This document provides formulas, constants, and conversions for various scientific and engineering topics. It includes sections on SI and imperial units for distance, area, volume, mass, density, and other physical quantities. It also includes mathematical formulas, trigonometry, geometry, mechanics, thermodynamics, fluid mechanics, and electricity. The document is intended for use by students and examination candidates as a reference for various physical constants and engineering formulae.
This document contains solutions to physics problems involving unit conversions and vector calculations.
1) It provides step-by-step workings and calculations for various conversion problems between units like inches, centimeters, liters, gallons, etc.
2) It also shows the decomposition of vectors into x and y components and calculations of resultant vectors and displacements by summing the x and y components.
3) The problems cover a wide range of physics concepts involving kinematics, forces, densities, areas, volumes, and conversions between different units of length, volume, speed and other physical quantities.
The document discusses data normalization and Codd's rules for database design. It covers normal forms including 1NF, 2NF, 3NF, and BCNF. The goals of normalization are to reduce redundancy, ensure data consistency, and avoid anomalies when data is updated, inserted or deleted. Normalization involves separating relations and attributes to eliminate transitive dependencies and potential anomalies. The document provides examples demonstrating how normalization progresses from 1NF to 2NF to 3NF to remove partial and transitive dependencies.
This study characterized the carcasses of pasture-raised meat goats in Maryland in 2009 and 2010. Nineteen goats were harvested and measurements of live weight, hot carcass weight, rib eye area, backfat thickness and carcass composition were taken. Regression analysis showed that ultrasound rib eye area and backfat thickness were good predictors of carcass lean percentage. A lower live weight, hot carcass weight and fat levels were observed in 2010, likely due to drought conditions. The results provide information on carcass quality of pasture-raised goats and the use of ultrasound to estimate carcass characteristics.
The document discusses thermodynamics, dimensions and units, and fundamental concepts of thermodynamics. It defines thermodynamics as the science of energy, and discusses the conservation of energy principle and the first law of thermodynamics. It also defines dimensions as characteristics of physical quantities, and primary and secondary dimensions. Finally, it provides examples of converting between different units for dimensions like length, mass, time, and others.
This document discusses the metric system and its units of measurement for length, mass, capacity, area, and volume. It provides:
1) An overview of the metric system and its adoption worldwide.
2) Details on complex and simple measurements and how to convert between them.
3) Tables listing the standard metric units for each measurement type and how they relate to each other through factors of 10.
The document discusses units of measurement in the metric system including prefixes, base units for length, mass and capacity. It provides examples of converting between metric units of length, mass, capacity, area, volume and time. Key details include the prefixes used in the metric system (kilo, centi, milli, micro), base units (metre, gram, litre), and formulas for converting between units (multiplying or dividing by powers of ten).
The document discusses various units of measurement in the metric system including units for length (meters, centimeters, millimeters), mass (kilograms, grams), capacity (liters, milliliters), area (square meters, hectares), and volume (cubic meters, liters). It provides examples for converting between metric units using multiplication or division by powers of ten. The document also briefly discusses units of time and provides examples of calculating time to complete multiple tasks.
This document provides an overview of topics in inorganic chemistry measurements including:
1) Scientific notation for expressing very large and small numbers
2) Significant figures rules for determining the precision of measurements
3) Conversion of units between different measurement systems like centimeters to kilometers using prefixes
4) Density calculations involving mass, volume, and unit conversions
The document includes examples and practice problems for each topic to illustrate concepts like significant figures, unit conversions using prefixes, and calculating density from mass and volume.
This document contains solutions to physics problems involving unit conversions and vector calculations.
1) It provides step-by-step workings and calculations for various conversion problems between units like inches, centimeters, liters, gallons, etc.
2) It also shows the decomposition of vectors into x and y components and calculations of resultant vectors and displacements by summing the x and y components.
3) The problems cover a wide range of physics concepts involving kinematics, forces, densities, areas, volumes, and conversions between different units of length, volume, speed and other physical quantities.
The document discusses data normalization and Codd's rules for database design. It covers normal forms including 1NF, 2NF, 3NF, and BCNF. The goals of normalization are to reduce redundancy, ensure data consistency, and avoid anomalies when data is updated, inserted or deleted. Normalization involves separating relations and attributes to eliminate transitive dependencies and potential anomalies. The document provides examples demonstrating how normalization progresses from 1NF to 2NF to 3NF to remove partial and transitive dependencies.
This study characterized the carcasses of pasture-raised meat goats in Maryland in 2009 and 2010. Nineteen goats were harvested and measurements of live weight, hot carcass weight, rib eye area, backfat thickness and carcass composition were taken. Regression analysis showed that ultrasound rib eye area and backfat thickness were good predictors of carcass lean percentage. A lower live weight, hot carcass weight and fat levels were observed in 2010, likely due to drought conditions. The results provide information on carcass quality of pasture-raised goats and the use of ultrasound to estimate carcass characteristics.
The document discusses thermodynamics, dimensions and units, and fundamental concepts of thermodynamics. It defines thermodynamics as the science of energy, and discusses the conservation of energy principle and the first law of thermodynamics. It also defines dimensions as characteristics of physical quantities, and primary and secondary dimensions. Finally, it provides examples of converting between different units for dimensions like length, mass, time, and others.
This document discusses the metric system and its units of measurement for length, mass, capacity, area, and volume. It provides:
1) An overview of the metric system and its adoption worldwide.
2) Details on complex and simple measurements and how to convert between them.
3) Tables listing the standard metric units for each measurement type and how they relate to each other through factors of 10.
The document discusses units of measurement in the metric system including prefixes, base units for length, mass and capacity. It provides examples of converting between metric units of length, mass, capacity, area, volume and time. Key details include the prefixes used in the metric system (kilo, centi, milli, micro), base units (metre, gram, litre), and formulas for converting between units (multiplying or dividing by powers of ten).
The document discusses various units of measurement in the metric system including units for length (meters, centimeters, millimeters), mass (kilograms, grams), capacity (liters, milliliters), area (square meters, hectares), and volume (cubic meters, liters). It provides examples for converting between metric units using multiplication or division by powers of ten. The document also briefly discusses units of time and provides examples of calculating time to complete multiple tasks.
This document provides an overview of topics in inorganic chemistry measurements including:
1) Scientific notation for expressing very large and small numbers
2) Significant figures rules for determining the precision of measurements
3) Conversion of units between different measurement systems like centimeters to kilometers using prefixes
4) Density calculations involving mass, volume, and unit conversions
The document includes examples and practice problems for each topic to illustrate concepts like significant figures, unit conversions using prefixes, and calculating density from mass and volume.
1. This document discusses scientific notation, significant figures, density, and unit conversions between metric and English units.
2. Scientific notation is used to express very large or small numbers in a standardized form. Significant figures are used to account for the precision of measurements in calculations.
3. The metric system and SI units are based on powers of ten. Common prefixes are used to modify unit names to indicate powers of ten. Density is a property used to compare how tightly packed particles are in materials.
Metric prefixes are powers of 10 that are used to indicate multiples or fractions of basic metric units like meters and grams. The most common prefixes are kilo (103), mega (106), and milli (10-3) and are used to easily convert between metric units. While less common prefixes exist up to yotta (1024) and zepto (10-21), they are primarily used in scientific contexts. In general, metric prefixes provide an easy way to scale metric units without needing to know the specific measurement amounts.
1. The document provides examples of converting between different units of measurement, such as miles to kilometers, gallons to liters, seconds to years, etc. Conversions involve setting up proportional relationships between units and calculating using conversion factors.
2. Examples show calculating uncertainties in measurements based on the precision of the measuring instrument. Uncertainty is estimated as a percentage error relative to the measured quantity.
3. To determine average values and uncertainties, the document uses the maximum and minimum possible values based on the precision of the original measurements. The uncertainty is taken as half the range between the maximum and minimum average values.
1. The document provides examples of converting between different units of measurement, such as miles to kilometers, gallons to liters, seconds to years, etc. Conversions involve setting up proportional relationships between units and calculating using conversion factors.
2. Examples show calculating uncertainties in measurements based on the precision of the measuring instrument. Uncertainty is estimated as a percentage error relative to the measured quantity.
3. To determine average values and uncertainties, the document uses the maximum and minimum possible values based on the precision of the original measurements. The uncertainty is taken as half the range between the maximum and minimum average values.
This document provides conversion factors between various units of measurement across different categories including acceleration, angle, area, density, electric charge, energy, force, frequency, heat flow rate, length, and others. For each category, equivalencies are given between units like meters and feet, grams and ounces, joules and BTUs, newtons and pounds force, and others. Standard prefixes like milli, centi, and kilo are also explained in terms of their multiplicative factors.
The document lists various metric prefixes that are used to denote powers of 10 both above and below the base unit. It shows prefixes ranging from atto- (10-18) up to tera- (1012), along with their associated symbols, numerals, and terminology for describing the value. The prefixes allow quantities to be expressed in a normalized manner across many orders of magnitude.
This document provides conversion factors for various units of measurement in the categories of length, area, volume, mass, velocity, density, force, energy, power, and pressure. Some examples of conversions included are:
- 1 kilometer = 1000 meters
- 1 liter = 1000 cubic centimeters
- 1 kilogram = 2.2046 pounds
- 1 joule = 1 newton meter = 0.7376 pound-feet
- 1 watt = 1 joule per second = 0.2389 calories per second
The document describes the "ladder method" for converting between metric units. It shows a ladder with the major metric units decreasing in powers of 10 from kilo to milli. It then provides examples of converting between units like kilometers to meters and liters to milliliters using this method by counting decimal place jumps up or down the ladder. Finally, it provides a series of practice problems converting between various metric units using this ladder method.
This document provides instructions for homework assignments on scientific conversions and the scientific method. Students are asked to complete conversions between various units including feet to centimeters, grams to millimeters, Celsius to Kelvin, and Kelvin to Fahrenheit. They are also asked to calculate volume, pressure, and moles using given formulas and values. The document defines Avogadro's number as the number of molecules or atoms in a mole of substance, which is used to determine the number of moles from a given number of atoms.
The document provides information on the International System of Measurement (SI), or the metric system, including common metric prefixes and their meanings. It notes that SI is used globally for scientific research and medicine. Examples are given for converting between metric units using prefixes and moving the decimal place, along with noting some key temperatures and units in the metric system.
The document provides information on the International System of Measurement (SI), or the metric system, including common metric prefixes and their meanings. It notes that SI is the standard system used in science and by most countries for measurement and lists some key metric units like meters, liters, and grams. Guidelines are given for converting between metric units using prefixes and decimal places.
This document contains examples and calculations related to statistics, physics, and engineering. It includes:
1) Calculations of distances, speeds, volumes, densities, and other physical quantities.
2) Examples of statistical analysis such as calculating means, standard deviations, and control limits from data sets.
3) Physics problems involving concepts like force, weight, pressure, and fluid dynamics.
This chapter discusses various physics concepts including:
1) Conversions between different units of time, distance, and speed.
2) Calculating the number of steps from Earth to a nearby star and the number of reports needed to describe the distance to the moon.
3) Determining the number of planes needed based on fuel consumption rates and crude oil production.
4) Calculating forces, weights, and densities in various physics problems.
The document outlines a lesson on metric conversions, including reviewing the base metric units of length, volume, and mass. It explains the metric system prefixes and how they relate to powers of 10, allowing conversions between units by moving the decimal point left or right. Examples are provided for converting between meters and kilometers, grams and milligrams, and liters and milliliters using the "ladder method" of counting jumps between prefixes.
The document discusses physics and chemistry, comparing what they have in common (studying matter) and what makes them different (physics studies phenomena that don't change matter composition, while chemistry studies phenomena that do change composition). It then provides an overview of the scientific method, including making observations and asking questions, developing hypotheses to test, conducting controlled experiments, analyzing results, and drawing conclusions. Finally, it covers scientific concepts like units, measurements, errors, and notation.
The document discusses metric prefixes that are used to modify units of measurement and make large or small quantities more manageable. It explains that prefixes like kilo (k), centi (c), and milli (m) multiply the base unit by factors of 1000, 100, and 1000 respectively. For example, 1 centimeter (cm) is equal to 0.01 meters, 1 millimeter (mm) is equal to 0.001 meters, and 1 kilometer (km) is equal to 1000 meters. The document provides a table of common metric prefixes and their scientific notation abbreviations to help memorize the system and properly apply prefixes when modifying units of measurement.
This document provides conversion factors and abbreviations for various units of measurement in the metric system including length, area, volume, weight, temperature, time, speed, force, pressure, power, angle, and other physical quantities. Some key conversions include:
- 1 meter = 100 centimeters
- 1 square meter = 10,000 square centimeters
- 1 liter = 1,000 cubic centimeters
- 1 kilogram = 1,000 grams
- 0 degrees Celsius = 32 degrees Fahrenheit
- 1 newton = 100,000 dynes
- 1 bar = 100,000 pascals
This document provides information on scientific notation and prefixes used with units of measurement:
1) Scientific notation is used to express very large or small numbers in a standardized way. Positive exponents increase the decimal place value while negative exponents decrease it.
2) Prefixes are used with units of measurement to express the scale of quantities being measured in a clear way. Common prefixes and their multipliers are provided in tables.
3) Examples show how to convert between standard and scientific notation forms and choose the most appropriate prefix for a given measurement quantity and scale. Practice problems apply these concepts.
1. Measurement of volume (3D concept)
2. Measurement of area (Estimate the area of irregular shape objects using graph paper)
3. Measurement of density of regular solid: Basic concepts, Formula,Simple Numericals
4. Calculation of speed: Basic oncept, Formula, Simple Numericals
This document discusses various metric units of measurement including length, mass, capacity, volume, and area. It provides prefixes and conversion factors between units. Examples are given to demonstrate how to use units of measurement to solve conversion problems between the metric system and everyday quantities.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
1. This document discusses scientific notation, significant figures, density, and unit conversions between metric and English units.
2. Scientific notation is used to express very large or small numbers in a standardized form. Significant figures are used to account for the precision of measurements in calculations.
3. The metric system and SI units are based on powers of ten. Common prefixes are used to modify unit names to indicate powers of ten. Density is a property used to compare how tightly packed particles are in materials.
Metric prefixes are powers of 10 that are used to indicate multiples or fractions of basic metric units like meters and grams. The most common prefixes are kilo (103), mega (106), and milli (10-3) and are used to easily convert between metric units. While less common prefixes exist up to yotta (1024) and zepto (10-21), they are primarily used in scientific contexts. In general, metric prefixes provide an easy way to scale metric units without needing to know the specific measurement amounts.
1. The document provides examples of converting between different units of measurement, such as miles to kilometers, gallons to liters, seconds to years, etc. Conversions involve setting up proportional relationships between units and calculating using conversion factors.
2. Examples show calculating uncertainties in measurements based on the precision of the measuring instrument. Uncertainty is estimated as a percentage error relative to the measured quantity.
3. To determine average values and uncertainties, the document uses the maximum and minimum possible values based on the precision of the original measurements. The uncertainty is taken as half the range between the maximum and minimum average values.
1. The document provides examples of converting between different units of measurement, such as miles to kilometers, gallons to liters, seconds to years, etc. Conversions involve setting up proportional relationships between units and calculating using conversion factors.
2. Examples show calculating uncertainties in measurements based on the precision of the measuring instrument. Uncertainty is estimated as a percentage error relative to the measured quantity.
3. To determine average values and uncertainties, the document uses the maximum and minimum possible values based on the precision of the original measurements. The uncertainty is taken as half the range between the maximum and minimum average values.
This document provides conversion factors between various units of measurement across different categories including acceleration, angle, area, density, electric charge, energy, force, frequency, heat flow rate, length, and others. For each category, equivalencies are given between units like meters and feet, grams and ounces, joules and BTUs, newtons and pounds force, and others. Standard prefixes like milli, centi, and kilo are also explained in terms of their multiplicative factors.
The document lists various metric prefixes that are used to denote powers of 10 both above and below the base unit. It shows prefixes ranging from atto- (10-18) up to tera- (1012), along with their associated symbols, numerals, and terminology for describing the value. The prefixes allow quantities to be expressed in a normalized manner across many orders of magnitude.
This document provides conversion factors for various units of measurement in the categories of length, area, volume, mass, velocity, density, force, energy, power, and pressure. Some examples of conversions included are:
- 1 kilometer = 1000 meters
- 1 liter = 1000 cubic centimeters
- 1 kilogram = 2.2046 pounds
- 1 joule = 1 newton meter = 0.7376 pound-feet
- 1 watt = 1 joule per second = 0.2389 calories per second
The document describes the "ladder method" for converting between metric units. It shows a ladder with the major metric units decreasing in powers of 10 from kilo to milli. It then provides examples of converting between units like kilometers to meters and liters to milliliters using this method by counting decimal place jumps up or down the ladder. Finally, it provides a series of practice problems converting between various metric units using this ladder method.
This document provides instructions for homework assignments on scientific conversions and the scientific method. Students are asked to complete conversions between various units including feet to centimeters, grams to millimeters, Celsius to Kelvin, and Kelvin to Fahrenheit. They are also asked to calculate volume, pressure, and moles using given formulas and values. The document defines Avogadro's number as the number of molecules or atoms in a mole of substance, which is used to determine the number of moles from a given number of atoms.
The document provides information on the International System of Measurement (SI), or the metric system, including common metric prefixes and their meanings. It notes that SI is used globally for scientific research and medicine. Examples are given for converting between metric units using prefixes and moving the decimal place, along with noting some key temperatures and units in the metric system.
The document provides information on the International System of Measurement (SI), or the metric system, including common metric prefixes and their meanings. It notes that SI is the standard system used in science and by most countries for measurement and lists some key metric units like meters, liters, and grams. Guidelines are given for converting between metric units using prefixes and decimal places.
This document contains examples and calculations related to statistics, physics, and engineering. It includes:
1) Calculations of distances, speeds, volumes, densities, and other physical quantities.
2) Examples of statistical analysis such as calculating means, standard deviations, and control limits from data sets.
3) Physics problems involving concepts like force, weight, pressure, and fluid dynamics.
This chapter discusses various physics concepts including:
1) Conversions between different units of time, distance, and speed.
2) Calculating the number of steps from Earth to a nearby star and the number of reports needed to describe the distance to the moon.
3) Determining the number of planes needed based on fuel consumption rates and crude oil production.
4) Calculating forces, weights, and densities in various physics problems.
The document outlines a lesson on metric conversions, including reviewing the base metric units of length, volume, and mass. It explains the metric system prefixes and how they relate to powers of 10, allowing conversions between units by moving the decimal point left or right. Examples are provided for converting between meters and kilometers, grams and milligrams, and liters and milliliters using the "ladder method" of counting jumps between prefixes.
The document discusses physics and chemistry, comparing what they have in common (studying matter) and what makes them different (physics studies phenomena that don't change matter composition, while chemistry studies phenomena that do change composition). It then provides an overview of the scientific method, including making observations and asking questions, developing hypotheses to test, conducting controlled experiments, analyzing results, and drawing conclusions. Finally, it covers scientific concepts like units, measurements, errors, and notation.
The document discusses metric prefixes that are used to modify units of measurement and make large or small quantities more manageable. It explains that prefixes like kilo (k), centi (c), and milli (m) multiply the base unit by factors of 1000, 100, and 1000 respectively. For example, 1 centimeter (cm) is equal to 0.01 meters, 1 millimeter (mm) is equal to 0.001 meters, and 1 kilometer (km) is equal to 1000 meters. The document provides a table of common metric prefixes and their scientific notation abbreviations to help memorize the system and properly apply prefixes when modifying units of measurement.
This document provides conversion factors and abbreviations for various units of measurement in the metric system including length, area, volume, weight, temperature, time, speed, force, pressure, power, angle, and other physical quantities. Some key conversions include:
- 1 meter = 100 centimeters
- 1 square meter = 10,000 square centimeters
- 1 liter = 1,000 cubic centimeters
- 1 kilogram = 1,000 grams
- 0 degrees Celsius = 32 degrees Fahrenheit
- 1 newton = 100,000 dynes
- 1 bar = 100,000 pascals
This document provides information on scientific notation and prefixes used with units of measurement:
1) Scientific notation is used to express very large or small numbers in a standardized way. Positive exponents increase the decimal place value while negative exponents decrease it.
2) Prefixes are used with units of measurement to express the scale of quantities being measured in a clear way. Common prefixes and their multipliers are provided in tables.
3) Examples show how to convert between standard and scientific notation forms and choose the most appropriate prefix for a given measurement quantity and scale. Practice problems apply these concepts.
1. Measurement of volume (3D concept)
2. Measurement of area (Estimate the area of irregular shape objects using graph paper)
3. Measurement of density of regular solid: Basic concepts, Formula,Simple Numericals
4. Calculation of speed: Basic oncept, Formula, Simple Numericals
This document discusses various metric units of measurement including length, mass, capacity, volume, and area. It provides prefixes and conversion factors between units. Examples are given to demonstrate how to use units of measurement to solve conversion problems between the metric system and everyday quantities.
Similar to Handbook of formulae and constants (20)
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
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Handbook of formulae and constants
1. Handbook of
Formulae and
Physical Constants
For The Use Of Students And Examination Candidates
Duplication of this material for student
in-class use or for examination
purposes is permitted without written
approval.
Approved by the Interprovincial Power Engineering
Curriculum Committee and the Provincial Chief
Inspectors' Association's Committee for the
standardization of Power Engineer's Examinations n
Canada.
www.powerengineering.ca Printed July 2003
2.
3. Table of Contents
TOPIC PAGE
SI Multiples..........................................................................................1
Basic Units (distance, area, volume, mass, density) ............................2
Mathematical Formulae .......................................................................5
Applied Mechanics .............................................................................10
Thermodynamics.................................................................................21
Fluid Mechanics..................................................................................28
Electricity............................................................................................30
Periodic Table .....................................................................................34
4. Names in the Metric System
VALUE EXPONENT SYMBOL PREFIX
1 000 000 000 000 1012 T tera
1 000 000 000 109 G giga
1 000 000 106 M mega
1 000 103 k kilo
100 102 h hecto
10 101 da deca
0.1 10-1 d deci
0.01 10-2 c centi
0.001 10-3 m milli
0.000 001 10-6 µ micro
0.000 000 001 10-9 n nano
0.000 000 000 001 10-12 p pico
Conversion Chart for Metric Units
To
To To To Metre, To To To
Milli- Centi- Deci- Gram, Deca- Hecto- Kilo-
Litre
Kilo- x 106 x 105 x 104 x 103 x 102 x 101
Hecto- x 105 x 104 x 103 x 102 x 101 x 10-1
Deca- x 104 x 103 x 102 x 101 x 10-1 x 10-2
To Convert
Metre,
Gram, x 103 x 102 x 101 x 10-1 x 10-2 x 10-3
Litre
Deci- x 102 x 101 x 10-1 x 10-2 x 10-3 x 10-4
Centi- x 101 x 10-1 x 10-2 x 10-3 x 10-4 x 10-5
Milli- x 10-1 x 10-2 x 10-3 x 10-4 x 10-5 x 10-6
Page 1
5. BASIC UNITS
SI IMPERIAL
DISTANCE
1 metre (1 m) = 10 decimetres (10 dm) 12 in. = 1 ft
= 100 centimetres (100 cm) 3 ft = 1 yd
= 1000 millimetres (1000 mm) 5280 ft = 1 mile
1760 yd = 1 mile
1 decametre (1 dam) = 10 m
1 hectometre (1 hm) = 100 m
1 kilometre (1 km) = 1000 m
Conversions:
1 in. = 25.4 mm
1 ft = 30.48 cm
1 mile = 1.61 km
1 yd = 0.914 m
1m = 3.28 ft
Area
1 sq metre (1 m2) = 10 000 cm2 1 ft2 = 144 in.2
= 1 000 000 mm2 1 yd2 = 9 ft2
1 sq mile = 640 acre = 1 section
1 sq hectometre (1 hm2) = 10 000 m2
= 1 hectare (1 ha)
1 sq km (1 km2) = 1 000 000 m2
Conversions:
1 in.2 = 6.45 cm2 = 645 mm2
1 m2 = 10.8 ft2
1 acre = 0.405 ha
1 sq mile = 2.59 km2
Page 2
6. SI IMPERIAL
Volume
1 m3 = 1 000 000 cm3 1 ft3 = 1728 in.3
= 1 x 109 mm3 1 yd3 = 27 ft3
1 dm3 = 1 litre 1(liquid) U.S. gallon = 231 in.3
1 litre = 1000 cm3 = 4 (liquid) quarts
1 mL = 1 cm3 1 U.S. barrel (bbl) = 42 U.S. gal.
1 m3 = 1000 litres 1 imperial gallon = 1.2 U.S. gal.
Conversions:
1 in.3 = 16.4 cm3
1 m3 = 35.3 ft3
1 litre = 61 in.3
1 U.S.gal = 3.78 litres
1 U.S. bbl = 159 litres
1 litre/s = 15.9 U.S. gal/min
Mass and Weight
1 kilogram (1 kg) = 1000 grams 2000 lb = 1 ton (short)
1000 kg = 1 tonne 1 long ton = 2240 lb
Conversions:
1 kg (on Earth) results in a weight of 2.2 lb
Density
mass weight
mass density = weight density =
volume volume
m ⎛ kg ⎞ w ⎛ lb ⎞
ρ= ⎜ ⎟ ρ= ⎜ ⎟
V ⎝ m3 ⎠ V ⎝ ft 3 ⎠
Conversions:
kg
(on Earth) a mass density of 1 results in a weight density of 0.0623 lb
m3 ft 3
Page 3
7. SI Imperial
RELATIVE DENSITY
In SI R.D. is a comparison of mass density In Imperial the corresponding quantity is
to a standard. For solids and liquids the specific gravity; for solids and liquids a
standard is fresh water. comparison of weight density to that of
water.
Conversions:
In both systems the same numbers
hold for R.D. as for S.G. since
these are equivalent ratios.
RELATIVE DENSITY (SPECIFIC GRAVITY) OF VARIOUS SUBSTANCES
Water (fresh)...............1.00 Mica............................2.9
Water (sea average) ....1.03 Nickel .........................8.6
Aluminum...................2.56 Oil (linseed) ................0.94
Antimony....................6.70 Oil (olive) ...................0.92
Bismuth.......................9.80 Oil (petroleum) ...........0.76-0.86
Brass ...........................8.40 Oil (turpentine) ...........0.87
Brick ...........................2.1 Paraffin .......................0.86
Calcium.......................1.58 Platinum....................21.5
Carbon (diamond).......3.4 Sand (dry) ...................1.42
Carbon (graphite)........2.3 Silicon.........................2.6
Carbon (charcoal) .......1.8 Silver.........................10.57
Chromium...................6.5 Slate ............................2.1-2.8
Clay.............................1.9 Sodium........................0.97
Coal.............................1.36-1.4 Steel (mild) .................7.87
Cobalt .........................8.6 Sulphur .......................2.07
Copper ........................8.77 Tin...............................7.3
Cork ............................0.24 Tungsten ...................19.1
Glass (crown)..............2.5 Wood (ash) .................0.75
Glass (flint).................3.5 Wood (beech) .............0.7-0.8
Gold ..........................19.3 Wood (ebony).............1.1-1.2
Iron (cast)....................7.21 Wood (elm).................0.66
Iron (wrought) ............7.78 Wood (lignum-vitae) ..1.3
Lead ..........................11.4 Wood (oak).................0.7-1.0
Magnesium .................1.74 Wood (pine)................0.56
Manganese..................8.0 Wood (teak) ................0.8
Mercury ....................13.6 Zinc.............................7.0
Page 4
9. Trigonometry
1. Basic Ratios
y x y
Sin A = , cos A = , tan A =
h h x
2. Pythagoras' Law
x2 + y2 = h2
3. Trigonometric Function Values
Sin is positive from 0° to 90° and positive from 90° to 180°
Cos is positive from 0° to 90° and negative from 90° to 180°
Tan is positive from 0° to 90° and negative from 90° to 180°
4. Solution of Triangles
a. Sine Law
a b c
= =
Sin A Sin B Sin C
b. Cosine Law
c2 = a2 + b2 - 2 ab Cos C
a2 = b2 + c2 - 2 bc Cos A
b2 = a2 + c2 - 2 ac Cos B
Page 6
10. Geometry
1. Areas of Triangles
a. All Triangles
base x perpendicular height
Area =
2
bc Sin A ab Sin C ac Sin B
Area = = =
2 2 2
and,
Area = s (s - a) (s - b) (s - c)
a+b+c
where, s is half the sum of the sides, or s =
2
b. Equilateral Triangles
Area = 0.433 x side2
2. Circumference of a Circle
C = πd
3. Area of a Circle
circumference x r π
A = πr2 = = d 2 = 0.7854d2
2 4
4. Area of a Sector of a Circle
arc x r
A=
2
θ°
A= x π r2 (θ = angle in degrees)
360
θ°r 2
A= (θ = angle in radians)
2
Page 7
11. 5. Area of a Segment of a Circle
A = area of sector – area of triangle
4 2 d
Also approximate area = h - 0.608
3 h
6. Ellipse
π
A= Dd
4
Approx. circumference = π
(D + d )
2
7. Area of Trapezoid
⎛a + b⎞
A= ⎜ ⎟h
⎝ 2 ⎠
8. Area of Hexagon
A = 2.6s2 where s is the length of one side
9. Area of Octagon
A = 4.83s2 where s is the length of one side
10. Sphere
Total surface area A =4πr2
Surface area of segment As = πdh
4 3
Volume V = πr
3
Volume of segment
Vs = πh (3r – h)
2
3
Vs = πh (h 2 + 3a 2) where a = radius of segment base
6
Page 8
12. 11. Volume of a Cylinder
π 2
V= d L where L is cylinder length
4
12. Pyramid
Volume
1
V= base area x perpendicular height
3
Volume of frustum
h
VF = (A + a + Aa ) where h is the perpendicular height, A and a are areas as shown
3
13. Cone
Area of curved surface of cone:
π DL
A=
2
Area of curved surface of frustum
π (D + d)L
AF =
2
Volume of cone:
base area × perpendicular height
V=
3
Volume of frustum:
perpendicular height × π (R 2 + r 2 + Rr)
VF =
3
Page 9
13. APPLIED MECHANICS
Scalar - a property described by a magnitude only
Vector - a property described by a magnitude and a direction
displacement
Velocity - vector property equal to
time
The magnitude of velocity may be referred to as speed
In SI the basic unit is m , in Imperial ft
s s
Other common units are km , mi
h h
m ft
Conversions: 1 = 3.28
s s
km mi
1 = 0.621
h h
Speed of sound in dry air is 331 m at 0°C and increases by about 0.61 m for each °C
s s
rise
Speed of light in vacuum equals 3 x 108 m
s
change in velocity
Acceleration - vector property equal to
time
m ft
In SI the basic unit is 2
, in Imperial 2
s s
m ft
Conversion: 1 = 3.28
s2 s2
m ft
Acceleration due to gravity, symbol "g", is 9.81 2
or 32.2 2
s s
Page 10
14. LINEAR VELOCITY AND ACCELERATION
u initial velocity v = u + at
v final velocity
s= v+u t
t elapsed time 2
s displacement s = ut + 1 at 2
a acceleration 2
v 2 = u 2 + 2 as
Angular Velocity and Acceleration
θ angular displacement (radians)
ω angular velocity (radians/s); ω1 = initial, ω2 = final
α angular acceleration (radians/s2)
ω2 = ω1 + α t
θ = ω1 + ω2 x t
2
θ = ω1 t + ½ α t2
ω2 2 = ω1 2 + 2 α θ
linear displacement, s = r θ
linear velocity, v = r ω
linear, or tangential acceleration, aT = r α
Page 11
15. Tangential, Centripetal and Total Acceleration
Tangential acceleration aT is due to angular acceleration α
a T = 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
FORCE
Vector quantity, a push or pull which changes the shape and/or motion of an object
kg m
In SI the unit of force is the newton, N, defined as a
s2
In Imperial the unit of force is the pound lb
Conversion: 9.81 N = 2.2 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 = 9.81 m/s2
In Imperial, the mass of an object (rarely used), in slugs, can be calculated from the known
weight in pounds
Weight
m= g g = 32.2 ft
s2
Page 12
16. Newton's Second Law of Motion
An unbalanced force F will cause an object of mass m to accelerate a, according to:
F = ma (Imperial F = w a, where w is weight)
g
Torque Equation
T=Iα where T is the acceleration torque in Nm, I is the moment of inertia in kg m2
and α is the angular acceleration in radians/s2
Momentum
Vector quantity, symbol p,
p = mv (Imperial p = w v, where w is weight)
g
kg m
in SI unit is s
Work
Scalar quantity, equal to the (vector) product of a force and the displacement of an object. In
simple systems, where W is work, F force and s distance
W = Fs
In SI the unit of work is the joule, J, or kilojoule, kJ
1 J = 1 Nm
In Imperial the unit of work is the ft-lb
Energy
Energy is the ability to do work, the units are the same as for work; J, kJ, and ft-lb
Page 13
17. Kinetic Energy
Energy due to motion
E k = 1 mv 2
2
In Imperial this is usually expressed as E k = w v 2 where w is weight
2g
Kinetic Energy of Rotation
1
E R = mk 2 ω 2 where k is radius of gyration, ω is angular velocity in rad/s
2
or
1
E R = Iω 2 where I = mk2 is the moment of inertia
2
CENTRIPETAL (CENTRIFUGAL) FORCE
mv 2
FC = where r is the radius
r
or
FC = m ω2 r where ω is angular velocity in rad/s
Potential Energy
Energy due to position in a force field, such as gravity
Ep = m g h
In Imperial this is usually expressed Ep = w h where w is weight, and h is height above some
specified datum
Page 14
18. 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. In Imperial, the unit of
electrical energy is the kWh
Conversions: 1 kWh = 3600 kJ
1 kWh = 3412 Btu = 2.66 x 106 ft-lb
Power
A scalar quantity, equal to the rate of doing work
In SI the unit is the Watt W (or kW)
1 W = 1J
s
In Imperial, the units are:
Mechanical Power - ft – lb , horsepower h.p.
s
Thermal Power - Btu
s
Electrical Power - W, kW, or h.p.
Conversions: 746 W = 1 h.p.
1 h.p. = 550 ft – lb
s
1 kW = 0.948 Btu
s
Page 15
19. Pressure
A vector quantity, force per unit area
In SI the basic units of pressure are pascals Pa and kPa
1 Pa = 1 N2
m
In Imperial, the basic unit is the pound per square inch, psi
Atmospheric Pressure
At sea level atmospheric pressure equals 101.3 kPa or 14.7 psi
Pressure Conversions
1 psi = 6.895 kPa
Pressure may be expressed in standard units, or in units of static fluid head, in both SI and
Imperial systems
Common equivalencies are:
1 kPa = 0.294 in. mercury = 7.5 mm mercury
1 kPa = 4.02 in. water = 102 mm water
1 psi = 2.03 in. mercury = 51.7 mm mercury
1 psi = 27.7 in. water = 703 mm water
1 m H2O = 9.81 kPa
Other pressure unit conversions:
1 bar = 14.5 psi = 100 kPa
1 kg/cm2 = 98.1 kPa = 14.2 psi = 0.981 bar
1 atmosphere (atm) = 101.3 kPa = 14.7 psi
Page 16
20. Simple Harmonic Motion
m
Velocity of P = ω R 2 - x 2
s
Acceleration of P = ω2 x m/s2
2π
The period or time of a complete oscillation = seconds
ω
General formula for the period of S.H.M.
displacement
T = 2π
acceleration
Simple Pendulum
L
T = 2π T = period or time in seconds for a double swing
g
L = length in metres
The Conical Pendulum
R/H = tan θ= Fc/W = ω2 R/g
Page 17
21. Lifting Machines
W = load lifted, F = force applied
load W
M.A. = =
effort F
effort distance
V.R. (velocity ratio) =
load distance
M.A.
η = efficiency =
V.R.
1. Lifting Blocks
V.R. = number of rope strands supporting the load block
2. Wheel & Differential Axle
2 πR
Velocity ratio =
2 π(r - r1 )
2
2R
= 2R
r - r1
Or, using diameters instead of radii,
2D
Velocity ratio =
(d - d 1 )
3. Inclined Plane
length
V.R. =
height
4. Screw Jack
circumference of leverage
V.R. =
pitch of thread
Page 18
22. Indicated Power
I.P. = Pm A L N where I.P. is power in W, Pm is mean or "average" effective pressure in
Pa, A is piston area in m2, L is length of stroke in m and N is number of
power strokes per second
Brake Power
B.P. = Tω where B.P. is brake power in W, T is torque in Nm and ω is angular
velocity in radian/second
STRESS, STRAIN and MODULUS OF ELASTICITY
load P
Direct stress = =
area A
extension ∆
Direct strain = =
original length L
Modulus of elasticity
direct stress P/A PL
E= = =
direct strain ∆ / L A∆
force
Shear stress τ =
area under shear
x
Shear strain =
L
Modulus of rigidity
shear stress
G=
shear strain
Page 19
23. General Torsion Equation (Shafts of circular cross-section)
T = τ = Gθ
J r L
1. For Solid Shaft T = torque or twisting moment in newton metres
π 4 πd 4 J = polar second moment of area of cross-section
J= r = about shaft axis.
2 32 τ = shear stress at outer fibres in pascals
r = radius of shaft in metres
2. For Hollow Shaft G = modulus of rigidity in pascals
π θ = angle of twist in radians
J = (r14 - r24 ) L = length of shaft in metres
2
d = diameter of shaft in metres
π 4
= (d 1 − d 4 ) 2
32
Relationship Between Bending Stress and External Bending Moment
M=σ=E
I y R
1. For Rectangle
M = external bending moment in newton metres
I = second moment of area in m4
σ = bending stress at outer fibres in pascals
y = distance from centroid to outer fibres in metres
E = modulus of elasticity in pascals
R = radius of currative in metres
BD 3
I=
12
2. For Solid Shaft
I = πD
4
64
Page 20
24. THERMODYNAMICS
Temperature Scales
5 9
° C = (° F − 32) °F = °C + 32
9 5
°R = °F + 460 (R Rankine) K = °C + 273 (K Kelvin)
Sensible Heat Equation
Q = mc∆T
m is mass
c is specific heat
∆T is temperature change
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
Gas Laws
1. Boyle’s Law
When gas temperature is constant
PV = constant or
P1V1 = P2V2
where P is absolute pressure and V is volume
2. Charles’ Law
V
When gas pressure is constant, = constant
T
V1 V2
or = , where V is volume and T is absolute temperature
T1 T2
Page 21
25. 3. Gay-Lussac's Law
P
When gas volume is constant, = constant
T
P1 P2
Or = , where P is absolute pressure and T is absolute temperature
T1 T2
4. General Gas Law
P1V1 P2V2
= = constant
T1 T2
PV=mRT 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 8.314 kJ/kmol/K
SPECIFIC HEATS OF GASES
Specific Heat at Specific Heat at Ratio of Specific
Constant Pressure Constant Volume Heats
kJ/kgK kJ/kgK γ = cp / c v
GAS or or
kJ/kg oC kJ/kg oC
Air 1.005 0.718 1.40
Ammonia 2.060 1.561 1.32
Carbon Dioxide 0.825 0.630 1.31
Carbon Monoxide 1.051 0.751 1.40
Helium 5.234 3.153 1.66
Hydrogen 14.235 10.096 1.41
Hydrogen Sulphide 1.105 0.85 1.30
Methane 2.177 1.675 1.30
Nitrogen 1.043 0.745 1.40
Oxygen 0.913 0.652 1.40
Sulphur Dioxide 0.632 0.451 1.40
Page 22
26. Efficiency of Heat Engines
T1 – T2
Carnot Cycle η = where T1 and T2 are absolute temperatures of heat source and
T1
sink
Air Standard Efficiencies
1. Spark Ignition Gas and Oil Engines (Constant Volume Cycle or Otto Cycle)
1 cylinder volume
η =1- (γ - 1)
where rv = compression ratio =
rv clearance volume
specific heat (constant pressure)
γ =
specific heat (constant volume)
2. Diesel Cycle
(R γ − 1)
η = 1 - γ -1 where r = ratio of compression
rv γ(R - 1)
R = ratio of cut-off volume to clearance volume
3. High Speed Diesel (Dual-Combustion) Cycle
kβ γ - 1
η =1-
rvγ - 1 [(k - 1) + γk(β - 1)]
cylinder volume
where rv =
clearance volume
absolute pressue at end of constant V heating (combustion)
k=
absolute pressue at beginning of constant V combustion
volume at end of constant P heating (combustion)
β=
clearance volume
4. Gas Turbines (Constant Pressure or Brayton Cycle)
1
η =1- ⎛ γ −1 ⎞
⎜
⎜ γ ⎟ ⎟
⎝ ⎠
r
p
Page 23
28. Heat Transfer by Conduction
Q = λAt∆T
d
where Q = heat transferred in joules
λ = thermal conductivity or coeficient of heat
transfer in 2J × m or W
m × s × °C m × °C
A = area in m 2
t = time in seconds
∆T = temperature difference between surfaces in °C
d = thickness of layer in m
COEFFICIENTS OF THERMAL CONDUCTIVITY
Material Coefficient of
Thermal Conductivity
W/m °C
Air 0.025
Aluminum 206
Brass 104
Brick 0.6
Concrete 0.85
Copper 380
Cork 0.043
Felt 0.038
Glass 1.0
Glass, fibre 0.04
Iron, cast 70
Plastic, cellular 0.04
Steel 60
Wood 0.15
Wallboard, paper 0.076
Page 25
29. 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 x 3
β = 3α
Page 26
30. Chemical Heating Value of a Fuel
Chemical Heating Value MJ per kg of fuel = 33.7 C + 144 H 2 - ( O2
8
) + 9.3 S
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
Theoretical Air Required to Burn Fuel
Air (kg per kg of fuel) = [8 C + 8 (H
3
2 -
O2
8
) + S] 100
23
Air Supplied from Analysis of Flue Gases
N2
Air in kg per kg of fuel = ×C
33 (CO 2 + CO)
C is the percentage of carbon in fuel by mass
N2 is the percentage of nitrogen in flue gas by volume
CO2 is the percentage of carbon dioxide in flue gas by volume
CO is the percentage of carbon monoxide in flue gas by volume
Boiler Formulae
m s (h 1 - h 2 )
Equivalent evaporation =
2257 kJ/kg
(h 1 - h 2 )
Factor of evaporation =
2257 kJ/kg
m s (h 1 - h 2 )
Boiler efficiency =
m f x calorific value of fuel
where m s = mass flow rate of steam
h1 = enthalpy of steam produced in boiler
h2 = enthalpy of feedwater to boiler
mf = mass flow rate of fuel
Page 27
31. FLUID MECHANICS
Discharge from an Orifice
Let A = cross-sectional area of the orifice = (π/4)d2
2
and Ac = cross-sectional area of the jet at the vena conrtacta = ((π/4) d c
then Ac = CcA
2
Ac ⎛ dc ⎞
or Cc = =⎜ ⎟
A ⎝ d ⎠
where Cc is the coefficient of contraction
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
= A cv
or Q = C cAC v 2gh
The coefficients of contraction and velocity are combined to give the coefficient of discharge,
Cd
i.e. C d = C cC v
and Q = C dA 2gh
Typically, values for Cd vary between 0.6 and 0.65
Circular orifice: Q = 0.62 A 2gh
Where Q = flow (m3/s) A = area (m2) h = head (m)
Rectangular notch: Q = 0.62 (B x H) 2 2gh
3
Where B = breadth (m) H = head (m above sill)
Triangular Right Angled Notch: Q = 2.635 H5/2
Where H = head (m above sill)
Page 28
32. Bernoulli’s Theory
P v2
H = h+ +
w 2g
H = total head (metres) w = force of gravity on 1 m3 of fluid (N)
h = height above datum level (metres) v = velocity of water (metres per second)
P = pressure (N/m2 or Pa)
Loss of Head in Pipes Due to Friction
Loss of head in metres = f L v
2
d 2g
L = length in metres v = velocity of flow in metres per second
d = diameter in metres f = constant value of 0.01 in large pipes to 0.02 in small
pipes
Note: This equation is expressed in some textbooks as
Loss = 4f L v where the f values range from 0.0025 to 0.005
2
d 2g
Actual Pipe Dimensions
Page 29
33. ELECTRICITY
Ohm's Law
E
I =
R
or E = IR
where I = current (amperes)
E = electromotive force (volts)
R = resistance (ohms)
Conductor Resistivity
L
R = ρ
a
where ρ = specific resistance (or resistivity) (ohm metres, Ω·m)
L = length (metres)
a = area of cross-section (square metres)
Temperature correction
Rt = Ro (1 + αt)
where Ro = resistance at 0ºC (Ω)
Rt = resistance at tºC (Ω)
α = temperature coefficient which has an average value for copper of 0.004 28
(Ω/ΩºC)
(1 + αt 2 )
R2 = R1
(1 + αt 1 )
where R1 = resistance at t1 (Ω)
R2 = resistance at t2 (Ω)
α Values Ω/ΩºC
copper 0.00428
platinum 0.00385
nickel 0.00672
tungsten 0.0045
aluminum 0.0040
Page 30
34. Dynamo Formulae
2Φ NpZ
Average e.m.f. generated in each conductor =
60c
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.m.f.
EB = generated back e.m.f.
Ia = armature current
Ra = armature resistance
Alternating Current
R.M.S. value of sine curve = 0.707 maximum value
Mean value of sine curve = 0.637 maximum value
R.M.S. value 0.707
Form factor of sinusoidal = = = 1.11
Mean value 0.637
pN
Frequency of alternator = cycles per second
60
Where p = number of pairs of poles
N = rotational speed in r/min
Page 31
35. Slip of Induction Motor
Slip speed of field - speed of rotor
x 100
Speed of field
Inductive Reactance
Reactance of AC circuit (X) = 2πfL ohms
where L = inductance of circuit (henries)
1.256T 2 µA
Inductance of an iron cored solenoid = henries
L x 10 8
where T = turns on coil
µ = magnetic permeablility of core
A = area of core (square centimetres)
L = length (centimetres)
Capacitance Reactance
1
Capacitance reactance of AC circuit = ohms
2πfC
where C = capacitance (farads)
⎛ 1 ⎞
Total reactance = ⎜ 2πfL - ⎟ohms
⎝ 2π fC ⎠
Impedence (Z) = (resistance) 2 + (reactance) 2
1 2
= R 2 + (2π fL - ) ohms
2 π fC
Current in AC Circuit
impressed volts
Current =
impedance
Page 32
36. Power Factor
true watts
p.f. =
volts x amperes
also p.f. = cos Φ, where Φ is the angle of lag or lead
Three Phase Alternators
Star connected
Line voltage = 3 x phase voltage
Line current = phase current
Delta connected
Line voltage = phase voltage
Line current = 3 x phase current
Three phase power
P = 3 EL IL cos Φ
EL = line voltage
IL = line current
cos Φ = power factor
Page 33
38. ION NAMES AND FORMULAE
MONATOMIC POLYATOMIC
Ag+ silver ion BO33- borate ion
Al3+ aluminum ion C2H3O2- acetate ion
Au+ and Au2+ gold ion ClO- hypochlorite ion
Be2+ beryllium ion ClO2- chlorite ion
Ca2+ calcium ion ClO3- chlorate ion
Co2+ and Co3+ cobalt ion ClO4- perchlorate ion
Cr2+ and Cr3+ chromium ion CN- cyanide ion
Cu+ and Cu2+ copper ion CO32- carbonate ion
Fe2+ and Fe3+ iron ion C2O42- oxalate ion
K+ potassium ion CrO42- chromate ion
Li+ lithium ion Cr2O72- dichromate ion
Mg2+ magnesium ion HCO3- hydrogen carbonate or bicarbonate ion
Na+ sodium ion H3O+ hydronium ion
Zn2+ zinc ion HPO42- hydrogen phosphate ion
H2PO4- dihydrogen phosphate ion
HSO3- hydrogen sulphite or bisulphite ion
HSO4- hydrogen sulphate or bisulphate ion
MnO4- permanganate ion
N3- azide ion
NH4+ ammonium ion
NO2- nitrite ion
NO3- nitrate ion
O22- peroxide ion
OCN- cyanate ion
OH- hydroxide ion
PO33- phosphite ion
PO43- phosphate ion
SCN- thiocyanate ion
SO32- sulphite ion
SO42- sulphate ion
S2O32- thiosulphate ion
Page 35
39.
40.
41.
42.
43. This material is owned by Power Engineering Training Systems and may not be modified from its original form.
Duplication of this material for student use in-class or for examination purposes is permitted without written approval.
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