UNITS

The FE exam and this handbook use both the metric system of units and the U.S. Customary System (USCS). In the USCS system of units, both force and mass are called pounds. Therefore, one must distinguish the pound-force (lbf) from the pound-mass (lbm). The pound-force is that force which accelerates one pound-mass at 32.174 ft/sec2. Thus, 1 lbf = 32.174 lbm-ft/sec2. The expression 32.174 lbm-ft/(lbf-sec2) is designated as gc and is used to resolve expressions involving both mass and force expressed as pounds. For instance, in writing Newton’s second law, the equation would be written as F = ma/gc, where F is in lbf, m in lbm, and a is in ft/sec2. Similar expressions exist for other quantities. Kinetic Energy, KE = mv2/2gc, with KE in (ft-lbf); Potential Energy, PE = mgh/gc, with PE in (ft-lbf); Fluid Pressure, p = ρgh/gc, with p in (lbf/ft2); Specific Weight, SW = ρg/gc, in (lbf/ft3); Shear Stress, τ = (µ/gc)(dv/dy), with shear stress in (lbf/ft2). In all these examples, gc should be regarded as a unit conversion factor. It is frequently not written explicitly in engineering equations. However, its use is required to produce a consistent set of units. Note that the conversion factor gc [lbm-ft/(lbf-sec2)] should not be confused with the local acceleration of gravity g, which has different units (m/s2 or ft/sec2) and may be either its standard value (9.807 m/s2 or 32.174 ft/sec2) or some other local value. If the problem is presented in USCS units, it may be necessary to use the constant gc in the equation to have a consistent set of units.

METRIC PREFIXES Multiple Prefix Symbol 10−18 atto a −15 10 femto f 10−12 pico p 10−9 nano n 10−6 micro µ 10−3 milli m 10−2 centi c 10−1 deci d 101 deka da 102 hecto h 103 kilo k 106 mega M 109 giga G 1012 tera T 1015 peta P 1018 exa E

COMMONLY USED EQUIVALENTS 1 gallon of water weighs

8.34 lbf

1 cubic foot of water weighs

62.4 lbf

1 cubic inch of mercury weighs

0.491 lbf

The mass of 1 cubic meter of water is

1,000 kilograms

TEMPERATURE CONVERSIONS ºF = 1.8 (ºC) + 32 ºC = (ºF – 32)/1.8 ºR = ºF + 459.69 K = ºC + 273.15

IDEAL GAS CONSTANTS The universal gas constant, designated as R in the table below, relates pressure, volume, temperature, and number of moles of an ideal gas. When that universal constant, R , is divided by the molecular weight of the gas, the result, often designated as R, has units of energy per degree per unit mass [kJ/(kg·K) or ft-lbf/(lbm-ºR)] and becomes characteristic of the particular gas. Some disciplines, notably chemical engineering, often use the symbol R to refer to the universal gas constant R .

FUNDAMENTAL CONSTANTS Quantity electron charge Faraday constant gas constant metric gas constant metric gas constant USCS gravitation - newtonian constant gravitation - newtonian constant gravity acceleration (standard) metric gravity acceleration (standard) USCS molar volume (ideal gas), T = 273.15K, p = 101.3 kPa speed of light in vacuum Stephan-Boltzmann constant

Symbol e F R R R R G G g g Vm c σ

Value 1.6022 × 10−19 96,485 8,314 8.314 1,545 0.08206 6.673 × 10–11 6.673 × 10–11 9.807 32.174 22,414 299,792,000 5.67 × 10–8

Units C (coulombs) coulombs/(mol) J/(kmol·K) kPa·m3/(kmol·K) ft-lbf/(lb mole-ºR) L-atm/(mole-K) m3/(kg·s2) N·m2/kg2 m/s2 ft/sec2 L/kmol m/s W/(m2·K4) UNITS

19

CONVERSION FACTORS Multiply

By

To Obtain

Multiply 2

acre ampere-hr (A-hr) ångström (Å) atmosphere (atm) atm, std atm, std atm, std atm, std

43,560 3,600 1 × 10–10 76.0 29.92 14.70 33.90 1.013 × 105

square feet (ft ) coulomb (C) meter (m) cm, mercury (Hg) in, mercury (Hg) lbf/in2 abs (psia) ft, water pascal (Pa)

bar barrels–oil Btu Btu Btu Btu/hr Btu/hr Btu/hr

1 × 105 42 1,055 2.928 × 10–4 778 3.930 × 10–4 0.293 0.216

Pa gallons–oil joule (J) kilowatt-hr (kWh) ft-lbf horsepower (hp) watt (W) ft-lbf/sec

calorie (g-cal) cal cal cal/sec centimeter (cm) cm centipoise (cP) centipoise (cP) centistoke (cSt) cubic feet/second (cfs) cubic foot (ft3) cubic meters (m3) electronvolt (eV)

3.968 × 10–3 1.560 × 10–6 4.186 4.184 3.281 × 10–2 0.394 0.001 1 1 × 10–6 0.646317 7.481 1,000 1.602 × 10–19

Btu hp-hr joule (J) watt (W) foot (ft) inch (in) pascal·sec (Pa·s) g/(m·s) m2/sec (m2/s) million gallons/day (MGD) gallon liters joule (J)

foot (ft) ft ft-pound (ft-lbf) ft-lbf ft-lbf ft-lbf

30.48 0.3048 1.285 × 10–3 3.766 × 10–7 0.324 1.356

cm meter (m) Btu kilowatt-hr (kWh) calorie (g-cal) joule (J)

ft-lbf/sec 1.818 × 10–3 horsepower (hp) gallon (US Liq) 3.785 liter (L) gallon (US Liq) 0.134 ft3 gallons of water 8.3453 pounds of water gamma (γ, Γ) 1 × 10–9 tesla (T) gauss 1 × 10–4 T gram (g) 2.205 × 10–3 pound (lbm) hectare hectare horsepower (hp) hp hp hp hp-hr hp-hr hp-hr hp-hr

1 × 104 2.47104 42.4 745.7 33,000 550 2,545 1.98 × 106 2.68 × 106 0.746

square meters (m2) acres Btu/min watt (W) (ft-lbf)/min (ft-lbf)/sec Btu ft-lbf joule (J) kWh

inch (in) in of Hg in of Hg in of H2O in of H2O

2.540 0.0334 13.60 0.0361 0.002458

centimeter (cm) atm in of H2O lbf/in2 (psi) atm

20

CONVERSION FACTORS

By

To Obtain –4

joule (J) J J J/s

9.478 × 10 0.7376 1 1

kilogram (kg) kgf kilometer (km) km/hr kilopascal (kPa) kilowatt (kW) kW kW kW-hour (kWh) kWh kWh kip (K) K

2.205 9.8066 3,281 0.621 0.145 1.341 3,413 737.6 3,413 1.341 3.6 × 106 1,000 4,448

pound (lbm) newton (N) feet (ft) mph lbf/in2 (psi) horsepower (hp) Btu/hr (ft-lbf )/sec Btu hp-hr joule (J) lbf newton (N)

liter (L) L L L/second (L/s) L/s

61.02 0.264 10–3 2.119 15.85

in3 gal (US Liq) m3 ft3/min (cfm) gal (US)/min (gpm)

meter (m) m m/second (m/s) mile (statute) mile (statute) mile/hour (mph) mph mm of Hg mm of H2O

3.281 1.094 196.8 5,280 1.609 88.0 1.609 1.316 × 10–3 9.678 × 10–5

feet (ft) yard feet/min (ft/min) feet (ft) kilometer (km) ft/min (fpm) km/h atm atm

newton (N) newton (N) N·m N·m

0.225 1 0.7376 1

lbf kg·m/s2 ft-lbf joule (J)

pascal (Pa) Pa Pa·sec (Pa·s) pound (lbm, avdp) lbf lbf-ft lbf/in2 (psi) psi psi psi

9.869 × 10–6 1 10 0.454 4.448 1.356 0.068 2.307 2.036 6,895

atmosphere (atm) newton/m2 (N/m2) poise (P) kilogram (kg) N N·m atm ft of H2O in. of Hg Pa

radian

180/π

degree

stokes

1 × 10–4

m2/s

therm ton (metric) ton (short)

1 × 105 1,000 2,000

Btu kilogram (kg) pound (lb)

watt (W) W W weber/m2 (Wb/m2)

3.413 1.341 × 10–3 1 10,000

Btu/hr horsepower (hp) joule/s (J/s) gauss



Btu ft-lbf newton·m (N·m) watt (W)

CHEMISTRY Avogadro’s Number: The number of elementary particles in a mol of a substance. 1 mol = 1 gram mole 1 mol = 6.02 × 1023 particles A mol                many particles as 12 grams of 12C (carbon 12). The elementary particles may be atoms, molecules, ions, or electrons.

ACIDS, BASES, and pH (aqueous solutions)

Equilibrium Constant of a Chemical Reaction aA + bB E cC + dD c d 6 @ 6 @ Keq = C a D b 6 A@ 6 B @

Le Chatelier's Principle for Chemical Equilibrium – When a stress (such as a change in concentration, pressure, or temperature) is applied to a system in equilibrium, the equilibrium shifts in such a way that tends to relieve the stress.

[H+] = molar concentration of hydrogen ion, in gram moles per liter

Heats of Reaction, Solution, Formation, and Combustion – Chemical processes generally involve the absorption or evolution of heat. In an endothermic process, heat is absorbed (enthalpy change is positive). In an exothermic process, heat is evolved (enthalpy change is negative).

Acids have pH < 7.

Solubility Product of a slightly soluble substance AB:

pH = log10 e 1 o , where 7 H+A

Bases have pH > 7.

AmBn → mAn+ + nBm–

ELECTROCHEMISTRY

Solubility Product Constant = KSP = [A+]m [B–]n

Cathode – The electrode at which reduction occurs.

Metallic Elements – In general, metallic elements are distinguished from nonmetallic elements by their luster, malleability, conductivity, and usual ability to form positive ions.

Anode – The electrode at which oxidation occurs. Oxidation – The loss of electrons. Reduction – The gaining of electrons. Oxidizing Agent – A species that causes others to become oxidized. Reducing Agent – A species that causes others to be reduced. Cation – Positive ion Anion – Negative ion

DEFINITIONS Molarity of Solutions – The number of gram moles of a substance dissolved in a liter of solution. Molality of Solutions – The number of gram moles of a substance per 1,000 grams of solvent. Normality of Solutions – The product of the molarity of a solution and the number of valence changes taking place in a reaction. Equivalent Mass – The number of parts by mass of an element or compound which will combine with or replace directly or indirectly 1.008 parts by mass of hydrogen, 8.000 parts of oxygen, or the equivalent mass of any other element or compound. For all elements, the atomic mass is the product of the equivalent mass and the valence. Molar Volume of an Ideal Gas [at 0°C (32°F) and 1 atm (14.7 psia)]; 22.4 L/(g mole) [359 ft3/(lb mole)]. Mole Fraction of a Substance – The ratio of the number of moles of a substance to the total moles present in a mixture of substances. Mixture may be a solid, a liquid solution, or a gas.

100

CHEMISTRY

Nonmetallic Elements – In general, nonmetallic elements are not malleable, have low electrical conductivity, and rarely form positive ions. Faraday’s Law – In the process of electrolytic changes, equal quantities of electricity charge or discharge equivalent quantities of ions at each electrode. One gram equivalent weight of matter is chemically altered at each electrode for 96,485 coulombs, or one Faraday, of electricity passed through the electrolyte. A catalyst is a substance that alters the rate of a chemical reaction and may be recovered unaltered in nature and amount at the end of the reaction. The catalyst does not affect the position of equilibrium of a reversible reaction. The atomic number is the number of protons in the atomic nucleus. The atomic number is the essential feature which distinguishes one element from another and determines the position of the element in the periodic table. Boiling Point Elevation – The presence of a nonvolatile solute in a solvent raises the boiling point of the resulting solution compared to the pure solvent; i.e., to achieve a given vapor pressure, the temperature of the solution must be higher than that of the pure substance. Freezing Point Depression – The presence of a solute lowers the freezing point of the resulting solution compared to that of the pure solvent.

CHEMISTRY

101

21

39

Y

88.906

57*

40.078

38

Sr

87.62

K

39.098

37

Rb

85.468

Ac

88

Ra

226.02

87

Fr

(223)

**Actinide Series

*Lanthanide Series

89**

137.33

132.91

227.03

138.91

La

56

Ba

55

Cs

44.956

Sc

20

Ca

19

24.305

22.990

22

23

91 Pa 231.04

90

Th

232.04

140.91

140.12

59 Pr

58

Ce

(262)

Ha

105

180.95

Ta

73

92.906

Nb

41

50.941

V

(261)

Rf

104

178.49

Hf

72

91.224

Zr

40

47.88

Ti

24

238.03

U

92

144.24

Nd

60

183.85

W

74

95.94

Mo

42

51.996

Cr

25

237.05

Np

93

(145)

Pm

61

186.21

Re

75

(98)

Tc

43

54.938

Mn

26

(244)

Pu

94

150.36

Sm

62

190.2

Os

76

101.07

Ru

44

55.847

Fe

27

(243)

Am

95

151.96

Eu

63

192.22

Ir

77

102.91

Rh

45

58.933

Co

29

30

(247)

(247)

(251)

98 Cf

97 Bk

96

162.50

Dy

66

200.59

Hg

80

112.41

Cd

48

65.39

Zn

Cm

158.92

Tb

65

196.97

Au

79

107.87

Ag

47

63.546

157.25

Gd

64

195.08

Pt

78

106.42

Pd

46

58.69

Ni

28 Cu

13

12

Mg

11

Na

10.811

9.0122

6.941

Atomic Weight

Be

(252)

Es

99

164.93

Ho

67

204.38

Tl

81

114.82

In

49

69.723

Ga

31

26.981

Al

B

(257)

Fm

100

167.26

Er

68

207.2

Pb

82

118.71

Sn

50

72.61

Ge

32

28.086

Si

14

12.011

C

6

5

Li

IV

III

4

3

Symbol

II

1.0079

Atomic Number

V

(258)

Md

101

168.93

Tm

69

208.98

Bi

83

121.75

Sb

51

74.921

As

33

30.974

P

15

14.007

N

7

VI

(259)

No

102

173.04

Yb

70

(209)

Po

84

127.60

Te

52

78.96

Se

34

32.066

S

16

15.999

O

8

VII 9

(260)

Lr

103

174.97

Lu

71

(210)

At

85

126.90

I

53

79.904

Br

35

35.453

Cl

17

18.998

F

(222)

Rn

86

131.29

Xe

54

83.80

Kr

36

39.948

Ar

18

20.179

Ne

10

4.0026

He

2

1

H

VIII

I

PERIODIC TABLE OF ELEMENTS

102

CHEMISTRY

Ethane

RH

Common Name

General Formula

Functional Group

Ethane

IUPAC Name

bonds

C–C

and

C–H

CH3CH3

Specific Example

Alkane

RC ≡ CR

R2C = CHR

C=C

R2C = CR2

–C ≡C–

RC ≡ CH

RCH = CHR

RCH = CH2

Acetylene

Acetylene

Ethylene

Ethylene

or

Ethyne

Ethene

or

HC ≡ CH

Alkyne

H2C = CH2

Alkene

Aromatic Ring

ArH

Benzene

Benzene

Arene

C

RX

X

Ethyl chloride

Chloroethane

CH3CH2Cl

Haloalkane

C

OH

ROH

Ethyl alcohol

Ethanol

CH3CH2OH

Alcohol

FAMILY

C

O C

ROR

Dimethyl ether

Methoxymethane

CH3OCH3

Ether

C

N

R3N

R2NH

RNH2

Methylamine

Methanamine

CH3NH2

Amine

IMPORTANT FAMILIES OF ORGANIC COMPOUNDS

CH3CCH3

CH3CH

C

O

RCH

O

H

Acetaldehyde

C

O

R1CR2

O

Dimethyl ketone

Acetone

O

O

Ethanal

Ketone

Aldehyde

CH3COCH3

CH3COH

C

O OH

RCOH

O

Acetic Acid

C

O O

RCOR

O

Methyl acetate

C

ethanoate

Methyl

O

O

Ethanoic Acid

Ester

Carboxylic Acid

Standard Oxidation Potentials for Corrosion Reactions* Corrosion Reaction

Potential, Eo, Volts vs. Normal Hydrogen Electrode

Au → Au3+ + 3e – 2H2O → O2 + 4H+ + 4e – Pt → Pt2+ + 2e – Pd → Pd2+ + 2e – Ag → Ag+ + e –

–1.498 –1.229 –1.200 –0.987 –0.799

2Hg → Hg22+ + 2e– Fe2+ → Fe3+ + e– 4(OH)– → O2 + 2H2O + 4e – Cu → Cu2+ + 2e– Sn2+ → Sn4+ + 2e –

–0.788 –0.771 –0.401 –0.337 –0.150

H2 → 2H+ + 2e – Pb → Pb2+ + 2e – Sn → Sn2+ + 2e – Ni → Ni2+ + 2e – Co → Co2+ + 2e–

0.000 +0.126 +0.136 +0.250 +0.277

Cd → Cd2+ + 2e – Fe → Fe2+ + 2e– Cr → Cr3+ + 3e– Zn → Zn2+ + 2e– Al → Al3+ + 3e –

+0.403 +0.440 +0.744 +0.763 +1.662

Mg → Mg2+ + 2e– Na → Na+ + e – K → K+ + e –

+2.363 +2.714 +2.925

* Measured at 25oC. Reactions are written as anode half-cells. Arrows are reversed for cathode half-cells. Flinn, Richard A. and Trojan, Paul K., Engineering Materials and Their Applications, 4th ed., Houghton Mifflin Company, 1990.

NOTE: In some chemistry texts, the reactions and the signs of the values (in this table) are reversed; for example, the half-cell potential of zinc is given as –0.763 volt for the reaction Zn2+ + 2e–→ Zn. When the potential Eo is positive, the reaction proceeds spontaneously as written.

CHEMISTRY

103

MATERIALS SCIENCE/STRUCTURE OF MATTER ATOMIC BONDING

TESTING METHODS

Primary Bonds Ionic (e.g., salts, metal oxides) Covalent (e.g., within polymer molecules) Metallic (e.g., metals)

Standard Tensile Test Using the standard tensile test, one can determine elastic modulus, yield strength, ultimate tensile strength, and ductility (% elongation). (See Mechanics of Materials section.)

CORROSION A table listing the standard electromotive potentials of metals is shown on the previous page. For corrosion to occur, there must be an anode and a cathode in electrical contact in the presence of an electrolyte.

Anode Reaction (Oxidation) of a Typical Metal, M Mo → Mn+ + ne– Possible Cathode Reactions (Reduction) ½ O2 + 2 e– + H2O → 2 OH– ½ O2 + 2 e– + 2 H3O+ → 3 H2O 2 e– + 2 H3O+ → 2 H2O + H2 When dissimilar metals are in contact, the more electropositive one becomes the anode in a corrosion cell. Different regions of carbon steel can also result in a corrosion reaction: e.g., cold-worked regions are anodic to noncoldworked; different oxygen concentrations can cause          regions; grain boundary regions are anodic to bulk grain; in multiphase alloys, various phases may not have the same galvanic potential.

DIFFUSION

Endurance Test     X     !  a cyclical loading of constant maximum amplitude. The plot (usually semi-log or log-log) of the maximum stress (σ) and the number (N) of cycles to failure is known as an S-N plot. ?        other metals; i.e., aluminum alloys, etc.

σ ENDURANCE LIMIT KNEE

LOG N (CYCLES)

The endurance stress (endurance limit or fatigue limit) is the    

     causing failure. The fatigue life is the number of cycles required to cause failure for a given stress level. Impact Test The Charpy Impact Test     ^  fracture and to identify ductile to brittle transition.

%   D = Do e−Q/(RT), where D ‰    Do = proportionality constant, Q = activation energy, R = gas constant [8.314 J/XO³!Z  T = absolute temperature.

THERMAL AND MECHANICAL PROCESSING Cold working (plastically deforming) a metal increases strength and lowers ductility. Raising temperature causes (1) recovery (stress relief), (2) recrystallization, and (3) grain growth. Hot working allows these processes to occur simultaneously with deformation. Quenching is rapid cooling from elevated temperature, preventing the formation of equilibrium phases. In steels, quenching austenite [FCC (γ) iron] can result in martensite instead of equilibrium phases—ferrite [BCC (α) iron] and cementite (iron carbide).

104

MATERIALS SCIENCE/STRUCTURE OF MATTER

Impact tests determine the amount of energy required to cause failure in standardized test samples. The tests are repeated over a range of temperatures to determine the ductile to brittle transition temperature.

Creep Creep occurs under load at elevated temperatures. The general equation describing creep is: df = Av ne- Q dt

]RT g

where: ¬ ‰   t = time, A = pre-exponential constant, & ‰   

 n = stress sensitivity. For polymers below, the glass transition temperature, Tg, n is typically between 2 and 4, and Q  Æ_””¸™ˆTg, n is typically between 6 and 10, and Q is ~ 30 kJ/mol. For metals and ceramics, n is typically between 3 and 10, and Q is between 80 and 200 kJ/mol.

Representative Values of Fracture Toughness Material A1 2014-T651 A1 2024-T3 52100 Steel 4340 Steel Alumina Silicon Carbide

K Ic (MPa$m 1/2 ) 24.2 44 14.3 46 4.5 3.5

K Ic (ksi$in 1/2 ) 22 40 13 42 4.1 3.2

HARDENABILITY OF STEELS Hardenability is the “ease” with which hardness may be attained. Hardness is a measure of resistance to plastic deformation. ♦

STRESS CONCENTRATION IN BRITTLE MATERIALS When a crack is present in a material loaded in tension,   

    ?       

    member to support a tensile load. KI = yv ra KI = the stress intensity in tension, MPaum1/2, y = is a geometric parameter,

in.

y = 1 for interior crack (#2) and (#8) indicate grain size

y = 1.1 for exterior crack

JOMINY HARDENABILITY CURVES FOR SIX STEELS

& ‰     

  a = is crack length as shown in the two diagrams below. ♦

a

EXTERIOR CRACK (y = 1.1)

2a

INTERIOR CRACK (y = 1)

The critical value of stress intensity at which catastrophic crack propagation occurs, KIc, is a material property.

COOLING RATES FOR BARS QUENCHED IN AGITATED WATER ♦Van Vlack,

L., Elements of Materials Science & Engineering, Addison-Wesley, Boston, 1989.

MATERIALS SCIENCE/STRUCTURE OF MATTER

105

♦

ˆ            the strains of the two components are equal. (ΔL/L)1 = (ΔL/L)2 ΔL = change in length of the composite, L

= original length of the composite. Material

RELATIONSHIP BETWEEN HARDNESS AND TENSILE STRENGTH For steels, there is a general relationship between Brinell hardness and tensile strength as follows: TS _ psii - 500 BHN

TS ^MPah - 3.5 BHN

ASTM GRAIN SIZE SV = 2PL

^

h

N_0.0645 mm2i = 2 n - 1

Nactual N , where = Actual Area _0.0645 mm 2i SV = PL = N = n =

grain-boundary surface per unit volume, number of points of intersection per unit length between the line and the boundaries, number of grains observed in a area of 0.0645 mm2, and grain size (nearest integer > 1).

COMPOSITE MATERIALS tc = Rfi ti Cc = Rfici -1

f