Introduction to S.I. Units
The International System of Units (S.I.) is organized into three primary categories:
Base Units
Derived Units
Supplementary Units
While the separation into these groups may appear somewhat arbitrary from a purely scientific perspective, it does not affect the fundamental principles of physics. Instead, this classification was adopted to establish a unified, practical, and globally recognized system. Such a system benefits international collaboration, education, and scientific research.
Recognizing these advantages, the General Conference endorsed the use of six well-defined base units, as summarized in the table below:
📚 SI Base Units 🧪
| Quantity | Name | Symbol |
|---|---|---|
| 📏 Length | Metre | m |
| ⚖️ Mass | Kilogram | kg |
| ⏱️ Time | Second | s |
| ⚡ Electric Current | Ampere | A |
| 🌡️ Thermodynamic Temperature | Kelvin | K |
| 💡 Luminous Intensity | Candela | cd |
| 🧪 Amount of Substance | Mole | mol |
The second category, the derived units, consists of those that are formulated by algebraically combining the base units. These combinations reflect the relationships between various physical quantities. In many cases, these expressions are simplified by assigning unique names and symbols, which in turn serve as building blocks for additional derived units.
Classification of Derived S.I. Units
Derived units arise from combining base units according to algebraic relationships among physical quantities. They can be broadly categorized into three groups. The following tables offer examples for each classification:
1. Derived Units Expressed Directly in Terms of Base Units
These units are formed by the direct algebraic combination of the base units. For instance, measurements like area, volume, and speed are expressed as follows
📐 Derived SI Units in Terms of Base Units 📊
| Quantity | Name | Symbol | Base Units |
|---|---|---|---|
| ⬛ Area | Square metre | m² | m² |
| 📦 Volume | Cubic metre | m³ | m³ |
| 🏃 Speed | Metre per second | m/s | m/s |
| 🚀 Acceleration | Metre per second² | m/s² | m/s² |
| 🌊 Wave Number | Reciprocal metre | m⁻¹ | m⁻¹ |
| ⚖️ Density | Kilogram per cubic metre | kg/m³ | kg/m³ |
| 🧪 Concentration | Mole per cubic metre | mol/m³ | mol/m³ |
| ☢️ Radioactivity | Reciprocal second | s⁻¹ | s⁻¹ |
| 📦 Specific Volume | Cubic metre per kilogram | m³/kg | m³/kg |
| 💡 Luminance | Candela per square metre | cd/m² | cd/m² |
2. Derived Units with Special Names
Many derived units have been given specific names and symbols to simplify usage. These units can also be expressed in terms of base units, which underlines the inherent relationships between physical quantities:
🔬 Derived Units with Special Names ⚛️
| Quantity | Name | Symbol | Base Units |
|---|---|---|---|
| 🌊 Frequency | Hertz | Hz | s⁻¹ |
| 🚀 Force | Newton | N | m·kg/s² |
| 🏋️ Pressure | Pascal | Pa | m⁻¹·kg/s² |
| ⚡ Energy | Joule | J | m²·kg/s² |
| 🔌 Power | Watt | W | m²·kg/s³ |
| ⚡ Charge | Coulomb | C | A·s |
| 🔋 Voltage | Volt | V | m²·kg/s³·A⁻¹ |
| 🔋 Capacitance | Farad | F | m⁻²·kg⁻¹·s⁴·A² |
| 🔌 Resistance | Ohm | Ω | m²·kg/s³·A² |
| 📈 Conductance | Siemens | S | m⁻²·kg⁻¹·s³·A² |
| 🧲 Magnetic Flux | Weber | Wb | m²·kg/s²·A⁻¹ |
| 🧲 Flux Density | Tesla | T | kg/s²·A⁻¹ |
| 🌀 Inductance | Henry | H | m²·kg/s²·A⁻² |
| 💡 Luminous Flux | Lumen | lm | cd·sr |
| 🔦 Illuminance | Lux | lx | m⁻²·cd·sr |
3. Derived Units Expressed by Means of Special Names
Some derived units, although initially defined through base units, are commonly expressed using names that reflect specific applications. These include units that are frequently encountered in areas like mechanics, thermodynamics, and electromagnetism:
🔥 Derived Units with Special Names ⚗️
| Quantity | Name | Symbol | Base Units |
|---|---|---|---|
| 🌊 Dynamic Viscosity | Pascal second | Pa·s | m⁻¹·kg/s |
| 🔩 Moment of Force | Newton metre | N·m | m²·kg/s² |
| 💧 Surface Tension | Newton per metre | N/m | kg/s² |
| ☀️ Heat Flux Density | Watt per square metre | W/m² | kg/s³ |
| 🌡️ Heat Capacity | Joule per kelvin | J/K | m²·kg/s²·K⁻¹ |
| ❄️ Specific Heat | Joule per kg kelvin | J/(kg·K) | m²/s²·K⁻¹ |
| ⚡ Specific Energy | Joule per kilogram | J/kg | m²/s² |
| 🔥 Thermal Conductivity | Watt per metre kelvin | W/(m·K) | m·kg/s³·K⁻¹ |
| 📦 Energy Density | Joule per cubic metre | J/m³ | m⁻¹·kg/s² |
| ⚡ Electric Field | Volt per metre | V/m | m·kg/s³·A⁻¹ |
| 📊 Charge Density | Coulomb per m³ | C/m³ | m⁻³·s·A |
| 📈 Flux Density | Coulomb per m² | C/m² | m⁻²·s·A |
| 🧲 Permittivity | Farad per metre | F/m | m⁻³·kg⁻¹·s⁴·A² |
| 📊 Current Density | Ampere per m² | A/m² | (directly defined) |
| 🧭 Magnetic Strength | Ampere per metre | A/m | (directly defined) |
| 🌀 Permeability | Henry per metre | H/m | m·kg/s²·A⁻² |
| ⚗️ Molar Energy | Joule per mole | J/mol | m²·kg/s²·mol⁻¹ |
| ⚗️ Molar Heat Capacity | Joule per mole kelvin | J/(mol·K) | m²·kg/s²·K⁻¹·mol⁻¹ |
S.I. Supplementary Units
The third category within the S.I. system—known as “Supplementary Units”—can be interpreted either as additional base units or as derived units. Their dual role allows for a flexible approach in various scientific applications. The supplementary units are primarily used to quantify angular measurements, as shown in the table below.
📏 S.I. Supplementary Units 🎯
| Quantity | Name | Symbol |
|---|---|---|
| 📐 Plane Angle | Radian | rad |
| 🌐 Solid Angle | Steradian | sr |
Derived Units Formed Using Supplementary Units
Supplementary units are also used to derive additional units for expressing various rotational and radiative quantities. The following table lists several examples of such derived units:
📐 SI Derived Units with Supplementary Units 🌌
| Quantity | Name | Symbol |
|---|---|---|
| 🔄 Angular Velocity | Radian per second | rad/s |
| 📈 Angular Acceleration | Radian per second squared | rad/s² |
| 💡 Radiant Intensity | Watt per steradian | W/sr |
| ☀️ Radiance | Watt per square metre steradian | W·m⁻²·sr⁻¹ |
S.I. Prefixes
S.I. prefixes provide a convenient way to express multiples or submultiples of S.I. units. They are based on powers of ten and are standardized to facilitate clarity and precision in measurements. The table below summarizes common S.I. prefixes:
🔼 S.I. Prefixes 🔽
| Large Scales | Small Scales | ||||
|---|---|---|---|---|---|
| Factor | Prefix | Symbol | Factor | Prefix | Symbol |
| 🚀 10¹² | tera | T | 🐜 10⁻¹ | deci | d |
| 🌍 10⁹ | giga | G | 🔬 10⁻² | centi | c |
| 📡 10⁶ | mega | M | 🧬 10⁻³ | milli | m |
| 🔺 10³ | kilo | k | 🌌 10⁻⁶ | micro | µ |
| 🏢 10² | hecto | h | 🧪 10⁻⁹ | nano | n |
| 📏 10¹ | deca | da | 🔎 10⁻¹² | pico | p |
| 🌀 10⁻¹⁵ | — | f | Additional submultiplicative factors included | ||
| 🌠 10⁻¹⁸ | atto | a | |||
Conversion Factors
🔄 Unit Conversion Factors ⚖️
| Conversion Type | Equivalence | Formula |
|---|---|---|
| 💪 Force | ||
| Newton ↔ Kilogram-force | 1 N = 0.102 kgf | 1 kgf = 9.81 N = 1 kg·m/s² |
| 🏋️ Pressure | ||
| Bar Conversions | 1 bar = 750.06 mmHg = 0.9869 atm | 1 bar = 10⁵ Pa = 10³ kg/(m·s²) |
| Atmosphere | 1 atm = 760 mmHg | 1 atm = 1.01325×10⁵ N/m² |
| ⚡ Energy/Work/Heat | ||
| Joule Conversions | 1 J = 0.239 cal = 2.778×10⁻⁷ kWh | 1 kcal = 4184 J = 427 kgf·m |
| kWh Equivalence | 1 kWh = 3.6×10⁶ J | 1 kgf·m = 9.81 J |
| 🚀 Power | ||
| Power Units | 1 W = 0.86 kcal/h | 1 h.p. = 735.3 W |
| 🌡️ Thermal Properties | ||
| Specific Heat | 1 kcal/(kg·K) = 4184 J/(kg·K) | 1 W/(m·K) = 0.86 kcal/(h·m·°C) |
| Heat Transfer | 1 W/(m²·K) = 0.86 kcal/(m²·h·°C) | 1 kcal/(m²·h·°C) = 1.163 W/(m²·K) |
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Learn more about the Units of Measurements and their importance in civil engineering.
Visit the PageIMPORTANT ENGINEERING CONSTANTS AND EXPRESSIONS IN S.I. UNITS
⚙️ Engineering Constants & Expressions 📐
| Item | Constant/Expression | SI Units/Value |
|---|---|---|
| 1 | 🌍 Gravitational Acceleration (g₀) | 9.81 m/s² |
| 🔬 Gas Properties | ||
| 2 | Universal Gas Constant (R) 1 kgf-m = 9.81 J |
8314 J/kg-mole·K 848 × 9.81 = 8314 |
| 3 | Gas Constant for Air | 287 J/kg·K |
| 🌡️ Specific Heats (Air) | ||
| 4 | Constant Volume (cᵥ) 0.17 kcal/kg·K → SI |
0.71128 kJ/kg·K 0.17 × 4.184 = 0.71128 |
| 4 | Constant Pressure (cₚ) 0.24 kcal/kg·K → SI |
1.00416 kJ/kg·K 0.24 × 4.184 = 1.00416 |
| 📐 Key Engineering Formulas | ||
| 5 | 🚀 Nozzle Exit Velocity C₂ = 44.7√U (U in kJ) |
C₂ = 44.7√(Δh) |
| 6 | ❄️ Refrigeration: 1 Ton | 210 kJ/min 50 kcal/min × 4.184 = 209.2 |
| 7 | 🔥 Stefan-Boltzmann Law Q = σT⁴ |
5.67 × 10⁻⁸ W/m²K⁴ σ = 5.67e-8 W/m²K⁴ |
