test supplement 13

8/12/2019 Test Supplement 13

1/16

UNITS

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 asgcand is used to resolve expressions involving both mass and force expressed as pounds. For

instance, in writing Newtons second law, the equation would be written asF = ma/gc, whereFis in lbf, min lbm, and ais in ft/sec2

Similar expressions exist for other quantities. Kinetic Energy,KE = mv2/2gc, withKEin (ft-lbf); Potential Energy,PE = mgh/gc, with

PEin (ft-lbf); Fluid Pressure,p= gh/gc, withpin (lbf/ft2); Specifc Weight, SW= g/gc, in (lbf/ft

3); Shear Stress, = (/gc)(dv/dy)

with shear stress in (lbf/ft2). In all these examples,gcshould be regarded as a unit conversion factor. It is frequently not writtenexplicitly in engineering equations. However, its use is required to produce a consistent set of units.

Note that the conversion factorgc[lbm-ft/(lbf-sec2)] should not be confused with the local acceleration of gravityg, which has

different units (m/s2or ft/sec2) and may be either its standard value (9.807 m/s2or 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 gcin the equation to have a consistent set of units

1018 atto a

1015 femto f

1012 pico p

109 nano n106 micro

103 milli m

102 centi c

101 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

METRIC PREFIXES

Multiple Prefix SymbolCOMMONLY 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 lbfThe mass of 1 cubic meter of water is 1,000 kilograms

TEMPERATURE CONVERSIONS

F = 1.8 (C) + 32

C = (F 32)/1.8

R = F + 459.69

K = C + 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/(kgK) or ft-lbf/(lbm-R)] and becomes characteristic of the particular gas. Some

disciplines, notably chemical engineering, often use the symbolRto refer to the universal gas constant R .

FUNDAMENTAL CONSTANTS

Quantity Symbol Value Units

electron charge e 1.6022 1019 C (coulombs)

Faraday constant F 96,485 coulombs/(mol)

gas constant metric R 8,314 J/(kmolK)

gas constant metric R 8.314 kPam3/(kmolK)

gas constant USCS R 1,545 ft-lbf/(lb mole-R)

R 0.08206 L-atm/(mole-K)

gravitation - newtonian constant G 6.673 1011 m3/(kgs2)

gravitation - newtonian constant G 6.673 1011 Nm2/kg2

gravity acceleration (standard) metric g 9.807 m/s2

gravity acceleration (standard) USCS g 32.174 ft/sec2

molar volume (ideal gas), T = 273.15K,p = 101.3 kPa Vm

22,414 L/kmol

speed of light in vacuum c 299,792,000 m/s

Stephan-Boltzmann constant 5.67 108 W/(m2K4)

19


2/16

20CONVERSION FACTORS

CONVERSION FACTORS

Multiply By To Obtain Multiply By To Obtain

joule (J) 9.478 104 BtuJ 0.7376 ft-lbfJ 1 newtonm (Nm)J/s 1 watt (W)

kilogram (kg) 2.205 pound (lbm)

kgf 9.8066 newton (N)kilometer (km) 3,281 feet (ft)km/hr 0.621 mphkilopascal (kPa) 0.145 lbf/in2(psi)kilowatt (kW) 1.341 horsepower (hp)kW 3,413 Btu/hrkW 737.6 (ft-lbf )/seckW-hour (kWh) 3,413 BtukWh 1.341 hp-hrkWh 3.6 106 joule (J)kip (K) 1,000 lbfK 4,448 newton (N)

liter (L) 61.02 in3

L 0.264 gal (US Liq)

L 103

m3

L/second (L/s) 2.119 ft3/min (cfm)L/s 15.85 gal (US)/min (gpm)

meter (m) 3.281 feet (ft)m 1.094 yardm/second (m/s) 196.8 feet/min (ft/min)mile (statute) 5,280 feet (ft)mile (statute) 1.609 kilometer (km)mile/hour (mph) 88.0 ft/min (fpm)mph 1.609 km/hmm of Hg 1.316 103 atmmm of H2O 9.678 10

5 atm

newton (N) 0.225 lbf

newton (N) 1 kgm/s2

Nm 0.7376 ft-lbfNm 1 joule (J)

pascal (Pa) 9.869 106 atmosphere (atm)Pa 1 newton/m2(N/m2)Pasec (Pas) 10 poise (P)pound (lbm, avdp) 0.454 kilogram (kg)lbf 4.448 Nlbf-ft 1.356 Nmlbf/in2(psi) 0.068 atmpsi 2.307 ft of H2Opsi 2.036 in. of Hgpsi 6,895 Pa

radian 180/ degree

stokes 1 104 m2/s

therm 1 105 Btuton (metric) 1,000 kilogram (kg)ton (short) 2,000 pound (lb)

watt (W) 3.413 Btu/hrW 1.341 103 horsepower (hp)W 1 joule/s (J/s)weber/m2(Wb/m2) 10,000 gauss

acre 43,560 square feet (ft2)ampere-hr (A-hr) 3,600 coulomb (C)ngstrm () 1 1010 meter (m)atmosphere (atm) 76.0 cm, mercury (Hg)atm, std 29.92 in, mercury (Hg)atm, std 14.70 lbf/in2abs (psia)atm, std 33.90 ft, water

atm, std 1.013 105

pascal (Pa)

bar 1 105 Pabarrelsoil 42 gallonsoilBtu 1,055 joule (J)Btu 2.928 104 kilowatt-hr (kWh)Btu 778 ft-lbfBtu/hr 3.930 104 horsepower (hp)Btu/hr 0.293 watt (W)Btu/hr 0.216 ft-lbf/sec

calorie (g-cal) 3.968 103 Btucal 1.560 106 hp-hrcal 4.186 joule (J)cal/sec 4.184 watt (W)

centimeter (cm) 3.281 102

foot (ft)cm 0.394 inch (in)centipoise (cP) 0.001 pascalsec (Pas)centipoise (cP) 1 g/(ms)centistoke (cSt) 1 106 m2/sec (m2/s)cubic feet/second (cfs) 0.646317 million gallons/day (MGD)cubic foot (ft3) 7.481 galloncubic meters (m3) 1,000 literselectronvolt (eV) 1.602 1019 joule (J)

foot (ft) 30.48 cmft 0.3048 meter (m)ft-pound (ft-lbf) 1.285 103 Btuft-lbf 3.766 107 kilowatt-hr (kWh)ft-lbf 0.324 calorie (g-cal)

ft-lbf 1.356 joule (J)

ft-lbf/sec 1.818 103 horsepower (hp)gallon (US Liq) 3.785 liter (L)gallon (US Liq) 0.134 ft3

gallons of water 8.3453 pounds of watergamma (, ) 1 109 tesla (T)gauss 1 104 Tgram (g) 2.205 103 pound (lbm)

hectare 1 104 square meters (m2)hectare 2.47104 acreshorsepower (hp) 42.4 Btu/minhp 745.7 watt (W)

hp 33,000 (ft-lbf)/minhp 550 (ft-lbf)/sechp-hr 2,545 Btuhp-hr 1.98 106 ft-lbfhp-hr 2.68 106 joule (J)hp-hr 0.746 kWh

inch (in) 2.540 centimeter (cm)in of Hg 0.0334 atmin of Hg 13.60 in of H2Oin of H2O 0.0361 lbf/in

2(psi)in of H2O 0.002458 atm


3/16

100 CHEMISTRY

CHEMISTRY

Avogadros Number: The number of elementary particles in a

mol of a substance.

1 mol = 1 gram mole

1 mol = 6.02 1023particles

A mol

many particles as 12 grams of12

C (carbon 12). The elementaryparticles may be atoms, molecules, ions, or electrons.

ACIDS, BASES, and pH (aqueous solutions)

pH logH

1 , where10=+

e o7 A[H+] = molar concentration of hydrogen ion, in gram moles

per liter

Acids have pH < 7.

Bases have pH > 7.

ELECTROCHEMISTRY

Cathode The electrode at which reduction occurs.

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 directlyor 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 0C (32F) 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.

Equilibrium Constant of a Chemical Reaction

aA bB cC dD

KA B

C Da b

c d

eq

E+ +

=6 66 6

@ @@ @

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

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).

Solubility Product of a slightly soluble substanceAB:

AmBn mAn+

+ nBm

Solubility Product Constant =KSP= [A+

]m

[B

]n

Metallic Elements In general, metallic elements are

distinguished from nonmetallic elements by their luster,

malleability, conductivity, and usual ability to form positive

ions.

Nonmetallic Elements In general, nonmetallic elements are

not malleable, have low electrical conductivity, and rarely

form positive ions.

Faradays 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 electrodefor 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 solutein 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.


4/16


5/16

ChemistryConceptsHenrysLawKH=Pgas/Ceq Pgasasatm,Ceqasmol/L,KHasatmL/mol

Solublities

AlkalinityALK(mg/LCaCO

3)=(HCO

3

)+(CO3

2)+(OH

) (H+)


6/16

AirPollution

0.5

StabilityT/Z

=

change

in

temperature/change

in

distance

Inversionz=0.47(LH)

C=E/20.5yL

L=inversionlayerlength

=windspeed

0.5

nAirDispersio Model


7/16


8/16

PopulationDynamics


9/16


10/16


11/16


12/16


13/16


14/16


15/16

WaterTreatmentCoagulationAl2(SO4)314H2O+6HCO3

=2Al(OH)3(s)+6CO2+14H2O+3SO42


16/16

test supplement 13

Documents