PF Blue + Charcoal
Transcript of PF Blue + Charcoal
This document contains useful information and formulas to assist you during your Remote Proctor Exam. Please note that the exam is a closed-book exam, so this document is the only reference material you are permitted to use during your exam session.
PF Blue + Charcoal
PF Blue + White
SP####(yymm)
RULES OF MULTIPLICATION
AB 5 A B 5 A ⋅ B
Rule 1: There can be only two factors involved at one time in a multiplication problem.
Rule 2: The product of two whole numbers is always a whole number.Example: 9 3 4 5 36
Rule 3: The product of any number and zero is always zero.Examples: 7 3 0 5 0 65.29 3 0 5 0
Rule 4: The product of any number and 1 is always that same number.Examples: 14 3 1 5 14 556 3 1 5 556 654.321 3 1 = 654.321
Rule 5: The order in which you multiply two numbers doesn’t change the product.Examples: 5 3 4 5 20 4 3 5 5 20
Rule 6: The way you group numbers in a series of multiplication problems doesn’t change the final product.Examples: 2 3 5 3 4 5 40 5 3 2 3 4 5 40
(Note: There are three factors in this problem. You must multiply the first two factors before you multiply the product of those two factors by the third number.)
RULES OF DIVISION
Rule 1: Zero (0) divided by any number equals 0. (If you have nothing and divide it, you still have nothing.)Examples: 0 4 4 5 0 0 4 2,627 5 0 0 4 29.42 5 0
Rule 2: The number zero (0) can’t be used as a divisor. In other words, you can’t divide any number by 0.
Rule 3: Any number divided by 1 is equal to that same number.Examples: 15 4 1 5 15 3,500 4 1 5 3,500 999.68 4 1 5 999.68
Rule 4: Any number divided by itself equals 1.Examples: 5 4 5 5 1 346 4 346 5 1 54.21 4 54.21 5 1
Rule 5: The order in which you divide numbers changes the quotient.Examples: 4 4 2 isn’t the same as 2 4 4
PF Blue + Charcoal
PF Blue + White
186009(1606)
The shaded area in each circle graphically represents the fractions shown below it.
Graphic Representation of Proper and Improper Fractions
PF Blue + Charcoal
PF Blue + White
186010(1606)
186010(1606)
EXPRESSING FRACTIONS AS DECIMALS
Fraction Equivalent Decimal
1
10.1
1
100.01
1
1 000,.001
1
10 000,.0001
1
100 000,.00001
1
1 000 000, ,.000001
ROUNDING OFF A NUMBER
Step 1: Find the digit you want to round to. (It may help if you circle this digit.)
Step 2: Look at the digit immediately to the right of the circled digit.
Step 3: If the digit to the right is 5 or more, then round up by increasing the circled digit by 1. If the digit to the right is less than 5, you round down—you don’t change the circled digit.
Step 4: Drop all digits (including zeros) to the right of the rounded digit.
FRACTIONS AND DECIMAL EQUIVALENTS
Pages 29—30
SOLVING PERCENT PROBLEMS
To Find UsePercentage (P) P 5 R 3 B
Rate (R) R 5 P 4 B
Base (B) B 5 P 4 R
RULES FOR SETTING UP DIRECT PROPORTIONS
1. The units used in the first ratio must be alike, and the units used in the second ratio must be alike.
2. Both ratios must be set up in a similar manner (larger to smaller or smaller to larger).
The shaded areas in each of the clocks indicate the angles. The hands of the clock in A show a straight angle (180); in B, a right angle (90); and in C, a 270 angle.
FRACTIONS AND DECIMAL EQUIVALENTS
Fraction Decimal Fraction Decimal
1
640.015625
33
640.515625
1
32.03125
17
32.53125
3
64.046875
35
64.546875
1
16.0625
9
16.5625
(Continued)
FRACTIONS AND DECIMAL EQUIVALENTS
Fraction Decimal Fraction Decimal
5
64.078125
37
64.578125
3
32.09375
19
32.59375
7
64.109375
39
64.609375
1
8.125
5
8.625
9
64.140625
41
64.640625
5
32.15625
21
32.65625
11
64.171875
43
64.671875
3
16.1875
11
16.6875
13
64.203125
45
64.703125
7
32.21875
23
32.71875
15
64.234375
47
64.734375
(Continued)
FRACTIONS AND DECIMAL EQUIVALENTS
Fraction Decimal Fraction Decimal
1
4.25
3
4.75
17
64.265625
49
64.765625
9
32.28125
25
32.78125
19
64.296875
51
64.796875
5
16.3125
13
16.8125
21
64.328125
53
64.828125
11
32.34375
27
32.84375
23
64.359375
55
64.859375
3
8.375
7
8.875
25
64.390625
57
64.890625
13
32.40625
29
32.90625
(Continued)
FRACTIONS AND DECIMAL EQUIVALENTS
Fraction Decimal Fraction Decimal
27
64.421875
59
64.921875
7
16.4375
15
16.9375
29
64.453125
61
64.953125
15
32.46875
31
32.96875
31
64.484375
63
64.984375
1
20.500 1.000 1.000
FRACTIONAL EQUIVALENTS OF COMMON PERCENTS
Fraction Percent Fraction Percent
1
205%
1
3331/3%, 33.3%
1
1661/4%, or 6.25%
1
250%
1
8121/2%, or 12.5%
2
3662/3%, or 66.7%
1
520%
3
475%
1
425%
7
8871/2%, or 87.5%
In each of the angles here, the point C at which the two lines meet is called the ver-tex of the angle. Lines AC and BC are the sides of the angles.
FORMULA FOR DISTANCE
d rt= distance 5 rate 3 time
PERIMETER OF A RECTANGLE
P l w= +2 2 Perimeter 5 2(length) 1 2(width)
AREA OF A RECTANGLE
A lw= Area 5 length width
AREA OF A TRIANGLE
A bh=
2 A 5 area
b 5 base h 5 altitude
VOLUME OF A PYRAMID
V Bh=
3 V 5 volume of pyramid
B 5 area of the base around the pyramid h 5 altitude of the pyramid (The altitude of a pyramid is the distance from the base
to the top of the pyramid.)
CURRENT OF A CIRCUIT
I ER
= I 5 current, in amperes (A)
E 5 electromotive force, in volts (V) R 5 resistance, in ohms (Ω)
PITCH OF A SCREW THREAD
PN
=1 P 5 pitch
N 5 number of threads per inch
PF Blue + Charcoal
PF Blue + White
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CONDUCTANCE
GR
=1 G 5 conductance, in mhos
R 5 resistance, in ohms
AREA OF A SQUARE
A s= 2 A 5 areas 5 length of one side
AREA OF A CIRCLE
A r= p 2 A 5 areap 5 3.1416r 5 radius of the circle
VOLUME OF A SPHERE
V r=
43
3p V 5 volume p 5 3.1416
r 5 radius
LIQUID FLOW
Q CND= 3 Q 5 volume of liquid, in cubic feet per secondC 5 constant for a given design of impellerN 5 rotating speed of impeller, in revolutions per secondD 5 impeller diameter, in feet
SQUARE ROOTS FOR NUMBERS 1—200 Page 19
CURRENT IN A CIRCUIT
I PR
=I 5 current, in amperes
P 5 power, in watts R 5 resistance, in ohms
IMPEDANCE
Z R X= +2 2 Z 5 impedance, in ohms R 5 resistance, in ohms
X 5 reactance, in ohms
POWERS AND ROOTS
( )x x2 = A square root is a number that when multiplied by itself results in the original number.
Three measurements must be made to find the basic dimensions of this table. The rule should be held parallel with the edges being measured to get exact dimensions.
COMMON ENGLISH UNITS OF LENGTH
1 mile= 1760 yd.= 5280 ft.
1 yd.= 3 ft.= 36 in
1 ft.= 12 in= 1/3 yd.
1 in= 1/12 ft.= 1/36 yd.
COMMON SI METRIC UNITS OF LENGTH
1 m (meter)= 1000 mm (millimeters)= 100 cm (centimeters)= 0.001 km (kilometer)
1 km = 1000 m
1 cm = 0.01 m
1 mm = 0.001 m
PF Blue + Charcoal
PF Blue + White
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CONVERT FROM ENGLISH UNITS TO SI UNITS:
inches 5 millimeters 4 25.4
CONVERT SI UNITS TO ENGLISH UNITS:
millimeters 5 inches 3 25.4
PERIMETER OF A RECTANGLE
P 5 2a 1 2b
PERIMETER OF A SQUARE
P 5 4a
PERIMETER OF A SCALENE TRIANGLE
P 5 a 1 b 1 c
PERIMETER OF AN ISOSCELES TRIANGLE
P 5 a 1 2b
PERIMETER OF AN EQUILATERAL TRIANGLE
P 5 3a
CIRCUMFERENCE GIVEN DIAMETER
P 5 3.14d
CIRCUMFERENCE GIVEN RADIUS
P 5 6.28r
CONVERSION FACTORS
1 m = 39.37 in.1dm = 3.937 in.1 cm = 0.3937 in.1 mm = 0.03937 in.
1 dm = 0.1 m1 cm = 0.01 m1 mm = 0.001 m
1 in. = 0.0254 m1 in. = 0.254 dm1 in. = 2.54 cm1 in. = 25.4 mm
PF Blue + Charcoal
PF Blue + White
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186068(1606)
Factory Management Functions
PF Blue + Charcoal
PF Blue + White
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Chief ExecutiveO�cer (CEO)
Plant Manager
ProductionSupervisor
MaterialsManager
Test EngineeringInformationTechnology
Sales ForceCustomerService
Worker
CAD Designers
ProductionManagers
DevelopmentEngineers
Engineering Lab
FacilitiesManager
Chief FinancialO�cer (CFO)
Accounting
QualityAssuranceManager
HumanResourceManager
ManufacturingEngineering
Services
Sales andMarketingManager
ProductionSupervisor
Plant Manager
DepartmentShift Supervisor
(1st shift)
DepartmentShift Supervisor
(3rd shift)
OtherDepartments
Research andDevelopment
DepartmentShift Supervisor
(2nd shift)
Worker
Worker Worker
Worker Worker
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Factors of Production
Output
Product
Waste
Customer Requirements
Machines and Materials
Methods (Processes)
Men (People)
Capitol
ManufacturingSystem
Inspection / Metrology
Quality Control
Quality Assurance
Quality
Management
Total
Quality
Management
Quality Management System
SIX SIGMA METHODOLOGIES
TOOLS USED FOR SIX SIGMA PROJECTS
OO Customer Surveys
OO Process flowcharts
OO Stakeholder analysis
OO Histograms and Pareto charts
OO Statistical process control (SPC)
Existing Processes and Products New Processes and Products
DMAIC Define – Measure – Analyze – Improve – Control
DMADV Define – Measure – Analyze – Design – Verify
Define who are the customers, what are the require-ments, what are their expectations; project bound-aries and the beginning and end of the process; the processes to be improved by mapping flow and relationships.
Define goals of the design activity; what is being designed and why; goals that are consistent with cus-tomer demands and business strategies.
Measure the performance of the basic processes involved; develop a basic data collection plan; mea-sure data from multiple sources to determine types and rates of defects; compare results to customer requirements.
Measure baseline abilities of current processes for fu-ture comparisons; define critical measurement needs; translate customer requirements into project goals.
Analyze the data collected to determine possible causes; gaps between performance and goals; possi-ble sources of variations
Analyze proposed processes for potential trouble spots and possible resolutions.
Improve the process by developing solutions using technology, training.
Design the process and product to meet customer needs with an effective use of resources.
Control implementing of improvements, document the changes; institutionalization of the improvements by training, staffing changes or additions or changes of equipment.
Verify the design performance and ability to meet customer requirements and business goals.
OO Regression analysis
OO ANOVA (analysis of variance)
OO Brainstorming
OO Failure modes and effects analysis (FEMA)
OO Cause and effect diagrams (Fishbone charts
MOST COMMON LINE TYPES USED IN PRINT
PF Blue + Charcoal
PF Blue + White
186080(1606)
Type Use Appearance and Weight
Visible (Object) Line Primary Objects
(Thick)
Hidden (Object) Line Show Hidden Features
(Thin)
Cutting-Plane Reveal Internal Features B↑– – – – – – ↑B(Thick)
Dimension Line Specify Size or Location |←1.000→|
(Thin)
Extension Line Specify Size or Location
(Thin)
Leader Identify Features
(Thin)
Centerline Define Center Lines of Arcs
(Thin)
Section Line Internal Features or Varied Materials
Long (Thin)
Break Line Identify Breaks
Short (Thick)
Phantom Line Show Different Position or Repetitive Features
(Thin)
Extension LineDimension Line
TYPICAL SYMBOLS FOR SOME COMMON UTILITY LINES
PF Blue + Charcoal
PF Blue + White
186081(1606)
3527.00
Existing Spot Evaluation
_______527________Proposed Contour (Finished Grade)
Existing Sanitary Manhole
Existing Storm Manhole
Existing Inlets
Proposed Catch Basin
Property Line
Proposed Sanitary Lateral
E/T/CProposed Electric, Telephone, Cable
WProposed Water
ST STProposed Storm Sewer
GProposed Gas
ELECTRONIC COMPONENT SYMBOLS
Capacitor or Condensor
Older Symbol for Capacitor
Shielded Capacitor
Variable Capacitor
Capacitor Bushing for Circuit Breaker or Transformer
Inductor or Coil
Magnetic-Core Inductor (Optional)
Tapped Inductor
Saturable-Core Inductor or Reactor
Blowout Coil Found in High-Voltage
Resistor
Tapped Resistor
Variable Resistor
AC Power Supply
Switch
Transformer
Diode/Rectifier
Silicone Controlled Rectifier (SCR)
Bridge Rectifier (AC to DC)
OR
OR
OR
A
DC Power Supply
Ground
Chassis Ground
SI BASE UNITS
USEFUL CONVERSION FACTORS
PF Blue + Charcoal
PF Blue + White
186082(1606)
Quantity Name SymbolLength Meter m
Mass Kilogram kg
Time Second s
Electric current Ampere A
Temperature, scientific use Kelvin K
Temperature, general use Degree Celsius C
Luminous intensity Candela Cd
Amount of substance Mole mol
To convert from: To: Multiply by:Inches Meters 2.54 3 10-2
in2 m2 6.4516 3 10-4
Feet Meters 0.3048
ft2 m2 9.290304 3 10-2
*lbm(*pound mass)
kg 0.45359
*lbf/in2 (psi)(*pound force)
Pa 6.894757 3 103
D d A
EW
ABEC Bearing Classifications and Tolerances
ABEC
ABEC
ABEC
ABEC
Class 1
Class 3
Class 5
Class 7
+0.0000–0.0005+0.0000–0.0004+0.0000–0.0003+0.0000–0.0002
Dimension D
Bearings are classified by their ABEC class, with higher classes having closer tol-erances and higher costs. It’s not uncommon for the same-size bearing in a Class 7 or 9 to be ten to twenty times more expensive than the same bearing in a Class 1 or 2 specification.
110Arc LengthMMaximum Material Condition MMC
Least Material Condition LMC L
Projected Tolerance Zone P
Circularity
Straightness
Cylindricity
Perpendicularity
Flatness
Surface Profile
Line Profile
Counterbore or Spotface
Depth
Dimension Origin
Quantity
Countersink
Square
Reference (35)
6.375Basic or Exact Dimension
Datum Feature Symbol
Feature Control Frame
B
Datum Target
¯.010 M B C
A2
Parallelism
Angularity
Position
Concentricity
Circular Runout
Total Runout
Symmetry
All Around
Conical Taper
Flat Taper Slope
Radius R
Spherical Radius
Spherical Diameter
SR
SD
Diametrical Symbol
.001 M A B C
Geometric Characteristic
Symbol
Zone Descriptor
Feature Tolerance
Modifier
Primary Datum Reference
Secondary Datum Reference
Tertiary Datum Reference
A feature control frame is a shorthand way of telling the print reader how to interpret the dimensions of a feature, and how it relates to other part features. The frame is read from left to right.
A few basic dimen-sional requirements will determine almost all the rest of the gear geometry, as shown in this table of formulas.
nPOutside Diameter
Pitch Diameter
Pitch Point
nG
Pitch Circle Center Distance
Tooth Profile(Involute)
Circular Pitch
Tooth Thickness
Width of Space
Pitch Circle
Bottom Land
Flank
FaceAddendum CircleTo
p Lan
d
Face W
idth
Addendum
Dedendum
Clearance Fillet Radius
DedendumCircle Clearance
Circle
NG = 18
NP= 11
Number of Teeth in Pinion
Number of Teeth in Gear
The gear ratio is the ratio of pitch diameters of the drive gear to the driven gear, which is the same as the ratio of the numbers of teeth on the respective gears.
M
L
P
F
T
ST
S
Maximum Material Condition
Least Material Condition
Projected Tolerance Zone
Free State Variation
Tangent Plane
All Around
Between Symbol
Statistical Tolerance
RFS–Often Omitted
These modifiers are applied to the geometric tolerances to alter their application or interpretation.
The pitch diameter of the gears determines almost all the important geometry of the gear set.
Circular Pitch
Outside Diameter
Root Diameter
Pitch Diamter
Standard TolerancesUnless Otherwise Specified
Inch Millimeter
Fractional 1/64+–2 Place Decimal .01+–
3 Place Decimal .005 + – 4 Place Decimal .0005 +–
Whole Number 0.5 + –1 Place Decimal 0.2 + –
2 Place Decimal 0.03 + – 3 Place Decimal 0.013+ –
Limits on Angular Dimensions +–
Finish: Break All Sharp Corners
12
To save the drafter from applying a tolerance to every num-ber, a tolerance block in the title block area can give general tolerances that apply to not otherwise toleranced.
Knowing how these symbols are interpreted can help you understand what the designer intended for the finished part.
Straightness
Flatness
Cylindricity
Roundness
Surface Profile
Line Profile
Angularity
Parallelism
Perpendicularity
Characteristic Symbol
Form
Profile
Orientation
Location
Runout
Type of Tolerance
Position
Concentricity
Symmetry
Circular Runout
Total Runout
ANSI STANDARD FITS
Type of Fit Designation Purpose
Running and Sliding Fit RC
This category of fit provides for nine classes of running or sliding clearance fits, RC1 to RC9, which give similar performance with proper lubrication. RC1 is the most ac-curate fit for parts that must fit together without pay, and RC8 and RC9 have the largest allowances when loose fits are necessary.
Clearance Locational Fit LC
Clearance Locational fits are used for parts that don’t move but must be freely assembled or diassembled with precise locations. There are 11 classes of LC fits, LC1 to LC11.
Transition Locational Fit LT
Transitional Locational fits are for stationary parts that have a need for locational accuracy, but don’t need to be repeatedly assembled or disassembled and allow some light interference fits. There are six classes of LT fits, LT1 to LT6.
Interference Locational Fit LN
Interference Locational fits are for applications requiring high locational precision for alignment and rigidity, but don’t transmit torque or friction, as in drive shafts. There are three classes of LN fits, LN1 to LN3.
Force and Shrink Fit FN
Force fits and shrink fits require assembly of compo-nents by high pressure and/or heating or cooling of component parts to change the dimensions of the parts for assembly. FN fits can be designed to transmit torques and friction and maintain rigidity under a wide range of conditions. There are five classes of FN fits, FN 1 to FN5, with FN5 having the largest negative allow-ance.
PF Blue + Charcoal
PF Blue + White
186083(1606)
Capacitor or Condenser
Older Symbol for Capacitor
Shielded Capacitor
Variable Capacitor
Capacitor Bushing for CircuitBreaker or Transformer
Inductor or Coil (General)
Magnetic-Core Inductor (Optional)
Tapped Inductor
Blowout Coil Found in High-VoltageSwitch Gear
Saturable-Core Inductor or Reactor
Resistor
Variable Resistor
Tapped Resistor
AC Power Supply
OP AMP
Transformer
Diode/Rectifier
Silicone Controlled Rectifier (SCR)
AC
Bridge Rectifier (AC to DC)
DC Power Supply
Ground
Chassis Ground
Transistor
Semiconductor Chip
OP Amp
Capacitor or Condenser
Older Symbol for Capacitor
Shielded Capacitor
Variable Capacitor
Capacitor Bushing for CircuitBreaker or Transformer
Inductor or Coil (General)
Magnetic-Core Inductor (Optional)
Tapped Inductor
Blowout Coil Found in High-VoltageSwitch Gear
Saturable-Core Inductor or Reactor
Resistor
Variable Resistor
Tapped Resistor
AC Power Supply
OP AMP
Transformer
Diode/Rectifier
Silicone Controlled Rectifier (SCR)
AC
Bridge Rectifier (AC to DC)
DC Power Supply
Ground
Chassis Ground
Transistor
Semiconductor Chip
OP Amp
General Outlet
Convenience Outlet
Switch Outlets
Panels, Circuits and Miscellaneous
Ceiling Wall
Outlet
Drop Cord
Electrical Outlet: for use only whencircle used alone might be confusedwith columns plumbing symbols, etc.
Fan Outlet
Single-Pole Switch
D
E E
F F
J J
L L
L LPS PS
S S
V V
X X
C C
1,3
GFI
GR
W P
S
R
SS DIM
S 2
S 3
S 4
S D
S K
S P
S CB
S W CB
S MC
S RC
S W P
S F
G
M
I
MC
Flush-Mounted Panel Board
Surface-Mounted Panel Board
Switchboard, Power Control
Flush-Mounted Terminal Cabinet
Pull Box
Unit Substations
Surface-Mounted Terminal Cabinet
T T T
B B B
Trolley Duct
Busway,Service, Feeder, Plug In
BP BP BP Cable Through, Ladderor Feeder
W W W Wireway
Special Outlets
a, b, c, etc.
S
a, b, c, etc.
S a, b, c, etc.
WF
Junction Box
Lamp Holder
Lamp Holder with Pull Switch
Pull Switch
Outlet for Vapor Discharge Lamp
Exit Light Outlet
Clock Outlet (Specify Voltage)
Duplex Convenience Outlet
Convenience Outlet Other than Duplex1-Single, 3-Triplex, Etc.
Ground Fault Interrupter Outlet
Duplex Convenience OutletSplit Wire
Duplex Convenience OutletGrounding Type
Weatherproof Convenience Outlet
Range Outlet
Switch and Convenience Outlet
Special-Purpose Outlet
Floor Outlet
Dimmer Switch
Double-Pole Swtch
Three-Way Switch
Four-Way Switch
Automatic Door Switch
Key Operated Switch
Switch and Pilot Lamp
Circuit Breaker
Weatherproof Circuit Breaker
Momentary Contact Switch
Remote Control Switch
Weatherproof Switch
Fused Switch
Weatherproof Fused Switch
Any standard symbol given as above withthe addition of a lowercase subscript lettermay be used to designate some specialvariation of standard equipment of particular interest.
Lighting Panel
Power Panel
Branch Circuit–Concealed in Ceiling or Wall
Branch Circuit–Concealed in Floor
Branch Circuit–Exposed
Home run to panel board. IndicateNumber of circuits by number of arrows.Note: Any circuit without furtherdesignation indicates a two-wire circuit.For greater number of wires indicateas follows # (3 wires), # (4 wires) etc.
Note: For double or single systems,eliminate one or two lines. This symbol isequally adaptable to auxiliary system layout.
Feeders Note: Use heavy linesand designate by number corresonding to listing in feeder schedule.
Under Floor Duct and JUnction Box Triple System
Generator
Motor
Instrument
Pull Box
Motor or Power Controller
Externally Operated Disconnect Switch
Combination Controller andDisconnection Means
Tail
Field Weld Symbol
Weld-All-Around Symbol
Arrow to Joint
Weld Info for Opposite Side
Weld Info for Arrow Side
Basic Weld Symbol(A)
Arrow Side Opposite Side
Side Definition(B)
Reference Specification,Frequency of Weld,
Process Identification
Bevel
V-Notch
Filet
Square
Spot
Slot
Weld Symbol Defining Joint Type
Length and/or Pitch Information
(C)
Unit Heater Propeller, Plan
Unit Ventilator, Plan
Check Valve
Diaphragm Valve
Gate Valve
Globe Valve
M
Lock and Shield Valve
Motor-Operated Valve
Reducing Pressure Valve
Relief Valve
Vent Point
R
Vent
12 x 20Duct (First #, Width, Second #, Depth)
Direction of Flow
Flexible Connection
Ductwork withAcoustical Lining
FD ADFire Damperwith Acess DoorManual Volume Damper VD
Automatic Volume DamperExhaust, Return orOutside Air Duct-Section
20 x 12Supply Duct-Section
Ceiling DiffuserSupply Outlet 20° DIA CD
1000 CFM
Ceiling DiffuserSupply Outlet
20 x 12 CD
700 CFM
96 x 6-LD400 CFM
Linear Diffuser
Floor Register 20 x 12 FR700 CFM
Turning Valves
Fan and Motor
Louver Opening
Ductwork
ADAccess Door
Adjustable Blank Off
TR 20 x 12
p-20 x 12-700 CFM
Blanked Outlet
p-20°Ø-700 CFM
High-Pressure Steam HPS
Medium-Pressure Steam MPS
Low-Pressure Steam LPS
High-Pressure Return HPR
Medium-Pressure Return MPRLow-Pressure Return LPR
Boiler Blow Off BD
Condensate or VacuumPump Discharge
VPD
Feedwater Pump Discharge
PPD
Makeup Water MU
Air Relief Line V
Fuel Oil Suction FOS
Fuel Oil Return FOR
Fuel Oil Vent FOV
Compressed Air A
Hot Water Heating Supply
HW
Hot Water Heating Return
HWR
Boiler/Heating System Piping
Refrigerant Liquid RL
Refrigerant Discharge RD
Condenser Water Supply CWS
Condenser Water Return CWR
Chilled Water Supply CHWS
Chilled Water Return CHWR
Makeup Water MU
Humidification Line H
Drain D
PA
H
Air Eliminator
Anchor
Expansion Joint
Hanger or Support
Heat Exchanger
Heat Transfer Surface(Indicate Type)Pump (Indicate Type) M
Strainer
Tank (Indicate Type)
Thermometer
Thermostat
REC
T
Boiler Return Trap
F
Blast Thermostatic Trap
Float Trap
Float and Thermostatic Trap
Thermostatic Trap
Unit HeaterCentrifugal Plan
Heating Symbols (Continued)
Air Conditioning Piping
Refrigerant Suction RS
Fluid Conditioner
Basic Cooler Symbols
or
Temperature Controller Symbols
or
Filter Strainer Separator with Manual Drain
Filter/Separator with Manual
Drain
Filter/Separator with Automatic
Drain
Lubricator with Manual Drain
Lubricator with No Drain
Dessicator
Basic Heater Symbols
Single-Path Valve with Port Connections
Multipath Valve with Port Connections
Single-Path Valve, Closed Position
Flow Paths
Multipath Valve, Closed Position
Multipath Valve, Actuated to the Left
Flow Directionin Multipath Valves
Single-Path Valve, Normally Open Position
Single-Path Valve, Normally Closed Position
Single-Path Valve, Open Position
Control Valve,Neutral Position
Actuated Control Valve,Shifted Right
Actuated Control Valve,Shifted Left
P T
A B
Open Control Valve,Ports A and B Blocked
A B
P TControl Valve, Open
A B
P TControl Valve in the
Neutral Position, Closed
A B
P TOpen Control Valve,
Port B Blocked
A B
P TOpen Control Valve,
Port A Blocked
A B
P T
A B
P TClosed Control Valve,A Drains to the Tank
A B
P TClosed Control Valve,B Drains to the Tank
A B
P TClosed Control Valve,
A and B Drain to the Tank
A B
P TOpen Control Valve,
All Ports Drain to the Tank
Control Valve,Pressure to Ports A and B
Fluid ConnectionCylinder
Piston Rod
Piston
Single-Acting Cylinder
Cylinder
Fluid Connection
Double-Acting Cylinder
Fluid Connection
Piston Rod
Piston
CylinderFluid Connection
Double-End Rod
Fluid Connection
Piston Rod
Piston
Fluid Connection
Modified Cylinder
Internal Spring
External Drain
Reservoir
Fixed Cushion,Advance and Retract
Adjustable Cushion,Advance Only
MV
Fixed-Displacement Motor
THERM
Complete Motor Symbol withStandard Abbreviations
Complete Symbol Simplified Symbol
Unit Is Unidirectional as Either Pump or Motor
Complete Symbol Simplified Symbol
Unit Operates as a Pump in OneDirection and as a Motor in the Other
Unidirectional Bidirectional
Piston RodCylinder
Piston
Relief Valve
Vertical
Remotely ControlledRelief Valves with
Fully Adjustable Positioning
Horizontal
Unloading Valve with Drain Line
MECH
Deceleration Valve
Signal Source
NonrelievingReducing Valve
Signal Source
R
Older Newer
Relieving Reducing Valves Drawnto Older and Newer Standards
V
PC
Adjustable Control Valve
Pressure-CompensatedFlow Control Valve
Manual Shutoff ValvesVariable Pressure-CompensatedFlow Control Valves Drawn
to Older and Newer Standard
Complete Symbols forOn/Off Logic
Older Newer
OffOn
Check ValveCheck Valve with Orifice
Pilot-OperatedCheck Valve
Pressure to Open
Pilot-OperatedCheck Valve
Pressure to Close
Double CheckValve with
Cross-Bleed
Double CheckValve withoutCross-Bleed
Fluid Reservoir SubmergedTerminating Work
Line
OpenTerminating Work
Line
SubmergedTerminating Drain
Line
PneumaticStorage Tank
Vented Manifold
Pressure Gages Temperature Gages
Totalizing Flow MeterFlow Meter
0.1 5 one-tenth 0.01 5 one one-hundredth 0.001 5 one one-thousandth 0.0001 5 one ten-thousandth 0.00001 5 one hundred-thousandth 0.000001 5 one-millionth
1 place to the right 5 tenths 2 places to the right 5 hundredths 3 places to the right 5 thousandths 4 places to the right 5 ten-thousandths 5 places to the right 5 hundred-thousandths 6 places to the right 5 millionths
PF Blue + Charcoal
PF Blue + White
186100(1606)
Required Quantity Name/Symbol Formula
Acceleration m/s2
Velocity m/s
Area m2
Volume m³
Work joule/J N ∙ m
Power watt/W J/s
Force newton/N kg ∙ m/s2
Voltage volt/V W/A
Electrical resistance ohm/Ω V/A
Pressure pascal/Pa kg/m³
Taper Per Inch (TPI) Dd/ LT where:
OO D 5 larger diameter
OO d 5 smaller diameter
OO LT 5 length of taper in inches
REDUCTION RATIOS
Ratio 5 Diameter of Driven Pulley /Diameter of Driver PulleyRatio 5 No. of Teeth in Driven Gear/ No. of Teeth in Driver Gear Ratio 5 Driver rpm/ Driven rpm
INCREASER RATIOS
COMPOUND RATIOS
AREA OF A RECTANGLE OR SQUARE
A 5 ab
AREA OF THE DOVETAIL TRAPEZOID
Aa b h
=+( )
2
CIRCUMFERENCE OF A CIRCLE
C 5 pd or C 5 pr
AREA OF A CIRCLE
A 5 p2 or
5 pd2
4or
=0.7854(d2)
AREA OF RINGS
A 5 pR2 2 pr2 5 p(R2 2 r2)
AREA OF AN ELLIPSE
A 5 pab
PYTHAGOREM THEOREM
c2 5 a2 1 b2
AREA OF A RIGHT TRIANGLE
Aab
=2
PF Blue + Charcoal
PF Blue + White
186101(1606)
AREA OF A TRIANGLE
A 5 K(K 2 a)(K 2 b)(K 2 c)
VALUE OF ANGLES IN PENTAGON
=−180 2( )N
N
N=number of sides
AREA OF A PENTAGON
A 5 1.72(S2) S=length of one side
The area of a pentagon may also be approximated by drawing a circle tangent to the vertices of the angles, or by drawing a circle tangent to the sides of the polygon: A 5 2.378(R2) or 5 3.633(r2)
AREA OF A HEXAGON
A 5 2.598(S2)
OTHER FORMULAE APPLYING TO HEXAGONS
R 5 1.155(r) and r 5 0.866(S)
AREA OF OCTAGONS
A 5 4.828(S2) 4.828(S2) or A 5 2.828(R2)
VOLUME OF CUBES AND RECTANGLES
V 5 lwh V 5 volume l 5 length w 5 width h 5 height
VOLUME OF CYLINDERS
V 5 Ah or 5 pr2h
VOLUME OF A SPHERE
V r=4
3
3p or
=
1
6
3pd
DIRECT HEIGHT OF A CONE
dh a r= +2 2
SIDE AREA OF A CONE
Ac dh
=( )
2 C 5 circumference of the base
dh 5 direct height
VOLUME OF A CONE
Va h
=( )
3
a 5 area h 5 altitude
TO FIND ANGLE A: TO FIND ANGLE B:
sin
cos
Ahypotenuse
a
c
A
= =
=
side opposite angle A
side adjacent aangle A
side opposite angle A
side adjace
hypotenuse
b
c
A
=
=tannnt angle A
side adjacent angle A
side opposite angl
=
=
a
b
Acotee A
side adjacent angle A
=
= =
=
b
a
Ahypotenuse c
b
Ahypoten
sec
cscuuse c
aside opposite angle A=
sin
cos
Bhypotenuse
B
c
B
= =
=
side opposite angle B
side adjacent aangle B
side opposite angle B
side adjace
hypotenuse
a
c
B
=
=tannnt angle B
side adjacent angle B
side opposite angl
=
=
b
a
Bcotee B
side adjacent angle B
=
= =
=
a
b
Bhypotenuse c
a
Ahypoten
sec
cscuuse c
bside opposite angle B=
Place names and values of decimals for number 9,683,112.243576.
PF Blue + Charcoal
PF Blue + White
186103(1606)
100,0001
hundred-thousandths
0.00001
1,000,000
1
millionths
0.00001
8 43 5
83
1
78
9 11435 13
87 15
6 32 53 6
To Find: Use the Formula:
Percentage (P) P 5 R 3 B
Rate (R) RP
B=
Base (B) BP
R=
MULTIPLYING BY POWERS OF 10
Number
Multiply by
10 100 1,000 10,000
52 520 5,200 52,000 520,000
37.4 374 3,740 37,400 374,000
0.3625 3.625 36.25 362.5 3,625
0.041 0.41 4.1 41 410
470 4,700 47,000 470,000 4,700,000
DIVIDING BY POWERS OF 10
Number
Divide by
10 100 1,000 10,000
560 56 5.6 0.56 0.056
6542.1 654.21 65.421 6.5421 0.65421
6.35 0.635 0.0635 0.00635 0.000635
27 2.7 0.27 0.027 0.0027
86,342 8634.2 863.42 86.342 8.6342
PRODUCTIVITY REQUIREMENTS
A Number is Divisble By: If
2 The number ends in 2, 4, 6, 8, or 0. (Numbers divisible by 2 are called even numbers.)
3The sum of its digits is divisible by 3. (351 is divisible by 3 because 3 1 5 1 1 5 9 and 9 is divisible by 3.)
4The last two digits, taken as a whole number, are divisible by 4. (224 is divisible by 4 because 24 is divisible by 4.)
5 The number ends in 0 or 5. (65 and 120 are divisible by 5.)
6The number is divisible by both 2 and by 3. (114 is divisible by 6 because it’s also divisi-ble by both 2 and 3.)
8The last three digits, taken as a whole number, are divisible by 8. (8,232 is divisible by 8 because 232 is divisible by 8.)
9The sum of the digits is divisible by 9. (2,376 is divisible by 9 because 2 1 3 1 7 1 6 5 18 is divisible by 9.)
10 The ones digit is 0. (20,160 and 5,740 are divisible by 10.)
DECIMALS AND THEIR EQUIVALENT FRACTIONS
Decimals In Words As a Fraction
0.7 seven tenths7
10
0.08 eight hundreths8
100
0.009 nine thousandths9
1 000,
0.0013 thirteen then thousandths13
10 000,
2.3 two and three tenths 23
10