Chapter 2
Calculation tools. Systems and units
Enrique Roca Bordello
Dpt. Chemical Engineering
Outline
Chapter 2. Calculation tools. Systems and units
1. Introduction
2. Dimensions and systems of units
3. Conversion of units
4. Dimensional consistency
5. Process variables: degrees of freedom
, 1. Introduction
•In many cases, the answers to the calculations are not what was expected
and, often, this is due to a lack of experience in handling units.
•Using units in combination with numbers in calculations requires more
attention than is currently being paid.
Objectives
•To introduce the student to the types of calculations that process
engineers carry out in their daily work.
•To review some concepts: dimensions, units, systems of units,
conversion of units and dimensional consistency.
2. Dimensions and Systems of units
Dimensions and Units
• Dimension is any property or physical quality that can be measured and,
therefore, it can be expressed quantitatively.
• Units are the way of explicitly expressing dimensions, that is, they are the
quantification of dimensions.
• A distinction is made between:
• Fundamental (or basic) dimensions/units are those that can be measured
independently and are sufficient to describe most physical quantities.
Examples: length, time, mass, temperature.
• Derived dimensions/units are those that can be expressed as potential
functions of the fundamental dimensions/units. Examples: volume,
density, speed, etc.
, 2. Dimensions and Systems of units
Rules for units handling
1) It is only possible to add, subtract or equal quantities if these quantities belong
to the same dimension and are expressed in the same units.
5 kilograms + 3 joules
3 cm – 1 cm
10 pounds + 5 grams
2) It is possible to multiply or divide different units.
3 N· 4 m
5 km / 2 h
7 km/h · 4 h
3m·4m
6 cm · 5 cm/s
(5 kg/s) / (0.20 kg/m3)
2. Dimensions and Systems of units
Systems of units
• A system of units has the following components:
• Fundamental units
• Multiple and submultiple units
• Derived units
• The two most commonly used systems of units are:
• The International System (SI) of units.
• The American Engineering (AE) system of units.
Calculation tools. Systems and units
Enrique Roca Bordello
Dpt. Chemical Engineering
Outline
Chapter 2. Calculation tools. Systems and units
1. Introduction
2. Dimensions and systems of units
3. Conversion of units
4. Dimensional consistency
5. Process variables: degrees of freedom
, 1. Introduction
•In many cases, the answers to the calculations are not what was expected
and, often, this is due to a lack of experience in handling units.
•Using units in combination with numbers in calculations requires more
attention than is currently being paid.
Objectives
•To introduce the student to the types of calculations that process
engineers carry out in their daily work.
•To review some concepts: dimensions, units, systems of units,
conversion of units and dimensional consistency.
2. Dimensions and Systems of units
Dimensions and Units
• Dimension is any property or physical quality that can be measured and,
therefore, it can be expressed quantitatively.
• Units are the way of explicitly expressing dimensions, that is, they are the
quantification of dimensions.
• A distinction is made between:
• Fundamental (or basic) dimensions/units are those that can be measured
independently and are sufficient to describe most physical quantities.
Examples: length, time, mass, temperature.
• Derived dimensions/units are those that can be expressed as potential
functions of the fundamental dimensions/units. Examples: volume,
density, speed, etc.
, 2. Dimensions and Systems of units
Rules for units handling
1) It is only possible to add, subtract or equal quantities if these quantities belong
to the same dimension and are expressed in the same units.
5 kilograms + 3 joules
3 cm – 1 cm
10 pounds + 5 grams
2) It is possible to multiply or divide different units.
3 N· 4 m
5 km / 2 h
7 km/h · 4 h
3m·4m
6 cm · 5 cm/s
(5 kg/s) / (0.20 kg/m3)
2. Dimensions and Systems of units
Systems of units
• A system of units has the following components:
• Fundamental units
• Multiple and submultiple units
• Derived units
• The two most commonly used systems of units are:
• The International System (SI) of units.
• The American Engineering (AE) system of units.
