Table of Contents
- Introduction
- Definition and Formula
- Units of Measurement
- Specific Weight of Water
- Factors Affecting the Specific Weight of Water
- Comparison with Other Liquids
- Why is Specific Weight Important?
Introduction
Specific weight is a fundamental concept in fluid mechanics and material science that describes the weight per unit volume of a substance. It is a measure of how heavy a material is relative to its size, and it plays a crucial role in understanding the behavior of fluids and solids in various applications.
Image: 1 cubic meter of water, bromine and mercury.
By understanding specific weight, engineers and scientists can make informed decisions about material selection, structural design, and fluid dynamics.
Definition and Formula
Specific weight, often denoted by the Greek letter gamma (γ), is defined as the weight of a substance divided by its volume. Mathematically, it is expressed as:
\[\gamma = \frac{W}{V}\]where:
γ – specific weight (typically measured in [N/m³] or [lb/ft³])
W – weight of the substance (measured in newtons [N] or pounds [lb])
V – volume of the substance (measured in cubic meters [m³] or cubic feet [ft³])
The weight of a substance (W) can also be calculated using its mass (m) and the acceleration due to gravity (g):
W = m · g
Therefore, the specific weight can also be written as:
\[\gamma = \frac{m \cdot g}{V} = \rho \cdot g\]where:
ρ – density of the substance (mass per unit volume, measured in [kg/m³] or [lb/ft³])
g – acceleration due to gravity (approximately 9.81 m/s² or 32.2 ft/s² on Earth)
This relationship shows that specific weight is directly proportional to density and gravity.
Units of Measurement
The specific weight of a substance is typically measured in:
- SI Units: Newtons per cubic meter [N/m³]
- Imperial Units: Pounds per cubic foot [lb/ft³]
For example, the specific weight of water at 4°C (39.2°F) is approximately:
- 9,810 N/m³ (SI units)
- 62.4 lb/ft³ (Imperial units)
Specific Weight of Water
To calculate the specific weight of water, we use the following formula:
γ = ρ · g
where:
γ – specific weight in [N/m³] or [lb/ft³]
ρ – density of water [kg/m³] or [lb/ft³]
g – acceleration due to gravity (9.81 m/s² or 32.2 ft/s²)
Step-by-Step Calculation of Specific Weight of Water
Step 1. Determine the density of water
At 20°C, the density of water (ρ) is approximately:
ρwater = 998 kg/m³
Step 2. Use the gravitational acceleration constant
The standard value for gravity (g) at sea level is:
g = 9.81 m/s²
Step 3. Calculate the specific weight of water
Substitute the values of ρ and g into the formula:
γwater = ρwater ⋅ g
γwater = 998 kg/m³ ⋅ 9.81 m/s²
γwater = 9790.38 N/m³
Since water density varies with temperature, the specific weight of water will be function of temperature.
| Water temperature [°F] | Water temperature [°C] | Water density [kg/m3] | Specific weight of water [N/m3] |
| 32 | 0 | 999.87 | 9808.7247 |
| 39.2 | 4 | 1000 | 9810 |
| 40 | 4.4 | 999.99 | 9809.9019 |
| 50 | 10 | 999.75 | 9807.5475 |
| 60 | 15.6 | 999.07 | 9800.8767 |
| 70 | 21 | 998.02 | 9790.5762 |
| 80 | 26.7 | 996.69 | 9777.5289 |
| 90 | 32.2 | 995.10 | 9761.931 |
| 100 | 37.8 | 993.18 | 9743.0958 |
| 120 | 48.9 | 988.70 | 9699.147 |
| 140 | 60 | 983.38 | 9646.9578 |
| 160 | 71.1 | 977.29 | 9587.2149 |
| 180 | 82.2 | 970.56 | 9521.1936 |
| 200 | 93.3 | 963.33 | 9450.2673 |
| 212 | 100 | 958.65 | 9404.3565 |
Source: U.S. Department of the Interior, Bureau of Reclamation, 1977, Ground Water Manual, from The Water Encyclopedia, Third Edition, Hydrologic Data and Internet Resources, Edited by Pedro Fierro, Jr. and Evan K. Nyler, 2007.
Factors Affecting the Specific Weight of Water
The specific weight of water is not a constant value; it varies depending on several factors. Understanding these factors is crucial for accurate calculations in engineering, science, and environmental studies. The primary factors that influence the specific weight of water are temperature, pressure, and impurities or salinity.
1. Temperature
Temperature has a significant impact on the specific weight of water. As water temperature changes, its density (ρ) changes, which directly affects its specific weight (γ = ρ ⋅ g).
- cold water (below 4°C): water is unique in that it reaches its maximum density at approximately 4°C (39.2°F). Below this temperature, water begins to expand as it approaches freezing, causing its density (and specific weight) to decrease.
- warm water (above 4°C): as water warms above 4°C, it expands, reducing its density and specific weight. For example, at 20°C, the density of water is about 998 kg/m³, resulting in a specific weight of 9,790 N/m³. At 100°C (boiling point), the density drops to approximately 958 kg/m³, reducing the specific weight further.
The specific weight of water decreases as temperature increases (above 4°C) and increases as water temperature decreases (below 4°C).
2. Pressure
Pressure also affects the specific weight of water, although its influence is less pronounced compared to temperature. Changes in pressure can slightly alter the density of water.
- high pressure: under high pressure, water molecules are compressed, increasing its density and specific weight. For example, in deep ocean environments, the specific weight of water is higher due to the immense pressure at great depths.
- low pressure: at lower pressures, such as at high altitudes, water expands slightly, reducing its density and specific weight.
The specific weight of water increases with pressure and decreases with reduced pressure.
3. Impurities and Salinity
The presence of impurities or dissolved salts (salinity) in water significantly affects its density and specific weight.
- freshwater: pure freshwater has a lower density and specific weight compared to saline water. For example, the specific weight of pure water at 20°C is approximately 9790 N/m³.
- saltwater (seawater): seawater contains dissolved salts, which increase its density. The average density of seawater is about 1025 kg/m³, resulting in a specific weight of approximately 10055 N/m³ at 20°C.
- other impurities: impurities such as minerals, pollutants, or suspended particles can also increase the density and specific weight of water.
The specific weight of water increases with higher salinity or the presence of impurities.
Comparison with Other Liquids
Water, bromine, and mercury are three substances with vastly different specific weights due to their unique densities. At 20°C and sea level atmospheric pressure, water has a specific weight of approximately 9790 N/m³, while bromine and mercury have significantly higher values of 30607 N/m³ and 132886 N/m³, respectively.
These differences arise from their molecular structures and densities, with mercury being exceptionally dense due to its heavy atomic composition. Comparing the specific weights of these substances highlights the importance of understanding material properties for practical applications, such as fluid dynamics, chemical processing, and structural design.
Here is a table of different liquids, their densities, and specific weights at 20 °C and sea level atmospheric pressure, sorted from lowest to highest specific weight. The specific weight is calculated using the formula γ = ρ ⋅ g, where g = 9.81 m/s².
| Liquid | Density (ρ) [kg/m³] | Specific Weight (γ) [N/m³ |
|---|---|---|
| Ethanol | 789 | 7740 |
| Gasoline | 720 | 7063 |
| Water | 998 | 9790 |
| Seawater | 1,025 | 10055 |
| Olive Oil | 920 | 9025 |
| Glycerin | 1,261 | 12370 |
| Bromine | 3,120 | 30607 |
| Mercury | 13,546 | 132886 |
The specific weight of water is much lower than that of bromine and mercury, reflecting their differences in density and molecular composition. Water’s relatively low specific weight makes it a versatile fluid for everyday use, while bromine’s higher value suits it for specialized chemical applications.
Mercury, with its exceptionally high specific weight, is often used in applications requiring dense fluids, such as barometers and thermometers. Understanding these differences allows engineers and scientists to select the appropriate materials for specific tasks, ensuring efficiency and safety in their designs. This comparison underscores the importance of specific weight as a fundamental property in both theoretical and applied sciences.
Why is Specific Weight Important?
Specific weight is a critical parameter in engineering and science because it helps determine how fluids and materials behave under different conditions. For example:
- in hydraulics, it is used to calculate pressure and buoyancy forces.
- in civil engineering, it helps design structures that can withstand the weight of materials like water, soil, or concrete.
- in environmental science, it aids in understanding the movement and distribution of fluids in natural systems.