mass * acceleration," is shown as "2*3" and "kg*m/s^2" in the input fields. The desired output units, "lbf", is entered in the next field. Pressing the "calculate" button allows the website to process the data and it returns 1.349 lbf. If "n" is entered in the output field, it returns 6.0 newtons which has been properly evaluated using the same input data.

Many units exist and a listing is provided at http://AnalysisChamp.com/EEx/AllUnitNames.htm. Units can be absolute or biased. Most units are absolute and can be converted from one system to another by using a factor. Length is an example of this. In the SI system, length is given in units of meter, m. An equivalent unit in the British system is the foot (ft), or the inch (in). 1 m = 3.28 ft = 39.37 in. Mass, time, luminesence and many other quantities use absolute units. Temperature is often measured using "biased" units however when expressed as degrees Fahrenheit or celsius. Absolute measurements (degrees Kelvin or Rankine) also exist. Much confusion exists when expressions involving temperature are attempted without converting into these absolute units first.

The British unit system has evolved during many centuries of traditional use. It has evolved in ways that do not recognize the distinction between pounds-force (such as weight) and pounds-mass. In most cases the two measurements are equivalent ie, a "3 pound" object weighs 3 "pounds" and has 3 "pounds" of mass. Unfortunately, this can be very confusing because the weight is dependant on the gravity field in which is is measured. The same stone weighs less in a different field but has the same mass. To correct for this, the British system uses the "slug" as a measure of mass. The "pound-mass" is also used to clarify measurements and the evaluation of expressions.

Mechanical Engineering Design Section 1-13 Conversion
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