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Formulas and Conversions
IDC Technologies
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IDC Technologies
Formulas and Conversions
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ISBN 978-87-403-0005-5
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1 Algebra
26
4
...
3 Trigonometry
34
4
...
5 Exponents
38
4
...
com/Mitas
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1 Electricity
41
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...
3 Thermodynamics
64
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...
1
Periodic Table of Elements
81
6
...
job
...
dk
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The objective of this booklet is to provide today’s engineer with useful technical information and as an aide-memoir when
you need to refresh your memory
...
Although IDC Technologies was founded in Western Australia many years ago, it now draws engineers from all countries
...
We have produced this booklet so that you will have important formulas and conversion at your fingertips
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Formulas and Conversions
Definition and Abbreviations for Physical Quantities
1
Definition and Abbreviations for
Physical Quantities
Symbol
m
kg
s
A
K
cd
Quantity
Plane angle
Force
Work, energy
Power
Frequency
Viscosity: kinematic
Viscosity: Dynamic
Pressure
Unit
meter
kilogram
second
ampere
kelvin
candela
Quantity
Length
Mass
Time
Electric current
Thermodynamic temp
Luminous intensity
Unit
radian
newton
heat
watt
hertz
-
Symbol
Prefix
T
G
M
k
h
da
d
c
m
μ
n
p
Symbol
rad
N
joule
W
Hz
m2/s
Ns/m2
Pa or N/m2
Tera
Giga
Mega
Kilo
Hecto
Deca
Deci
Centi
Milli
Micro
Nano
Pico
Quantity
Potential
Resistance
Charge
Capacitance
Electric field strength
Electric flux density
Equivalent
kg ∙ m/s2
J∙N∙m
J/s
s-1
10 c St (Centistoke)
103 cP (Centipoise)
pascal, Pa
Factor by which unit
is multiplied
1012
109
106
103
102
10
10-1
10-2
10-3
10-6
10-9
10-12
Electrical unit
Volt
Ohm
Coulomb
Farad
-
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Formulas and Conversions
Units of Physical Quantities
2 Units of Physical Quantities
Conversion Factors (general):
1 acre = 43,560 square feet
1 cubic foot = 7
...
305 meters
1 gallon = 3
...
34 pounds
1 grain per gallon = 17
...
746 kilowatts
1 million gallons per day = 694 gallons per minute
1 pound = 0
...
31 feet of water
Degrees Celsius = (Degrees Fahrenheit - 32) (5/9)
Degrees Fahrenheit = (Degrees Celsius) (9/5) + 32
1% = 10,000 mg/L
Name
Acceleration
Area
Area
Area
Area
Density
Density
Density
Density
Density
Energy
Energy
Energy
Energy
Energy
Energy
Energy
Energy
Force
Force
Force
Heat capacity
Heat transfer coefficient
Length
Length
Length
Length
Length
Length
Mass
Mass
Mass
To convert from
ft/sec2
acre
ft2
hectare
in2
g/cm3
lbm/ft3
lbm/in3
lb∙s2/in4
slug/ft3
BTU
cal
erg
eV
Ft∙lbf
kiloton TNT
KW∙hr
Megaton TNT
Dyne
Lbf
Ozf
BTU/lbm ∙ °F
BTU/hr∙ft2∙°F
AU
ft
in
mile
Nautical mile
parsec
amu
lbm
lb∙s2/in
To
m/s2
m2
m2
m2
m2
kg/m3
kg/m3
kg/m3
kg/m3
kg/m3
J
J
J
J
J
J
J
J
N
N
N
J/kg∙°C
W/m2∙°C
m
m
m
m
m
m
kg
kg
kg
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...
3048
4047
9
...
000E+04
6
...
02
2
...
069E+07
515
...
1859
1
...
602E-19
1
...
187E+12
3
...
187E+15
1
...
4484
0
...
6786
1
...
3048
2
...
085E+16
1
...
4535
1200
...
2810
2
...
7600
1
...
000E-03
6
...
614E-05
9
...
940E-03
9
...
2389
1
...
242E+18
0
...
388E-13
2
...
388E-16
1
...
2248
3
...
388E-04
0
...
685E-12
3
...
3700
6
...
397E-04
3
...
022E+26
2
...
711E-03
Formulas and Conversions
Name
Mass
Mass flow rate
Mass flow rate
Moment of inertia
Moment of inertia
Moment of inertia
Power
Power
Power
Pressure
Pressure
Pressure
Pressure
Pressure
Pressure
Pressure
Pressure
Pressure
Pressure
Pressure
Specific heat
Specific heat
Temperature
Thermal conductivity
Thermal conductivity
Thermal conductivity
Units of Physical Quantities
To convert from
slug
lbm/hr
lbm/sec
ft∙lb∙s2
in∙lb∙s2
oz∙in∙s2
BTU/hr
hp
tons of refrigeration
bar
dyne/cm2
in
...
water
kgf/cm2
lbf/ft2
lbf/in2
mbar
microns mercury
mm mercury
std atm
BTU/lbm∙°F
cal/g∙°C
°F
BTU/hr∙ft∙°F
BTU∙in/hr∙ft2∙°F
cal/cm∙s∙°C
To
kg
kg/s
kg/s
kg∙m2
kg∙m2
kg∙m2
W
W
W
Pa
Pa
Pa
Pa
Pa
Pa
Pa
Pa
Pa
Pa
Pa
J/kg∙°C
J/kg∙°C
°C
W/m∙°C
W/m∙°C
W/m∙°C
Multiply by
14
...
260E-04
0
...
3557
0
...
062E-03
0
...
71
3516
1
...
1000
3377
248
...
807E+04
47
...
00
0
...
3
1
...
5556
1
...
1442
418
...
853E-02
7937
2
...
7376
8
...
60
3
...
341E-03
2
...
000E-05
10
...
961E-04
4
...
020E-05
2
...
450E-04
1
...
501
7
...
869E-06
2
...
389E-04
1
...
5778
6
...
389E-03
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Formulas and Conversions
Name
Thermal conductivity
Time
Time
Torque
Torque
Torque
Velocity
Velocity
Velocity
Velocity
Viscosity – absolute
Viscosity – absolute
Viscosity – absolute
Viscosity – absolute
Viscosity – kinematic
Viscosity – kinematic
Volume
Volume
Volume
Volume
Volume flow rate
Volume flow rate
A
...
S
...
S
...
867E-03
8
...
156E+07
1
...
1130
7
...
079E-03
0
...
2778
0
...
000E-03
0
...
87
1
...
000E-06
9
...
831E-02
1
...
000E-03
3
...
719E-04
6
...
62
1
...
169E-08
0
...
8504
141
...
90
3
...
6000
2
...
089E-02
0
...
000E+06
10
...
3200
6
...
20
2119
1
...
03280840
0
...
8288*
0
...
48*
304
...
0254*
2
...
4*
0
...
37008
0
...
280840
0
...
093613
0
...
0254*
39
...
344*
1
...
003280840
0
...
0292*
0
...
com
11
Formulas and Conversions
To Convert
Cables
Cables
Cables
Centimeters
Centimeters
Centimeters
Centimeters
Chains, (Surveyor’s)
Chains, (Surveyor’s)
Chains, (Surveyor’s)
Fathoms
Fathoms
Feet
Feet
Feet
Feet
Feet
Feet
Furlongs
Furlongs
Furlongs
Furlongs
Furlongs
Hands (Height Of Horse)
Hands (Height Of Horse)
Inches
Inches
Inches
Inches
Inches
Kilometers
Kilometers
Leagues, Nautical
Leagues, Nautical
Leagues, Statute
Leagues, Statute
Links, (Surveyor’s)
Links, (Surveyor’s)
Links, (Surveyor’s)
Meters
Meters
Meters
Meters
Meters
Meters
Meters
Microns
Microns
Miles, Nautical
Miles, Nautical
Miles, Statute
Units of Physical Quantities
To
Fathoms
Meters
Yards
Meters
Yards
Feet
Inches
Rods
Meters
Feet
Meters
Feet
Statute Miles
Kilometers
Meters
Yards
Inches
Centimeters
Statute Miles
Meters
Yards
Feet
Inches
Inches
Centimeters
Meters
Yards
Feet
Centimeters
Millimeters
Statute Miles
Meters
Nautical Miles
Kilometers
Statute Miles
Kilometers
Chains
Inches
Centimeters
Statute Miles
Kilometers
Yards
Feet
Inches
Centimeters
Millimeters
Meters
Inches
Statute Miles
Kilometers
Kilometers
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456
240
0
...
01093613
0
...
3937008
4
20
...
8288
6
0
...
0003048
0
...
3333333
12
30
...
125
201
...
16
0
...
02777778
0
...
54
25
...
621371192
1000
3
5
...
828032
0
...
92
20
...
000621371
0
...
093613298
3
...
370079
100
1000
0
...
0000394
1
...
852
1
...
344
1760
5280
63360
160934
...
039370079
0
...
0254
30
76
...
013837
0
...
0292
5
...
5
9
22
...
00056818
0
...
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3937 in
1 m = 3
...
0936 yd
1 km = 0
...
25 yd2
1 cm2 = 0
...
764 ft2
1 km2 = 0
...
06102 in3
1 m3 = 35
...
024 in3
1 Litre = 0
...
2642 gal
...
S
...
0284 bu (U
...
)
1 Litre = 1000
...
5400 cm
1 ft = 0
...
9144 m
1 mile = 1
...
5 yd
1 in = 100 mils
1 light year = 9
...
540 x 10-5 m
1 acre = 160 rod2
1 acre = 43,560 ft2
1 mile2 = 640 acres
1 in2 = 6
...
0929 m2
1 mile2 = 2
...
387 cm3
1 ft3 = 0
...
0164 litre
1 ft3 = 28
...
7646 m3
1 gallon (US) = 3
...
785 x 10-3 m3
1 Litre = 1
...
(liquid) or 0
...
(dry)
1 bushel (US) = 35
...
957 x 10-5 m3
Liquid Volume
1 gill = 4 fluid ounces
1 pint = 4 gills
1 quart = 2 pints
1 gallon = 4 quarts
Dry Volume
1 quart = 2 pints
1 peck = 8 quarts
1 bushel = 4 pecks
1 stere = 1 m3
1 barrel = 31
...
2 in3
1 peck = 537
...
5 in3
B
...
856
meter2 (m2)
0
...
1550003
0
...
09290304*
hectare
inch2
foot2
meter2 (m2)
acre
centimeter
centimeter2
foot2
2
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...
03042
92,903
...
471054
645
...
4516
0
...
003
10
...
195990
0
...
00001076391
0
...
8361274
acre
millimeter2 (mm2)
centimeter2 (cm2)
meter2 (m2)
inch2
foot2
yard2
acre
foot2
inch2
meter2 (m2)
inch
inch2
inch2
meter2
meter2
meter2
meter2
millimeter2
millimeter2
yard2
2
millimeter2 (mm2)
C
...
06102376
foot3
0
...
31685
gallon (UK liquid)
0
...
546092
gallon (US liquid)
0
...
785412
inch3
16,387
...
38706
inch3
0
...
001*
Liter
0
...
2641720
Liter
0
...
9692
meter3
264
...
31466
meter3
1
...
*
3
meter
61,023
...
00006102376
Yard3
0
...
To obtain
inch3
meter3 (m3)
liter
meter3 (m3)
litre
meter3 (m3)
liter
millimeter3 (mm3)
centimeter3 (cm3)
meter3 (m3)
meter3 (m3)
gallon (UK liquid)
gallon (US liquid)
foot3
gallon (UK liquid)
gallon (US liquid)
foot3
yard3
liter
inch3
inch3
meter3 (m3)
Mass and Weight
Conversions
To Convert
Carat
Drams, Avoirdupois
To
Milligrams
Avoirdupois Ounces
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06255
Formulas and Conversions
Units of Physical Quantities
To Convert
Drams, Avoirdupois
Drams, Avoirdupois
Drams, Troy
Drams, Troy
Drams, Troy
Drams, Troy
Grains
Grains
Grains
Grains
Grains
Grains
Grains
Grains
Grains
Grains
Grains
Grams
Grams
Grams
Grams
Grams
Grams
Grams
Grams
Hundredweights, Long
To
Grams
Grains
Troy Ounces
Scruples
Grams
Grains
Kilograms
Avoirdupois Pounds
Troy Pounds
Troy Ounces
Avoirdupois Ounces
Troy Drams
Avoirdupois Drams
Pennyweights
Scruples
Grams
Milligrams
Kilograms
Avoirdupois Pounds
Troy Pounds
Troy Ounces
Avoirdupois Ounces
Avoirdupois Drams
Grains
Milligrams
Long Tons
Multiply By
1
...
344
0
...
8879346
60
6
...
00014286
0
...
00208333
0
...
0166
0
...
042
0
...
06479891
64
...
001
0
...
00267923
0
...
035273961
0
...
432361
1000
0
...
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Multiply By
0
...
056
50
...
04464286
0
...
05
45
...
0009842
0
...
00110231
0
...
204622622
2
...
15075
35
...
3834
1000
15432
...
015432358
0
...
0625
0
...
9114583
16
28
...
5
0
...
0833333
1
...
55429
20
31
...
05
1
...
000446429
0
...
0005
0
...
45359237
1
...
58333
16
256
453
...
373241722
0
...
16571
210
...
2417216
5760
0
...
46226
0
...
2959782
20
1
...
12
20
22
...
04691
2240
35840
0
...
1023113
10
19
...
04623
1000
2204
...
75
0
...
90718474
17
...
18474
2000
E
...
Gallon
Grains/US gallon
Grains/US gallon
Grams/cu
...
Cm
Grams/cu
...
in
Pounds/cu
...
ft
Pounds/1000 gal
Grains/gal
Parts/million
Pounds/mil-foot
Pounds/cu in
Grams/cu cm
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...
286
17
...
86
3
...
03613
62
...
062427
8
...
417
1000
3
...
00003613
0
...
To
Pound/cu ft
Parts/million
Pounds/mil-foot
Pounds/cu in
Grams/cu cm
Kgs/cu meter
Pounds/mil-foot
Gms/cu cm
Pounds/cu ft
Kgs/cu meter
Multiply By
0
...
456E-09
0
...
01602
16
...
000009425
27
...
00
2
...
03
8
...
56
0
...
70
0
...
80
0
...
86
8
...
87
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Formulas and Conversions
Units of Physical Quantities
Substance
Brick
Paraffin
Calcium
Platinum
Carbon (diamond)
Sand (dry)
Carbon (graphite)
Silicon
Carbon (charcoal)
Silver
Chromium
Slate
Clay
Sodium
Coal
Steel (mild)
Cobalt
Sulphur
Copper
Tin
Cork
Tungsten
Glass (crown)
Wood (ash)
Glass (flint)
Wood (beech)
Gold
Wood (ebony)
Iron (cast)
Wood (elm)
Iron (wrought)
Wood (lignum-vitae)
Lead
Magnesium
Manganese
Mercury
Lead
Magnesium
Manganese
Wood (oak)
Wood (pine)
Wood (teak)
Zinc
Wood (oak)
Wood (pine)
Wood (teak)
Zinc
Mercury
Relative Density
2
...
86
1
...
5
3
...
42
2
...
6
1
...
57
6
...
1-2
...
9
0
...
36-1
...
87
8
...
07
8
...
3
0
...
1
2
...
75
3
...
7-0
...
3
1
...
2
7
...
66
7
...
3
11
...
74
8
...
6
11
...
74
8
...
7-1
...
56
0
...
0
0
...
0
0
...
8
7
...
6
Download free eBooks at bookboon
...
Units of Physical Quantities
Greek Alphabet
Name
Alpha
Beta
Gamma
Delta
Epsilon
Zeta
Eta
Theta
Iota
Kappa
Lambda
Mu
Nu
Xi
Omicron
Pi
Rho
Sigma
Tau
Upsilon
Phi
Chi
Psi
Omega
Lower Case
α
β
γ
δ
ε
ζ
η
θ
ι
κ
λ
μ
ν
ξ
ο
π
ρ
σ and ς
τ
υ
φ
χ
ψ
ω
Upper Case
Α
Β
Γ
Δ
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
Think Umeå
...
teknat
...
se/english
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This system was formerly called the meter-kilogram-second (MKS) system
...
001
m
mF (Micro farads)
Nano
10-9
0
...
000000000001
p
pF (Pico farads)
hz (hertz)
F (Farads)
Conversion Chart
Multiply by
Into Milli
Into Centi
Into Deci
Into MGL*
Into Deca
Into Hecto
Into Kilo
To convert Kilo
106
105
104
103
102
101
1
To convert
Hecto
105
104
103
102
101
1
10-1
To convert Deca
104
103
102
101
1
10-1
10-2
To convert MGL*
103
102
101
1
10-1
10-2
10-3
To convert Deci
102
101
1
10-1
10-2
10-3
10-4
To convert Centi
101
1
10-1
10-2
10-3
10-4
10-5
To convert Milli
1
10-1
10-2
10-3
10-4
10-5
10-6
MGL = meter, gram, liter
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...
023 x 1026 /(kg mol)
Bohr magneton
B
9
...
380 x 10-23 J/k
Stefan-Boltzmann constant
d
5
...
602 x 10-19 J
Electron charge
e
1
...
109 x 10-31 kg
Electronic charge to mass ratio
e/me
1
...
65 x 107 C/(kg mol)
Permeability of free space
m0
4P x 10-7 H/m
Permittivity of free space
Eo
8
...
626 x 10-34 J s
Proton mass
mp
1
...
6
Standard gravitational acceleration
g
9
...
80665 N/kg
Universal constant of gravitation
G
6
...
314 kJ/(kg mol K)
Velocity of light in vacuum
C
2
...
67), 5/90R, 0C +
273
...
00 x 108 m s-1
Electron charge
e
-1
...
11 x 10-31 kg
Planck’s constant
h
6
...
com
23
Formulas and Conversions
System of Units
Name
Symbolic Representation
Numerical Equivalent
Universal gravitational constant
G
6
...
60 x 10-19 J
Mass of proton
mp
1
...
80 m s-2
Acceleration due to gravity on the
Moon
gM
1
...
37 x 106 m
Mass of the Earth
ME
5
...
96 x 108 m
Mass of the Sun
MS
1
...
74 x 106 m
Mass of the Moon
MM
7
...
84 x 108 m
Earth-Sun distance
-
1
...
00 x 108 m s-1
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Formulas and Conversions
System of Units
Name
Symbolic Representation
Numerical Equivalent
Electron charge
e
-1
...
11 x 10-31 kg
Planck’s constant
h
6
...
67 x 10-11 N m2 kg-2
Electron volt
1 eV
1
...
67 x 10-27 kg
Acceleration due to gravity on Earth
g
9
...
62 m s-2
Ton
1 ton
1
...
com
25
Formulas and Conversions
General Mathematical Formulae
4 General Mathematical Formulae
4
...
Expansion Formulae
Square of summation
• (x + y) 2 = x2 + 2xy + y2
Square of difference
• (x – y) 2 = x2 – 2xy + y2
Difference of squares
• x2 – y2 = (x + y) (x – y)
Cube of summation
• (x + y) 3 = x3 + 3x2y + 3xy2 + y3
Summation of two cubes
• x3 + y3 = (x + y) (x2 - xy + y2)
Cube of difference
• (x – y) 3 = x3 – 3x2y + 3xy2 – y3
Difference of two cubes
• x3 – y3 = (x – y) (x2 + xy + y2)
B
...
com
26
Formulas and Conversions
General Mathematical Formulae
The basic algebraic properties of real numbers a, b and c are:
Property
Description
Closure
a + b and ab are real numbers
Commutative
a + b = b + a, ab = ba
Associative
(a+b) + c = a + (b+c), (ab)c = a(bc)
Distributive
(a+b)c = ac+bc
Identity
a+0 = 0+a = a
Inverse
a + (-a) = 0, a(1/a) = 1
Cancellation
If a+x=a+y, then x=y
Zero-factor
a0 = 0a = 0
Negation
-(-a) = a, (-a)b= a(-b) = -(ab), (-a)(-b) = ab
Algebraic Combinations
Factors with a common denominator can be expanded:
a+b a b
= +
c
c c
Fractions can be added by finding a common denominator:
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2 Geometry
Item
Circumference /
Perimeter
Area
Surface Area
Volume
Square
4s
s2
NA
NA
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...
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29
Figure
Formulas and Conversions
Item
Circumference /
Perimeter
General Mathematical Formulae
Area
Surface Area
Volume
NA
NA
NA
Figure
NA
3s
Equilateral
triangle
where s is the length of
each side
Trapezoid
where θ and Φ are the
2 base angles
a +b
A=
h
2
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31
Figure
Formulas and Conversions
Item
Circumference /
Perimeter
General Mathematical Formulae
Area
Surface Area
Volume
NA
NA
NA
NA
A = 2
...
83 s2
Octagon
8s
Cube
NA
NA
6s2
s3
NA
NA
2 h + 2wh
+2 w
l×w×h
NA
NA
Right
cylinder
Where s is the
length of 1 side
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...
perimeter∙
slant height
+B
Figure
1 base area∙
3
perpendicular
height
...
com
33
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Formulas and Conversions
General Mathematical Formulae
Circumference /
Perimeter
Area
NA
Item
NA
NA
NA
Cone
Surface Area
Volume
Figure
V = lwh
pi∙r(r+sh)
4
...
Pythagoras’ Law
c2 = a2 + b2
c
a
B
...
com
34
Formulas and Conversions
General Mathematical Formulae
hypotenuse
opposite
θ
adjacent
Sine, Cosine and Tangent
sin θ =
opposite
hypotenus
cosθ =
adjacent
hypotenus
tan θ =
opposite
adjacent
Sine, Cosine and the Pythagorean Triangle
[sin θ ] + [cosθ ]
2
2
= sin 2 θ + cos 2 θ =1
Tangent, Secant and Co-Secant
tan
sin
cos
secθ =
1
cosθ
cscθ =
1
sin θ
C
...
com
35
Formulas and Conversions
General Mathematical Formulae
= cos(nθ ) + j sin(nθ )
e jnθ
e jθ + e− jθ
cosθ =
2
e jθ − e− jθ
sin θ =
2j
4
...
The number 8 written in index form as 8 = 23
The equation can be rewritten in logarithm form as log 2 8 = 3
Download free eBooks at bookboon
...
All logarithms must have the same base
...
e x − e− x
2
Hyperbolic sine = sinh x =
e x + e− x
2
Hyperbolic cosine = cosh x =
sinh x e x − e − x
= x
e + ex
Hyperbolic tangent = tanh x = cosh x
Download free eBooks at bookboon
...
5 Exponents
Summary of the Laws of Exponents
Let c, d, r, and s be any real numbers
...
6
Complex Numbers
A complex number is a number with a real and an imaginary part, usually expressed in Cartesian form
a + jb where j = √-1 and j ∙ j = -1
Complex numbers can also be expressed in polar form
Aejθ where A = √a2 +b2 and θ = tan-1 (b/a)
The polar form can also be expressed in terms of trigonometric functions using the Euler relationship
ejθ = cos θ + j sin θ
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Polar Form, Complex Numbers
The standard form of a complex number is
a + jb where j = √-1
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Formulas and Conversions
General Mathematical Formulae
But this can be shown to be equivalent to the form
Aejθ where A = √a2 +b2 and θ = tan-1 (b/a)
which is called the polar form of a complex number
...
Download free eBooks at bookboon
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1 Electricity
Ohm’s Law
I=
V
R
Or
V = IR
Where
I = current (amperes)
E = electromotive force (volts)
R = resistance (ohms)
Temperature correction
Rt = Ro (1 + αt)
Where
Ro = resistance at 0ºC (
...
)
α = temperature coefficient which has an average value for copper of 0
...
com
41
Formulas and Conversions
Engineering Concepts and Formulae
Values of alpha
Copper
0
...
00672
Tungsten
0
...
00428
Platinum
Current,
Ω/Ω ºC
0
...
Click here!
Download free eBooks at bookboon
...
m
...
generated in each conductor =
Where
Z = total number of armature conductors
c = number of parallel paths through winding between positive and negative brushes
Where c = 2 (wave winding), c = 2p (lap winding)
Φ = useful flux per pole (webers), entering or leaving the armature
p = number of pairs of poles
N = speed (revolutions per minute)
Generator Terminal volts = EG – IaRa
Motor Terminal volts = EB + IaRa
Where EG = generated e
...
f
...
m
...
Ia = armature current
Ra = armature resistance
Alternating Current
RMS value of sine curve = 0
...
637 of maximum value
Form factor = RMS value / Mean Value = 1
...
com
43
Formulas and Conversions
Engineering Concepts and Formulae
Slip of Induction Motor
[(Slip speed of the field – Speed of the rotor) / Speed of the Field] × 100
Inductors and Inductive Reactance
Physical Quantity
Equation
Inductors and Inductance
VL = L
Inductors in Series:
LT = L1 + L2 + L3 +
...
L T L1 L 2 L 3
di
dt
Current build up
(switch initially closed after having
been opened)
Current decay
(switch moved to a new position)
Alternating Current
Complex Numbers:
Polar form:
Inductive Reactance
Capacitive Reactance
Resistance
)
R
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...
Voltage Divider Rule
Vx = VT
Zx
ZT
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Z T Z1 Z 2 Z 3
Current Divider Rule
Ix = IT
Two impedance values in parallel
ZT =
ZT
Zx
Z1 Z 2
Z1 + Z 2
Capacitance
Q
Capacitors
C = V [F] (Farads)
Capacitor in Series
1
1
1
1
=
+
+
+
...
Charging a Capacitor
Discharging a Capacitor
Quantity
Equation
Capacitance
C=
Q
V
C=
Capacitance of a Parallel-plate
Capacitor
εA
E=
Download free eBooks at bookboon
...
• The introduction of the dielectric increases the capacitance of the capacitor
Current in AC Circuit
RMS Current
In Cartesian
form
I=
I=
V
⋅ R−
2
2
1
R + ωL −
ωC
V
2
1
[ R + ωL −
]
ωC
1
j ωL −
ωC
Amperes
∠ − φs
2
In polar form
1
ωL − ωC
φ s = tan
R
where
−1
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science
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I ) = V cos φ
I
Power in ac circuits
Quantity
Equation
Resistance
The mean power =
Inductance
The instantaneous power = (Io sin wt) (Vo sin (wt + π)
The mean power
P
Capacitance
The instantaneous power = (Io sin (wt + π/2)) (Vo sin
wt )
The mean power
P
Formula for a
...
power
The mean power =
=0
Star connected
3 • Phase Voltage
Line current = phase current
Delta connected
Line voltage = phase voltage
Line current =
= Irms Vrms = Irms2 R
= 0
Three Phase Alternators
Line voltage =
P
3 • Phase Current
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50
Formulas and Conversions
Engineering Concepts and Formulae
• The electric field at the surface of a conductor is perpendicular to the surface
...
Quantity
Equation
Suppose a point charge Q is at A
...
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B=
Force on a current-carrying conductor in a magnetic field
And Magnitude of
F
I
sin θ
Force on a moving charged particle in a magnetic field
Circulating Charges
Calculation of magnetic flux density
Physical Quantity
Equation
B=
Magnetic fields around a long straight wire carrying current
I
µo I
2pa
where a = perp
...
I: B =
n I, where n = number of turns per unit
length
...
com
52
µ o I1 I 2
2pa
Formulas and Conversions
Engineering Concepts and Formulae
Physical Quantity
Equation
T = F b sin θ
The torque on a rectangular coil in a magnetic field
=NI
B b sinθ
= N I A B sinθ
T = N I A B sin θ
If the coil is in a radial field and the plane of the coil is
always parallel to the field, then
= N I A B sin 90o
=NIAB
= B A cos θ
Magnetic flux f
and
Flux-linkage =
SI =
Current Sensitivity
θ
I
=
Nφ
NAB
c
Lenz’s law
The direction of the induced e
...
f
...
EMF Equations
E
...
f
...
m
...
induced between the center and the rim of a spinning
disc
E
...
f
...
c
...
com
53
ε=BLv
ε = B πr2f
Ε = N A B w sin wt
Formulas and Conversions
Engineering Concepts and Formulae
Quantity
Equation
When a great load (or smaller resistance) is
connected to the secondary coil, the flux
in the core decreases
...
m
...
, εp, in the
primary coil falls
...
Kirchoff ’s second law (Loop Theorem)
The net e
...
f
...
d
...
Physical Quantity
Equation
Power
Electric current
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Shaded areas represent regions of overlap
...
Gamma rays and X-rays occupy a common region
...
2
Applied Mechanics
5
...
1
Newton’s laws of motion
Newton’ first law of motion
The inertia of a body is the reluctance of the body to change its state of rest or motion
...
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“Third-law pair” of forces act on two different bodies
...
mp is the mass of the planet
...
com
56
Formulas and Conversions
Engineering Concepts and Formulae
Physical Quantity
Equations
Centripetal acceleration
Centripetal force
Newton’s Law of Universal
Gravitation
Gravitational field strength
Physical Quantity
Equations
Moment of a force
Principle of
moments
Stress
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...
28 ft/s
1km/h = 0
...
61 m/s for each °C rise
...
In SI the basic unit is m/s2
In Imperial ft/s2
Conversion:
Acceleration due to gravity, g is 9
...
2
...
com
58
Formulas and Conversions
Engineering Concepts and Formulae
Angular Velocity and Acceleration
Quantity
Equations
θ angular displacement (radians)
θ=
ω1 + ω 2
ω angular velocity (radians/s);
2
×t
1
2
θ = ω 1t + αt 2
ω1 = initial, ω2 = final
α angular acceleration (radians/s2)
Linear displacement
s=rθ
Linear velocity
v=rω
Linear, or tangential acceleration
aT = r α
Tangential, Centripetal and Total Acceleration
Quantity
Equations
Tangential acceleration aT is due to angular acceleration α
aT = rα
Centripetal (Centrifugal) acceleration ac is due to change in direction
only
ac = v2/r = r ω2
Total acceleration, a, of a rotating point experiencing angular
acceleration is the vector sum of aT and ac
a = aT + ac
5
...
3 Force
Vector quantity, a push or pull which changes the shape and/or motion of an object
In SI the unit of force is the newton, N, defined as a kg m
In Imperial the unit of force is the pound lb
Conversion: 9
...
2 lb
Weight
The gravitational force of attraction between a mass, m, and the mass of the Earth
In SI weight can be calculated from Weight = F = mg, where g = 9
...
com
59
Formulas and Conversions
Engineering Concepts and Formulae
Momentum
Vector quantity, symbol p,
p = mv [Imperial p = (w/g)v, where w is weight]
in SI unit is kgm / s
Work
Scalar quantity, equal to the (vector) product of a force and the displacement of an object
...
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Formulas and Conversions
Engineering Concepts and Formulae
Kinetic Energy of Rotation
Where I = mk2 is the moment of inertia
5
...
4
Centripetal (Centrifugal) Force
Where r is the radius
Where ω is angular velocity in rad/s
Potential Energy
Quantity
Equation
Energy due to position in a force field, such as
gravity
Ep = m g h
Ep = w h
In Imperial this is usually expressed
Where w is weight, and h is height
above some specified datum
Thermal Energy
In SI the common units of thermal energy are J, and kJ, (and kJ/kg for specific quantities)
In Imperial, the units of thermal energy are British Thermal Units (Btu)
Conversions
1 Btu = 1055 J
1 Btu = 778 ft-lb
Electrical Energy
In SI the units of electrical energy are J, kJ and kilowatt hours kWh
...
66 x 106 ft-lb
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...
p
...
p
...
3 kPa or 14
...
895 kPa
Pressure may be expressed in standard units, or in units of static fluid head, in both SI and Imperial systems
Download free eBooks at bookboon
...
294 in
...
5 mm mercury
• 1 kPa = 4
...
water = 102 mm water
• 1 psi = 2
...
mercury = 51
...
7 in
...
81 kPa
Other pressure unit conversions:
• 1 bar = 14
...
1 kPa = 14
...
981 bar
• 1 atmosphere (atm) = 101
...
7 psi
Simple Harmonic Motion
Velocity of P =
5
...
5
ω R2 − x
2
m
s
Stress, Strain And Modulus Of Elasticity
Young’s modulus and the breaking stress for selected materials
Download free eBooks at bookboon
...
70
2
...
16
4
...
90
4
...
93
3
...
10
11
...
55
10
Tungsten
4
...
17
1
...
3 Thermodynamics
5
...
1
Laws of Thermodynamics
• W = PΔV
• ΔU = Q – W
• W= nRT lnVf/Vi
• Q = CnΔT
• Cv= 3/2R
• Cp= 5/2R
• Cp/Cv = γ= 5/3
• e = 1 – Qc/Qh = W/Qh
• ec = 1 – Tc/Th
• COP = Qc/W (refrigerators)
• COP = Qh /W (heat pumps)
• Wmax= (1-Tc/Th)Qh
• ΔS = Q/T
5
...
2 Momentum
• p = mv
• ∑F = Δp/Δt
5
...
3 Impulse
I = Fav∆ t = mvf – mvi
Download free eBooks at bookboon
...
3
...
3
...
3
...
3
...
com
65
Formulas and Conversions
Engineering Concepts and Formulae
5
...
8 Gravity
• F = Gm1m2/r2
• T = 2π / √r3 /GMs
• G = 6
...
97 x 1024 kg
• RE = 6
...
3
...
QYURGGF 'PIKPGU /GFKWOURGGF 'PIKPGU 6WTDQEJCTIGTU 2TQRGNNGTU 2TQRWNUKQP 2CEMCIGU 2TKOG5GTX
6JG FGUKIP QH GEQHTKGPFN[ OCTKPG RQYGT CPF RTQRWNUKQP UQNWVKQPU KU ETWEKCN HQT /#0 &KGUGN
6WTDQ
2QYGT EQORGVGPEKGU CTG QHHGTGF YKVJ VJG YQTNFoU NCTIGUV GPIKPG RTQITCOOG s JCXKPI QWVRWVU URCPPKPI
HTQO VQ M9 RGT GPIKPG )GV WR HTQPV
(KPF QWV OQTG CV YYYOCPFKGUGNVWTDQEQO
Download free eBooks at bookboon
...
3
...
• fn = nv/4L (open at one end) n = 1,3,5,7………
5
...
11 Beats
• fbeats = | f1 – f2 |
• Fluids
• ρ = m/V
• P = F/A
• P2 = P1 + ρgh
• Patm = 1
...
7 lb/in2
• FB = ρfVg = Wf (weight of the displaced fluid)
• ρo/ρf = Vf /Vo (floating object)
• ρwater = 1000 kg/m3
• Wa=W-FB
Equation of Continuity: Av = constant
Bernoulli’s equation: P + ½ ρv2 + ρgy = 0
5
...
12
Temperature and Heat
• TF= (9/5) TC+32
• TC= 5/9(TF-32)
• ∆TF = (9/5) ∆TC
• T= TC+273
...
com
67
Formulas and Conversions
Engineering Concepts and Formulae
• ΔV = βVoΔT β=3α
• Q = mcΔT
• Q = mL
• 1 kcal = 4186 J
• Heat Loss = Heat Gain
• Q = (kAΔT)t/L,
• H = Q/t =(kAΔT)/L
• Q = eσT4At
• P = Q/t
• P = σAeT4
• P net= σAe(T4-TS4)
• σ = 5
...
3
...
31 J/mol K
• PV = NkT
• NA = 6
...
38 × 10-23 J/K
• M=NAm
• (KE)av=(1/2mv2 )av= 3/2kT
• U= 3/2NkT = 3/2nRT
5
...
14
Elastic Deformation
• P = F/A
• Y = FLo/A∆L
• S = Fh/A∆x
• B = –Vo∆F / A∆V
• Volume of the sphere = 4πr3/3
• 1 atm = 1
...
3
...
3
...
com
68
Formulas and Conversions
5
...
17
Engineering Concepts and Formulae
Latent Heat
• Latent heat of fusion of ice = 335 kJ/kg
• Latent heat of steam from and at 100°C = 2257 kJ/kg
• 1 tonne of refrigeration = 335 000 kJ/day = 233 kJ/min
5
...
18
Gas Laws
Boyle’s Law
When gas temperature is constant
PV = constant or
P1V1 = P2V2
Where P is absolute pressure and V is volume
Charles’ Law
When gas pressure is constant,
V
= const
...
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Formulas and Conversions
Engineering Concepts and Formulae
V1 V2
=
T1 T2
where V is volume and T is absolute temperature
Gay-Lussac’s Law
When gas volume is constant,
P
= const
...
T1
T2
P V = m R T where P = absolute pressure (kPa)
V = volume (m3)
T = absolute temp (K)
m = mass (kg)
R = characteristic constant (kJ/kgK)
Also
PV = nRoT where P = absolute pressure (kPa)
V = volume (m3)
T = absolute temperature K
N = the number of kmoles of gas
Ro = the universal gas constant 8
...
com
70
Formulas and Conversions
5
...
19
Engineering Concepts and Formulae
Specific Heats Of Gases
Specific Heat at
Constant Pressure
Specific Heat at
Constant Volume
Ratio of
Specific
kJ/kgK or kJ/kg oC
kJ/kgK or kJ/kg oC
γ= cp / cv
Air
1
...
718
1
...
060
1
...
32
Carbon Dioxide
0
...
630
1
...
051
0
...
40
Helium
5
...
153
1
...
235
10
...
41
Hydrogen Sulphide
1
...
85
1
...
177
1
...
30
Nitrogen
1
...
745
1
...
913
0
...
40
Sulphur Dioxide
0
...
451
1
...
3
...
com
71
Formulas and Conversions
Engineering Concepts and Formulae
High Speed Diesel (Dual-Combustion) Cycle
η =1
kβ γ − 1
rv
γ −1
[(k − 1) + γk ( β − 1)]
Where rv= cylinder volume / clearance volume
k = absolute pressure at the end of constant V heating (combustion) / absolute pressure at the beginning of constant
V combustion
β = volume at the end of constant P heating (combustion) / clearance volume
Gas Turbines (Constant Pressure or Brayton Cycle)
η =1−
1
γ −1
γ
rp
where rp = pressure ratio = compressor discharge pressure / compressor intake pressure
5
...
21
Heat Transfer by Conduction
Material
Coefficient of
Thermal Conductivity
W/m °C
Air
0
...
RUN LONGER
...
GAITEYE
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com
1349906_A6_4+0
...
85
Cork
0
...
0
Iron, cast
70
Steel
60
Wallboard, paper
0
...
6
Copper
380
Felt
0
...
04
Plastic, cellular
0
...
3
...
15
Thermal Expansion of Solids
Increase in length = L α (T2 – T1)
Where L = original length
α = coefficient of linear expansion
(T2 – T1) = rise in temperature
Increase in volume = V β (T2 – T1)
Where V = original volume
β = coefficient of volumetric expansion
(T2 – T1) = rise in temperature
Coefficient of volumetric expansion = Coefficient of linear expansion × 3
β = 3α
5
...
23
Chemical Heating Value of a Fuel
Chemical Heating Value MJ per kg of fuel =
C is the mass of carbon per kg of fuel
H2 is the mass of hydrogen per kg of fuel
O2 is the mass of oxygen per kg of fuel
S is the mass of sulphur per kg of fuel
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Change in
Internal
Energy
Change in
Enthalpy
Change in
Entropy
Formulas and Conversions
Isothermal
P V2
1
=
P2 V1
1
T=Constant
Isentropic
γ
S=Constant
Engineering Concepts and Formulae
P V2
1
=
P2 V1
γ
P V2
1
=
P2 V1
n
--
T1 P
= 1
T2 P2
Polytropic
PVn =
Constant
n
T1 P
= 1
T2 P2
P
mRT log e 1
P
2
--
γ −l
γ
n −l
n
T1 V2
=
T2 V1
P
mRT log e 1
P
2
0
0
γ −1
T1 V2
=
T2 V1
0
0
n −1
Thermodynamic Equations for perfect gases
*Can be used for reversible adiabatic processes
cv = Specific heat at constant volume, kJ/kgK
cp = Specific heat at constant pressure, kJ/kgK
cm = Specific heat for polytropic process =
H = Enthalpy, kJ
γ = Isentropic Exponent, cp/cv
n = polytropic exponent
P = Pressure, kPa
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Formulas and Conversions
Engineering Concepts and Formulae
R = Gas content, kJ/kgK
S = Entropy, kJ/K
T = Absolute Temperature, K = 273+˚C
U = Internal Energy, kJ
V = Volume, m3
m = Mass of gas, kg
Mean Specific Heat between 0
o
C
Specific Heat and Linear
Expansion of Solids
and 100
o
C
o
C
kJ/kgK or kJ/kg
Coefficient of Linear Expansion
between
o
o
C
C
0
and 100
(multiply by 10-6)
Aluminum
0
...
8
Antimony
0
...
5
Bismuth
0
...
4
Brass
0
...
4
Carbon
0
...
9
Cobalt
0
...
3
Copper
0
...
5
Glass
0
...
0
Gold
0
...
2
2
...
4
Iron (cast)
0
...
4
Iron (wrought)
0
...
0
Lead
0
...
0
Nickel
0
...
0
Platinum
0
...
6
Silicon
0
...
8
Silver
0
...
5
Steel (mild)
0
...
0
Tin
0
...
7
Zinc
0
...
5
Ice (between -20
o
C
&0
o
C
)
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Ammonia
0
...
138
12
...
643
1
...
139
1
...
633
Petroleum
2
...
093
12
...
800
9
...
183
3
...
4
Fluid Mechanics
5
...
1
11
...
com
77
d2
dc
2
Cc =
Ac d c
=
A d
2
Formulas and Conversions
Engineering Concepts and Formulae
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...
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Formulas and Conversions
Engineering Concepts and Formulae
At the vena contracta, the volumetric flow rate Q of the fluid is given by
• Q = area of the jet at the vena contracta ∙ actual velocity = AcV
• Or
• Typically, values for Cd vary between 0
...
65
• Circular orifice: Q = 0
...
62 (B ∙ H) 2/3 √2gh
Where B = breadth (m)
H = head (m above sill)
Triangular Right Angled Notch: Q = 2
...
4
...
01 in large pipes to 0
...
4
...
3
6
...
73
3
...
7
9
...
24
6717 × 10-5
3/8
17
...
5
2
...
236 × 10-4
1/2
21
...
8
2
...
960 × 10-4
Download free eBooks at bookboon
...
7
20
...
87
3
...
4
26
...
38
5
...
2
35
...
56
9
...
3
40
...
68
1
...
3
52
...
91
2
...
0
62
...
16
3
...
9
77
...
49
4
...
6
90
...
74
6
...
3
102
...
02
8
...
3
128
...
55
1
...
3
154
...
11
1
...
1
202
...
18
3
...
1
254
...
27
5
...
9
303
...
31
7
...
6
333
...
10
8
...
4
381
...
70
0
...
2
428
...
27
0
...
0
477
...
06
0
...
6
574
...
45
0
...
com
80
Formulas and Conversions
References
6 References
6
...
00
8
2A
2
3A
13
4A
14
5A
15
6A
16
7A
17
2
He
4
...
94
1
4
Be
9
...
8
1
6
C
12
...
0
1
8
O
16
...
0
0
10
Ne
20
...
9
9
12
Mg
24
...
9
8
14
Si
28
...
9
7
16
S
32
...
4
5
18
Ar
39
...
1
0
20
Ca
40
...
9
6
22
Ti
47
...
9
4
24
Cr
52
...
9
4
26
Fe
55
...
9
3
28
Ni
58
...
5
5
30
Zn
65
...
7
2
32
Ge
72
...
9
2
34
Se
78
...
9
0
36
Kr
83
...
4
7
38
Sr
87
...
9
1
40
Zr
91
...
9
1
42
Mo
95
...
9
44
Ru
101
...
9
46
Pd
106
...
9
48
Cd
112
...
8
50
Sn
118
...
8
52
Te
127
...
9
54
Xe
131
...
9
56
Ba
137
...
9
72
Hf
178
...
9
74
W
183
...
2
76
Os
190
...
2
78
Pt
195
...
0
80
Hg
200
...
4
82
Pb
207
...
(209) (210) (222)
0
64
Gd
157
...
9
66
Dy
162
...
9
68
Er
167
...
9
88
87
Ra
Fr
(223) 226
...
(261) (262) (266) (264) (265) (268)
0
58
Ce
140
...
9
62
61
60
Sm
Pm
Nd
144
...
4
2
90
Th
232
...
0
92
U
238
...
0
70
Yb
173
...
0
100 101 102 103
99
98
97
96
95
94
93
Lr
No
Md
Fm
Es
Cf
Bk
Am Cm
Pu
Np
237
...
com
81
Formulas and Conversions
6
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References
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