9.1_errata

7/21/2019 9.1_ERRATA

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ERRATA for

FE Reference Handbook , 9.1

ISBN: 978-1-932613-67-4Second printing December 2013

Errata posted June 1, 2014

Errata below will be corrected in FE Reference Handbook , 9.2. The

exam will be administered using the updated version of the handbook.

p. 10, col 1, CarcinogensThe new rst sentence in this section should read as follows:

For carcinogens, EPA considers an acceptable risk to be within the range of 10−4 to 10−6.

p. 10, col 1, Noncarcinogens

The hazard index and dose are dened as follows:

For noncarcinogens, a hazard index ( HI ) is used to characterize risk from all pathways and exposure routes. EPA considers

an HI > 1.0 as representing the possibility of an adverse effect occuring.

HI = CDI noncarcinogen

/ RfD

CDI noncarcinogen = chronic daily intake of noncarcinogenic compound

RESPONSE

NOAEL

THRESHOLD

DOSE

NONCARCINOGENIC DOSE

RESPONSE CURVE

RfD

Dose is expressed

body weight exposure timemass of chemical

:d n

NOAEL = No Observable Adverse Effect Level. The dose below which there are no harmful effects

p. 10, col 2, Reference Dose

The denition of reference dose should read as follows:

RfD = lifetime (i.e., chronic) dose that a healthy person could be exposed to daily without adverse effects

p. 13, Intake Rates

The exposure frequency for oral ingestion has been added and reads as follows:

Exposure frequency (EF) Oral ingestion 350 days/year

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p. 34, col 2, Sums of Random Variables

The title of this section should read Combinations of Random Variables.

The standard deviation of Y should be expressed as follows:Also, the standard deviation of Y is:

y y2

=v v

When Y = f ( X 1, X 2,.., X n) and X i are independent, the standard deviation of Y is expressed as:

y = ... X

f

X

f

X

f

1

2

2

2 2

X X n

X 1 2 n2

2

2

2

2

2v v v+ + +v d d dn n n

p. 35, col 1, Binomial Distribution

The variance should be expressed as σ2 = npq

p. 56, col 2, PROPERTIES OF MATERIALS/MechanicalTrue strain is dened as follows:

True strain

L

dLT =f

εT

= true strain

dL = differential change in length

L = initial length

εT = ln(1 + ε)

p. 63, col 2, MOMENT OF INERTIA

r p should be dened as follows:

r p = the radius of gyration (as dened on the next page)

p. 67, Half a Parabola

The gure of half a parabola should be shown as follows:

y

x

b

a

C

p. 70, col 1, Non-constant Acceleration

The equation for velocity should read as follows:

v t a d vt

t

t

00

x x= +^ ^h h #

In the equations, τ is the variable of integration.

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p. 70, col 2, One-Dimensional Motion of a Particle (Constant Mass)

In the equations where F x only depends on t , τ is the variable of integration.

p. 70, col 2, Work The equation for a spring should read as follows:

Spring s1

2 s 2

2−

1

2

where s1 and s2 are two different positions of the

applied force end of the spring with s2 > s1 .

U = sk

p. 81, Simply Supported Beam Slopes and Deections

The elastic curve equation for a beam that is uniformly loaded throughout the length of the beam (row 4)

should read as follows:

2

24 EI v

– wx= 3

x x L3) L2 + – (

p. 104, col 2, Mach Number

R should be dened as follows:

R ≡ specic gas constant =- R /(molecular weight)

p. 105, col 1, Isentropic Flow Relationships

The energy relation between two points should be added and read as follows:

h

V

h

V

2 21

1

2

2

2

2

+ = +

p. 105, col 2, Centrifugal Pump Characteristics

The equation for NPSH A

should read as follows:

NPSH g P

H H g

V g

P

2atm vapor

A s f

2

!t t

= - - -

P atm

and H s should be dened as follows:

P atm = atmospheric pressure at uid reservoir surface

H s = elevation difference between the level of the uid reservoir surface (zero datum) and the centerline of the pump

suction inlet

p. 142, col 1, Phase Relationships

The formulas for determining the degree of saturation (%) should read as follows:

S = (V W

/V V) × 100

S = ω GS/e

p. 142, col 2, Flow Nets

In the equation Q = kH ( N f / N

d), Q = ow per unit time

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p. 144, col 1, Horizontal Stress Proles and Forces

The gure should appear as follows:

γ2

γ1

0 0 0

0σ' = γ1 × H 1

EffectiveVerticalStress

PoreWater Pressure

EffectiveHorizontalForce

H 1

H 2

P A1 = σ1' K AH 1

P w = γw H 2

2

γ2 = saturated unit weight

σ2' = (γ1 × H 1) + (γ2 × H 2)

− (γw × H 2)

21

P A2 = (σ1' + σ2')K AH 221

21

p. 144, col 1, Ultimate Bearing Capacity (new section)The bearing capacity formula should be added and read as follows:

qULT

= cNc + γ ' D

f N

q +

2

1 γ ' BN

γ

Nc

= bearing capacity factor for cohesion

Nq

= bearing capacity factor for depth

Nγ

= bearing capacity factor for unit weight

Df

= depth of footing below ground surface

B = width of strip footing

p. 146, ASTM Table D2487-11

Notes K and L below the table should read as follows:

K If soil contains 15 to 30% plus No. 200, add "with sand" or "with gravel", whichever is predominant. LIf soil contains ≥ 30% plus No. 200, predominantly sand, add "sandy" to group name.

p. 163, col 1, Specic Energy Diagram

The alternate depths should read as follows:

y1 = ow depth at supercritical ow

y2 = ow depth at subcritical ow

y2 = y

Fr 2

1 8 11

1

2+ -_ i

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p. 165, Trafc Flow Relationships (q = kv)

Density and ow should be measured in vehicle/mi/ln as follows:

S f

0 0

SO

Sf

V m

V m

DO D j

0

DENSITY (veh/mi/ln)

DENSITY (veh/mi/ln)

FLOW (veh/mi/ln)

LEGEND

Oversaturated flow

V m Maximum flow=

F L O W ( v e h / h / l n )

S P E E D ( m p h )

S P E E D ( m p h )

S f

SO

DO

D j

DO D j

SO

= Theoretical speed selected by the first driver enteringa facility ( i.e., under zero density and zero flow rateconditions)

S f

= Optimum speed (often called critical speed)SO

Optimum density (sometimes called critical density)=DO

= Jam densityD j

p. 174, col 2, Selected Properties of Air

The molecular weight of air should be added to the list of properties and shown as follows:

Molecular weight of air 28.966 g/mol

p. 182, Comparison of Steady-State Retention Times (θ) for Decay Reactions of Different Order

The ideal batch equation for the second-order reaction should read as follows:

( )o t

o

C C – 1

kC

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p. 183, col 2, POPULATION MODELING

Three additional population projection equations have been added and are shown as follows:

Percent Growth P t = P 0(1 + k )n

where

P t = population at time t

P 0 = population at time zero

k = growth rate

n = number of periods

Ratio and Correlation Growth

P

P

P

P k

2

2

1

1

R R

= =

where

P 2 = projected population

P 2 R = projected population of a larger region

P 1 = population at last census

P 1 R = population of larger region at last census

k = growth ratio constant

Decreasing-Rate-of-Increase Growth

P t = P 0 + (S − P 0)(1 − e−k (t −t 0))

where

P t = population at time t

P 0 = population at time zero

k = growth rate constant

S = saturation population

t , t 0 = future time, initial time

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p. 208, col 1, Common Mode Rejection Ratio (CMRR)

The gure and denitions should read as follows:

v2+−

+−

v1

A(v1 − v2)+−

+

v0

−

Equivalent Circuit of an Ideal Op Amp

+

−

In the op amp circuit shown the differential input is dened as:

vid

= v

1−

v

2

The common-mode input voltage is dened as:

vicm

= (v

1 + v

2)/2

The output voltage is given by:

vO = Av

id + A

cmv

icm

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ERRATA for


ISBN 978-1-932613-67-4First printing September 2013

Errata posted December 9, 2013

Errata below will be corrected in FE Reference Handbook , 9.1. The

exam will be administered using the updated version of the handbook.

p. 6, col 1, Hazard AssessmentPosition D on the re/hazard diamond should read as follows:

Position D – (White)

ALKALI = alkali

OXY = oxidizer

ACID = acid

Cor = corrosive

W = use no water

= radiation hazard

p. 19, Roots

The formula should read as follows:

cos sinw r k

nk

jk

nk

360 360 k c ci i

= + + +c cm m< F

p. 25, col 1, Derivatives and Indenite Integrals

Formula 27 should read as follows:

27.

< / < /

csc

csc csc

dx

d u

u u dx

du

u u

1

1

0 2 2

1

2

1 1

# #

= -

-

- -r r r

-

- -

_

_ _

i

i i

p. 30, col 2, Multiplication of Two Matrices

The rst matrix should read as follows:

column matrix-r , 2ow-3A

A

C

E

B

D

F

A is a,3 2=

R

T

SSSS

V

X

WWWW

p. 81, Simply Supported Beams and Deections

The last beam should be shown as follows:

w0

1θ 2θ

v

L

x

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p. 117, col 1, Heat Exchangers

The description of the heat exchanger correction factor should read as follows:

F = correction factor for log mean temperature difference for more complex heat exchangers (shell and tube

arrangements with several tube or shell passes

or cross-ow exchangers with mixed and unmixed

ow); otherwise F = 1.

p. 135, col 2, last line, Two First-Order Irreversible Reactions in Series

The equation should read as follows:

1max D U k k =x

p. 153, col 2, Columns

Equations (a) and (b) should read as follows:

( ) . , .

( ) . , .

a When

b When

r

KL

F

E F F

r

KL

F

E F F

4 71 0 658

4 71 0 877>

cr

cr

y

e

y

y

F e

F y

# =

=

: D

p. 167, Vertical Curve Formulas

The gure should be shown as follows with tangent offset = y:

B A C K

T A N G

E N T

VERTICAL CURVE FORMULAS

NOT TO SCALE

DATUM

F O R W AR D T AN G E N T

L

x

y E

g 2

g 1

YPVC

PVC

PVT

PVI

p. 174, col 2, Selected Properties of Air

The units for density should read as follows:

Density

at 80°F 0.0734 lbm/ft3

at 100°F 0.0708 lbm/ft3

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p. 182, Comparison of Steady-State Retention Times (θ) for Decay Reactions of Different Order

The ideal batch equation for the second-order reaction should read as follows:

1

k

1

Ct

– 1

C0

p. 191, col 2, Rapid Mix and Flocculator Design

The variable for dynamic viscosity should read as follows:

µ = dynamic viscosity [lb/(ft-sec) or Pa•s]

p. 201, col 2, z-Transforms

The contour integral and z-transform table should read as follows:

The inverse transform is given by the contour integral

f k j F z 2

1 k 1

r-

C z dz = ^ h7 A #

and it represents a powerful tool for solving linear shift-invariant difference equations. A limited unilateral list of

z-transform pairs follows:

f [k ] F ( z )

δ[k ], Impulse at k = 0 1

u[k ], Step at k = 0 1/(1 – z –1

)

βk

1/(1 – β z –1

)

y[k – 1] z –1Y ( z )

y[k – 2] z –2

Y ( z )

y[k + 1] zY ( z ) – zy[0]

y[k + 2] z 2Y ( z ) – z

2 y[0] – zy[1]

[ ] [ ]0m x k m h m

∞

=−∑ H ( z ) X ( z )

[ ]0

limitk

f k →

( ) z F z ∞→limit

[ ]limitk

f k →∞

( ) ( ) z F z z

1

1

1limit −

→

−

p. 203, col 1, Decibels and Bode Plots

The equation for measuring the ratio of two voltages should read as follows:

dB = 20log10

(V2/V

1)

9.1_errata

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