Chapter 5 Engineering Problems and Fundamental Dimensions

Introduction In this chapter, we will explain fundamental engineering dimensions, such as: length and time, and their units, such as meter and second, and their role in engineering analysis and design. As an engineering student, and later as practicing engineer, when performing an analysis, you will find a need to convert from one system of units to another. In this chapter, we will also emphasize the fact that you must always show the appropriate units that go with your calculations.

and luminous intensity. Today, based on what we know about our physical world, we need seven fundamental or base dimensions to correctly express what we know of the natural world. They are: length, mass, time, temperature, electric current, amount of substance, and luminous intensity. شدة الإضاءة

Systems of Units International System (SI) of Units Throughout the world, there are several systems of units in use today. The most common systems of units are: International System (SI), British Gravitational (BG), and the U.S. Customary units International System (SI) of Units We begin our discussion of systems of units with the International System (SI) of units, because SI is the most common system of units used in the world. The origin of the present day International System of units can be traced back to 1799 with meter and kilogram as the first two units. A list of SI base (fundamental) units is given in Table 6.1

The CGPM in 1960 adapted the first series of prefixes and symbols of decimal multiples of SI units. Over the years, the list has been extended to include those listed in Table 6.2.

The units for other physical quantities used in engineering can be derived from the base units. For example, the unit for force is the Newton. One Newton is defined as a magnitude of a force that when applied to 1 kilogram of mass, will accelerate the mass at a rate of 1 meter per second squared (m/s2). That is: 1N =(1kg)(1m/s2). Examples of commonly derived SI units used by engineers are shown in Table below

Or T (oF) = 1.8 T (oC) + 32 Or T (oR) = 1.8 T (K) And T (K) = 273 + T (oC)

Example Or 1 mile=1.6 km 65 x 1.6 = 104 km

Example 1

Dimensional Homogeneity Another important concept that you need to understand completely is that all formulas used in engineering analysis must be dimensionally homogeneous. if we were to use the formula L= a+ b+ c, in which the variable L on the left-hand side of the equation has a dimension of length, then the variables a, b, and c on the right-hand side of equation should also have dimensions of length

Example 2 معامل مرونة

Example 3

Significant Digits (Figures) Engineers usually record the results of measurements and calculations using numbers. Significant digits (figures) represent and convey the extent to which recorded or computed data is dependable. If we are interested in measuring the temperature of room air using a thermometer, we can use; 1- the dimensions of an engineering ruler, and 2- the pressure of a fluid in a the pressure gage as shown later As you can see from these examples, the measurement readings fall between the smallest scale division of each instrument. In order to take the guess reading and for consistency, we record the measurement to one half of the smallest scale division of the measuring instrument.

Significant Digits (Figures) For example, referring to Figure next page, it should be clear that the least count for the thermometer is 1F as the smallest division for the thermometer is 2 F for the ruler is 0.05 inches (as smallest division is 0.1 for the pressure gage is 0.5 inches of water. Therefore, using the given thermometer, it would be incorrect to record the air temperature as 71.25 F Instead, it should be recorded as 71 ±1F. This way, you are telling the reader or the user of your measurement that the temperature reading falls between 70F and 72F.