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.


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)



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)



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)



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

186012(1606)

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

186021(1606)

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

186068(1606)

186068(1606)

Factory Management Functions

PF Blue + Charcoal

PF Blue + White

186078(1606)

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)


(3rd shift)

OtherDepartments

Research andDevelopment


(2nd shift)

Worker

Worker Worker

Worker Worker

186078(1606)

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


Shielded Capacitor

Variable Capacitor

Capacitor Bushing for CircuitBreaker or Transformer

Inductor or Coil (General)


Tapped Inductor

Blowout Coil Found in High-VoltageSwitch Gear


Resistor

Variable Resistor

Tapped Resistor

AC Power Supply

OP AMP

Transformer

Diode/Rectifier


AC


DC Power Supply

Ground

Chassis Ground

Transistor

Semiconductor Chip

OP Amp

Capacitor or Condenser


Shielded Capacitor

Variable Capacitor

Capacitor Bushing for CircuitBreaker or Transformer

Inductor or Coil (General)


Tapped Inductor

Blowout Coil Found in High-VoltageSwitch Gear


Resistor

Variable Resistor

Tapped Resistor

AC Power Supply

OP AMP

Transformer

Diode/Rectifier


AC


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


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


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

pf blue + charcoal

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