lesson 1_ converting units and problem solving.pdf

Lesson 1:Converting Units and Problem Solving

Objective

In this section we will answer the following questions:

Recognize units used in the SI and English Systems.Covert units within the same system and convert units to another system.Apply the problem solving process.

Reading Assignment

Read the online lecture and sections 2.2.2, 2.2.3, 2.2.4, 2.2.5 in Water Hydraulics bySpellman.

Lecture

Units

The measurement of any quantity is represented by a value and a particular unit. Forexample we can make a measurement of the length of an object and say that it is 10 ft. Tosay that something is 10 has no meaning. As a water/wastewater technician it is important tounderstand units in both the English and SI systems. It is also important to use a consistent setof units when making calculations.

The most widely used system of measurement in the world is the Systme International(French for International System), which is abbreviated SI. The base quantities are listed inFigure 1-1. The SI system is by far the easiest system to use when dealing with the laws andequations of water hydraulics. However, students typically find it difficult to visualize orconceptualize these units because they are unfamiliar with them. There will be problemsthroughout the semester that will use these units. Along with the base units comes the use ofprefixes to define larger and smaller units in multiples of ten and those are listed in Figure 1-2.

Quantity Unit AbbreviationLength Meter MTime Second SMass Kilogram Kg

ElectricCurrent

Ampere A

Temperature Kelvin K

Lesson 1: Converting Units and Problem Solving http://water.me.vccs.edu/courses/CIV240/lesson1_print.htm

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Amount ofSubstance

Mole Mol

LuminousIntensisty

candela cd

Figure 1-1. SI Base Quantities

Prefix Abbreviation ValueGiga GMega MKilo k

Hecto hDeka daDeci dCenti cMilli mmicro nano n

Figure 1-2. SI Prefixes

In the United States, the most common system of measurement is the English system. Thissystem consists of familiar units such as the pound, foot, inch, and so on. In this course, theEnglish will be the primary system used. The English system is difficult to use because thelist of units is extensive. There are, however, conversions we can use to aid us in problem

solving. The most common base units are listed in Figure 1-3.

QuantityUnit Abbreviation

Force Pound lbLength Foot ftTime Second sTemperature Fahrenheit F

Figure 1-3. English Base Quantites

In both systems, physical units can be placed into two categories: base units and derivedunits. The base units listed in Figures 1-1 and 1-3 are defined in terms of a standard. For

example, the meter is defined as the length of path traveled by light in vacuum during a timeinterval of 1/299,792,458 m/s. English base units are defined in terms of their SI counterpart.


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Derived units are defined in terms of base quantities. For example, pressure is defined as theforce per unit area with force and length being the base quantities.

Converting Units

We know that any quantity measured is made up of a number and a unit. Many times we aregiven a quantity in one set of units, but we need to express it in another set of units. To dothis we need a conversion factor. Suppose that we measure a length of rope to be 18 in. long,and we want to express this in centimeters. We will need to use the conversion factor

1 in. = 2.54 cm or 1 in. = 2.54 cm/in.

Since mathematics tells us that dividing any number by itself equals 1 and multiplying by 1does not change anything, the length of our rope is

Note that the units of inches cancelled out and we were left with centimeters.

Example: How many yards are in the 100 m dash?

We know that

1 yd = 3ft = 36 in. =

(note: 100 cm in 1 m)

The conversion is

Next we set up the equation to solve.


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Example: Express 55 miles per hour in meters/second and kilometers/hour.

Conversion factors

1 mi = 1609 m 1 hr = 60 min. = 3600s 12 in. = 1 ft

2.54 cm = 1 in. 100 cm = 1 m

Solution

Convert 1 mile to meters1.

Convert mi/hr to m/s2.

Combine answers from parts (1) and (2) to solve. Note 1609 m = 1.609 km3.

Problem Solving

Problem solving is a skill water/wastewater operators and maintenance personnel will use ona daily basis. The ability to understand a problem and arrive at a reasonable solution, makesone a valuable employee. The following is a systematic approach to solving problemsencountered not only throughout the course but on the JOB as well.


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Lesson 1: Converting Units and Problem Solving

Problem Solving Steps

Read/reread the problem carefully. (Did I leave out a word or misunderstand?)1. Draw an accurate picture or diagram of the situation. (Where are the forces or directionof flow?)

2.

APPLY the physical principle to the problem. (What equation or relationship shouldI use?)

3.

Solve the problem. (How do I manipulate the equation algebraically to solve for thedesired variable? Are there any unit conversions?)

4.

Report answer with correct units.5. Check answer to see if the answer is reasonable.6.

Sources

Giancoli, Douglas C. Physics for Scientists and Engineers. 3rd ed. Upper Saddle River, NJ:Prentice Hall, 2000. Print.

Spellman, Frank R., and Joanne Drinan. Water Hydraulics. Lancaster, PA: Technomic Pub.,2001. Print.

Assignment

Answer the following questions and either email or fax to the instructor.

Define the term conversion factor.1. Explain the difference between a base unit and a derived unit.2. Convert 100 ft3/min to MGD3. Convert 124 lbs. to kilograms.4. Convert 364 in3 to m3.5.


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lesson 1_ converting units and problem solving.pdf

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