by Dale Baker
It often occurs that a high-quality product that comes out of an effective design process (including math and science) is taken for granted, such as a bridge standing for decades or centuries with no problems. Such a situation is illustrated with the Golden Gate Bridge, which has stood for more than seven decades since it was opened on May 27, 1937 (Figure 3). When an inferior solution comes out of a flawed design process, catastrophe may result, and a bridge may collapse with possible loss of lives. Such an occurrence is illustrated below by the Tacoma Narrows Bridge Collapse (Figure 3). On November 11, 1940, this bridge, located at Puget Sound, Washington, began swaying strongly in the wind and eventually broke up due to the resonance of the bridge which twisted until it broke up. There are mathematical tools available to analyze for waves and resonance of structures, but they were not applied in the design process of the bridge. This demonstrates the importance and need to broadly explore and utilize mathematics and science appropriate to the engineering design problem at hand.
Figure 5.3
The Golden Gate Bridge and the Tacoma Narrows Bridge. The Golden Gate Bridge, a signature landmark of San Francisco, had the worlds longest span when opened May 27, 1937. The Tacoma Narrows Bridge, Puget Sound, Washington, broke up after in a strong wind on November 11, 1940.
Activity - Impact of disaster on an industry's design practice.
There have been many other disasters that occurred because of a flawed design process. One is the consecutive crashes of two British Comet jets in 1954. Go to the two web sites that describe the investigation and the resulting design changes: http://en.wikipedia.org/wiki/De_Havilland_Comet and http://judkins.customer.netspace.net.au/comet.htm. How did the disasters cause engineers to change the airplane’s design?
What Is Science?
The meaning of what science is can be debated and has changed over time. It is reasonable to think today of science as a process by which humans try to understand how the natural world works and how it came to be that way. The branches of science most frequently used by engineers include physics, chemistry, and biology. This is reflected by the fact that almost all undergraduate engineering programs require students to take foundational courses in those subjects. An example of how such science connects to engineering can be shown with the global problem of the lack of access to clean water by populations in some of the developing countries around the world. In developed countries turning on the bathroom faucet gives safe and drinkable water gushing from the tap. This safe and convenient water is actually a luxury that is not present everywhere. When it is not available, and water is not purified, people can become sick or even die from causes such as dehydration, cholera, dysentery, and cancer. So how have engineers figured out how to find, transport, purify, sanitize, and deliver water to those who need it? The following example should help answer that question as well as give a concrete example of how science connects with engineering.
Although more than half of the surface of the earth is covered with water, it is not accessible to plants, animals, or humans because of its % salt content. So, can we just remove the salt? No, because it is not so easy and can be costly. Science provides a variety of phenomena that can be used to desalinate water, and a few will be presented here. Chemistry tells us that there are many ways to desalinate water. One of the ways that water can be purified is by evaporation and condensation, which leaves the impurities in the original water. Another way is that, in freezing water the ice leaves the impurities behind in the unfrozen liquid. Another way is based on the fact that certain pore sizes of molecular membranes will allow water to diffuse through the membrane under pressure while leaving behind larger complexes of sodium and chlorine. Chemistry also has data on a variety of physical properties of water and salt water, including the thermodynamic data of heat of evaporation, heat of condensation, and heat of freezing. So what can be done with the different phenomena and all the data that are available?
The first question to answer is: Are there any types of engineering fields with individuals that work with such phenomena and data with the goal of desalinating water? The answer is yes. Chemical engineers are trained to use such phenomena and data to design and build large-scale processing plants for producing products such as cosmetics, antibiotics, and gasoline as well as purified water. Today, millions of gallons of water are being desalinated by flash evaporation, which uses evaporation and condensation phenomena, and by reverse osmosis, which uses molecular membrane technology based on membrane diffusion principles. A nuclear driven flash evaporation plant located on the Caspian Sea is shown in Figure 4.
Figure 5.4
Nuclear powered flash distillation desalination equipment located on the Caspian Sea.
What Is Mathematics?
Math is utilized in a variety of ways within many fields of engineering. The most crucial aspects of math within this field involve cost–benefit–risk analysis and the use of mathematical models. “Mathematical models may include a set of rules and instructions that specifies precisely a series of steps to be taken, whether the steps are arithmetic, logical, or geometric. Sometimes even very simple rules and instructions can have consequences that are difficult to predict without actually carrying out the steps. ... Often, it is fairly easy to find a mathematical model that fits a phenomenon over a small range of conditions ... but it may not fit well over a wide range.” (AAAS) Given the importance of having an end result that not only works, but also is safe and dependable, it is easy to understand why the use of mathematical models is an invaluable aspect of the engineering design process, as well as how these models would be applied to various steps within this process. Nearly every aspect of mathematics can be, and is, applied to the engineering design process in some way. All fields within engineering require an advanced knowledge of, and the ability to properly use, many math skills, including (but not limited to) algebra, calculus, geometry, measurements, tables and graphic representations of results, mathematical formulas, and time lines.
Activity—What kinds of science and math do engineers need to address some of today’s global societal issues?
Consider the list of contemporary global societal issues shown in Table 1. From the list, select two or three global issues of interest to you and write them down. Think about them and then write about the math and science that might be used to address each of the particular issues.
Drought in the Southwest United States.
Lack of drinkable water in many nations.
Aging bridges that are prone to collapse.
Lack of accessible and reliable public transportation.
Need for renewable energy sources.
Children and others disabled by landmines and other weapons.
Environmental polution from oil and chemical spills (Figure 5).
Need for safer cars.
Global warming from carbon emissions from burning fossil fuels (Figure 5).
Unsafe and unpleasant airports around the world.
Figure 5.5
Icebergs breaking off glaciers and an oil spill.
Review Questions
The following questions will help you assess your understanding of the What Is the Role of Science and Mathematics in Engineering? section. There may be one, two, three, or even four correct answers to each question. To demonstrate your understanding, you should find all of the correct answers.
Mathematical models describe scientific phenomena
can evaluate cost
require a calculator
are easier to build than physical models
Engineers use mathematics and science to understand the world
solve problems
build models
design a process
An example of a mathematical model is the budget for product development
drawings used to design a product
the engineering design process
rate of the flow of water through a hose
Review Answers
What Is the Role
of Science and Mathematics in Engineering?
a,b
b,c,d
d
How Do Math and Science Connect with Engineering in High School and College?
Preparatory High School and College Courses
Many high school and college courses are needed to prepare for an engineering education.
Precollege Courses
If a student wants to consider the possibility of pursuing a college degree in engineering, what types of K-12 courses should he/she take? Before even entering high school, students should investigate the admittance requirements of the universities for a student’s high school education. Universities set guidelines of prerequisite requirements upon applying. Most require a minimum of four years of high school mathematics, including at least the basic math courses (algebra one and two, geometry, trigonometry, and analytical geometry), and a minimum of four years of science, again covering at least the basic courses (chemistry, biology, and physics). Also, along with these set requirements for course work, most reputable engineering programs require submitting a placement exam (such as ACT or SAT) scores and show no deficiencies in either math or science.
College Courses
Once admitted into a college engineering program students will be required to complete a year of college math and physics (about 10 courses). This would include fundamental science courses (Chemistry, Biology, Physics) and basic math courses (Calculus I, II, III and Differential Equations). These are usually the minimum level required for engineers in general, but specific engineering disciplines may require more. Most programs also require about a semester (5 courses) of “engineering science courses” where the understandings of math and science are directed toward broad applied science and math courses. They might include courses such as Circuits, Statics, Dynamics, Fluids, Materials, Thermodynamics, and Statistics. The connections of math and science to engineering in these applied courses are quite obvious, for example, with the chemistry and differential equations used in Engineering Thermodynamics.
Science and Mathematics Courses Connected to Engineering
Basic math and science provide the tools of mathematical techniques and science phenomena that engineers use to address design problems related to phenomena of the natural world. They build on similar math and science foundational courses in high school that are introductory with a lower level of math that describe natural phenomena. The college level math and science courses provide a base for advanced math and science courses necessary to address more complex problems in a given engineering discipline. The basic math and science courses have also been utilized for a broad range of practical engineering applications to develop courses that are referred to as engineering science courses such as Thermodynamics, Circuits, and Fluids. For example, the Engineering Science course of Fluids is typically taken by Chemical, Mechanical, Aerospace, and Biomedical Engineering students. That is because the general principles of Fluids apply to fluid flow of air for airplanes as well as flow of gases in internal combustion engines while fluid flow of liquid is used to analyze blood flow in humans as well as flow of chemicals in chemical processing plants. Thus, the connection of basic math and science to engineering is shown directly and unambiguously both as a base for advanced courses as well as being integrated into broadly subscribed Engineering Science courses. Brief descriptions of the basic math and science courses are presented here followed by short descriptions of the most widely subscribed Engineering Science courses.
Physics. Physics is the science of matter and the interaction of matter. It describes and predicts phenomena about matter, movement and forces, space and time, and other features of the natural world.
Chemistry. Chemistry is the science of the phenomena about composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions, especially as related to various atoms, molecules, crystals, and other aggregates of matter.
Biology and Biological Sciences. Biology is the science of living organisms that describes and predicts phenomena related to the structure, function, growth, origin, evolution, and distribution of living things as well as the interactions they have with each other and with the natural environment.
Calculus. Calculus is the mathematics of change which includes the study of limits, derivatives, integrals, and infinite series; many disciplines in engineering address problems that must be solved by differential calculus and integral calculus.
Differential Equations. Differential equations are equations with variables that relate the values of the function itself to its derivatives of various orders. Differential equations are used for engineering applications where changing quantities modeled by functions and their rates of change expressed as derivatives are known or postulated giving solutions that are dependent on boundary conditions.
Engineering Courses Connected to Science and Mathematics
As discussed previously, the basic math and science courses have been utilized for a broad range of practical engineering applications to develop courses that are referred to as engineering science courses such as Thermodynamics, Circuits, and Fluids. For example, the Engineering Science course of Fluids is typically taken by Chemical, Mechanical, Aerospace, and Biomedical Engineering students. That is because the general principles of Fluids apply to fluid flow of air for airplanes as well as flow of gases in internal combustion engines while fluid flow of liquid is used to analyze blood flow in humans as well as flow of chemicals in chemical processing plants. Thus, the connection of basic math and science to engineering is shown directly and unambiguously both as a base for advanced courses as well as being integrated into broadly subscribed Engineering Science courses. Brief descriptions of the basic math and science courses are presented here followed by short descriptions of the most widely subscribed Engineering Science courses. Similar arguments apply to other engineering science courses that are also broadly subscribed by many disciplines. The courses will be briefly described in this section.
Dynamics. The field of dynamics uses the knowledge of classical mechanics that is concerned with effects of forces on motion of objects. Engineers use the concepts in design of any moving parts, such as for engines, machinery and motors. For example, a mechanical engineer would have used Dynamics extensively in the design of the pneumatically powered, multirow seed planter that was invented in 1956.
Electric Circuits. The field of circuits applies physics of electrical phenomena to the design, analysis, and simulation of linear electric circuits and measurements of their properties. The principles are used in circuit designs for wide ranging applications such as motors, cell phones, and computers. For example, an electrical engineer would have used Circuits extensively in the design in 1980 of the first circuit board with built-in self-testing technology.
Fluids. The subject of fluid mechanics uses physics of fluids to understand and predict the behavior of gases and liquids at rest and in motion which are referred to as fluid statics and fluid dynamics. As described previously, there are a broad set of engineering applications including air flow for airplanes and in internal combustion engines as well as fluid flow of liquid blood in humans as well as flow of chemicals in chemical processing plants. For example, a chemical engineer would have used the subject of Fluids extensively in the design of deep-draft pumping of oil from a depth of 4800 feet in the Gulf of Mexico begun in 2000.
Materials Science and Engineering. This subject utilizes the synthesis techniques of chemistry and the characterization tools of physics, such as the atomic force microscope, to control and characterize the properties of the structure and properties of solid materials. The principles of materials science are broadly used by a variety of engineering disciplines including electronics, aerospace, telecommunications, information processing, nuclear power, and energy conversion. Applications vary from structural steels to computer microchips. A materials engineer would have applied the principles of Materials Science extensively in the design of synthetic skin which ca
n act as a framework for live cells that grow into a layer of skin while the framework is absorbed by the body.
Mechanics of Solids. This subject uses concepts and knowledge of continuum mechanics emerging from physics and mathematics to understand and predict the behavior of solid matter under external actions, such as external forces, temperature changes, and displacement or strain. The principles are broadly used on a variety of topics for a number of engineering disciplines. It is part of a broader study known as continuum mechanics. Engineers use the principles to determine what happens when a stress is applied to a component. Concepts are useful anytime that a component departs away from the rest shape due to stress. The amount of departure from rest, which is initially elastic or proportional to stress, is safe as long as the material is below its yield strength. For example, an aerospace engineer would have used Mechanics of Solids extensively in the design of the Space Shuttle first launched on April 12, 1981.
Statics. This is the engineering application of a branch of physics called Mechanics. It describes bodies which are acted upon by balanced forces and torques so that they remain at rest or in uniform motion. In statics, the bodies being studied are in equilibrium. The equilibrium conditions are very similar in the planar, or two-dimensional, and the three-dimensional rigid body statics. These are that the vector sum of all forces acting upon the body must be zero; and the resultant of all torques about any point must be zero. Thus it is necessary to understand the vector sums of forces and torques. For example, a civil engineer would have used Statics extensively in the design of the Golden Gate Bridge in 1937.