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Fundamental Dimensions and Units Chapter 6. Dr. Bahaa Al-Sheikh & Eng. Mohammed Al- Sumady Intoduction to Engineering. Engineering Problems and Fundamental Dimensions. when someone asks you how old you are, you reply by saying “I am 19 years old.”
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Fundamental Dimensions and Units Chapter 6 Dr. Bahaa Al-Sheikh & Eng. Mohammed Al-Sumady Intoduction to Engineering
Engineering Problems and Fundamental Dimensions when someone asks you how old you are, you reply by saying “I am 19 years old.” You don’t say that you are approximately 170,000 hours old or 612,000,000 seconds old, even though these statements may very well be true at that instant!
Engineering Problems and Fundamental Dimensions 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.
Systems of Units The most common systems of units are : • International System (SI) . • British Gravitational (BG) . • U.S. Customary units.
International System (SI) of Units 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. It is derived from Newton’s second law of motion. 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).
British Gravitational (BG) System In the British Gravitational (BG) system of units, the unit of length is a foot (ft), which is equal to 0.3048 meter The unit of temperature is expressed in degree Fahrenheit (F) or in terms of absolute temperature degree Rankine (R). The relationship between the degree Fahrenheit and degree Rankine is given by:
British Gravitational (BG) System The relationship between degree Fahrenheit and degree Celsius is given by: The relationship between the degree Rankine and the Kelvin by:
U.S. Customary Units The unit of length is a foot (ft), which is equal to 0.3048 meter. The unit of mass is a pound mass (lbm), which is equal to 0.453592 kg; and the unit of time is a second (s). The units of temperature in the U.S. Customary system are identical to the BG system
Unit Conversion Read about accident caused by NASA loosing a spacecraft in Pg. :138-139.
Unit Conversion Example 6.1 : A person who is 6 feet and 1 inch tall and weighs 185 pound force (lbf) is driving a car at a speed of 65 miles per hour over a distance of 25 miles. The outside air temperature is 80F and has a density of 0.0735 pound mass per cubic foot (lbm/ft3). Convert all of the values given in this example from U.S. Customary Units to SI units.
Unit Conversion (Example 6.2 ) Work out Example 6.2 at home .If you have any question ask me .
Dimensional Homogeneity What do we mean by “dimensionally homogeneous?” Can you, say, add someone’s height who is 6 feet tall to his weight of 185 lbf and his body temperature of 98F?! Of course not!
For Equation 6.1 to be dimensionally homogeneous, the units on the left-hand side of the equation must equal the units on the right-hand side. This equality requires the modulus of elasticity to have the units of N/m2, as follows:
Numerical versus Symbolic Solutions • When you take your engineering classes, you need to be aware of two important things: (1) understanding the basic concepts and principles associated with that class (2)how to apply them to solve real physical problems (situations) • Homework problems in engineering typically require either a numerical or a symbolic solution. • For problems that require numerical solution, data is given. In contrast, in the symbolic solution, the steps and the final answer are presented with variables that could be substituted with data.
Numerical versus Symbolic Solutions (Example 6.4) Determine the load that can be lifted by the hydraulic system shown. All of the necessary information is shown in the Figure.
Numerical versus Symbolic Solutions (Example 6.4) • Numerical Solution: We start by making use of the given data and substituting them into appropriate equations as follows.
Numerical versus Symbolic Solutions (Example 6.4) • Symbolic Solution: For this problem, we could start with the equation that relates F2 to F1, and then simplify the similar quantities such as p and g in the following manner:
Significant Digits (Figures) One half of the smallest scale division commonly is called the least count of the measuring instrument. For example, referring to Figure 6.4, it should be clear that the least count for the thermometer is 1F (the smallest division is 2F), for the ruler is 0.05 in., and 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 71.25F and later use this value to carry out other calculations. 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.
Significant Digits (Figures) Significant digits are numbers zero through nine. However, when zeros are used to show the position of a decimal point, they are not considered significant digits. For example, each of the following numbers 175, 25.5, 1.85, and 0.00125 has three significant digits. Note the zeros in number 0.00125 are not considered as significant digits, since they are used to show the position of the decimal point
Significant Digits (Figures) The number of significant digits for the number 1500 is not clear. It could be interpreted as having two, three, or four significant digits based on what the role of the zeros is. In this case, if the number 1500 was expressed by 1.5 *10^3, 15*10^2, or 0.015 *10^5, it would be clear that it has two significant digits. By expressing the number using the power of ten, we can make its accuracy more clear. However, if the number was initially expressed as 1500.0, then it has four significant digits and would imply that the accuracy of the number is known to 1/10000.
Significant Digits (Figures) • Addition and Subtraction Rules • Multiplication and Division Rules
Engineering Components and Systems The primary function of a car is to move us from one place to another in a reasonable amount of time. The car must provide a comfortable area for us to sit within. Furthermore, it must shelter us and provide some protection from the outside elements, such as harsh weather and harmful objects outside. The automobile consists of thousands of parts. When viewed in its entirety, it is a complicated system. Thousands of engineers have contributed to the design, development, testing, and supervision of the manufacture of an automobile. These include electrical engineers, electronic engineers, combustion engineers, materials engineers, aerodynamics experts, vibration and control experts, airconditioning specialists, manufacturing engineers, and industrial engineers.
Engineering Components and Systems When viewed as a system, the car may be divided into major subsystems or units, such as electrical, body, chassis, power train, and air conditioning (see the following figure) the electrical system of a car consists of a battery, a starter, an alternator, wiring, lights, switches, radio, microprocessors, and so on each of these components can be further divided into yet smaller components. In order to understand a system, we must first fully understand the role and function of its components.
Engineering Components and Systems During the next four or five years you will take a number of engineering classes that will focus on specific topics. You may take a statics class, which deals with the equilibrium of objects at rest. You will learn about the role of external forces, internal forces, and reaction forces and their interactions
Engineering Components and Systems Later, you will learn the underlying concepts and equilibrium conditions for designing parts. You will also learn about other physical laws, principles, mathematics, and correlations that will allow you to analyze, design, develop, and test various components that make up a system. It is imperative that during the next four or five years you fully understand these laws and principles so that you can design components that fit well together and work in harmony to fulfill the ultimate goal of a given system
Physical Laws and Observations in Engineering The key concepts that you need to keep in the back of your mind are the physical and chemical laws and principles and mathematics. we use mathematics and basic physical quantities to express our observations in the form of a law. Even so, to this day we may not fully understand why nature works the way it does. We just know it works.
Physical Laws and Observations in Engineering There are physicists who spend their lives trying to understand on a more fundamental basis why nature behaves the way it does. Some engineers may focus on investigating the fundamentals, but most engineers use fundamental laws to design things. Engineers are also good bookkeepers.
Physical Laws and Observations in Engineering To better understand this concept, consider the air inside a car tire. If there are no leaks, the mass of air inside the tire remains constant. This is a statement expressing conservation of mass, which is based on our observations. If the tire develops a leak, then you know from your experience that the amount of air within the tire will decrease until you have a flat tire. Furthermore, you know the air that escaped from the tire was not destroyed; it simply became part of the surrounding atmosphere. The conservation of mass statement is similar to a bookkeeping method that allows us to account for what happens to the mass in an engineering problem.
Physical Laws and Observations in Engineering Conservation of energy is another good example. It is again similar to a bookkeeping method that allows us to keep track of various forms of energy and how they may change from one form to another. Another important law that all of you have heard about is Newton’s second law of motion. Newton expressed his observations using mathematics, but simply expressed, this law states that unbalanced force is equal to mass times acceleration.
Learning Engineering Fundamental Concepts and Design Variables from Fundamental Dimensions
SUMMARY You should understand the importance of fundamental dimensions in engineering analysis. You should also understand what is meant by an engineering system and an engineering component. You should also realize that physical laws are based on observation and experimentation. You should know the most common systems of units: SI, BG, and U.S. Customary. You should know how to convert values from one system of units to another. You should understand the difference between numerical and symbolic solutions.
