Fresh water density is a critical parameter in various fields, including environmental science, engineering, and physics. The density of fresh water is primarily determined by temperature and pressure, with salinity playing a negligible role compared to seawater. Understanding the factors that influence fresh water density and the methods used to measure it is essential for a wide range of applications.
Understanding the Factors Affecting Fresh Water Density
Temperature
The density of fresh water is highly dependent on temperature. At 4°C and standard atmospheric pressure, the density of fresh water is approximately 1000 kg/m³. As the temperature increases, the density decreases, and as the temperature decreases, the density increases. For example, the density of fresh water at 0°C is approximately 999.87 kg/m³, while at 20°C, it is approximately 998.20 kg/m³.
Pressure
Pressure also affects the density of fresh water. As the pressure increases, the density of fresh water also increases. For instance, at a depth of 10 meters in fresh water, the pressure is approximately 0.1 MPa, and the density of fresh water is approximately 1000.02 kg/m³.
Dissolved Gases
In addition to temperature and pressure, the presence of dissolved gases, such as oxygen and carbon dioxide, can also affect the density of fresh water. The solubility of these gases decreases with increasing temperature, which can lead to changes in density.
Measuring Fresh Water Density
Measuring the density of fresh water typically involves measuring the temperature, pressure, and salinity of the water. While salinity is not a significant factor in fresh water, it is still measured to ensure accuracy. The density is then calculated using a formula that takes into account the measured variables.
The density of fresh water can be calculated using the following formula:
ρ = ρ_0 [1 – β(T – T_0)]
Where:
– ρ is the density of fresh water at temperature T
– ρ_0 is the density of fresh water at a reference temperature T_0 (typically 4°C)
– β is the thermal expansion coefficient of fresh water (approximately 0.00020/°C at 4°C)
– T is the temperature of the fresh water
– T_0 is the reference temperature (typically 4°C)
Physics Examples and Numerical Problems
Example 1: Density of Fresh Water at 20°C
A container is filled with fresh water at 20°C. What is the density of the fresh water?
Using the formula above, with T_0 = 4°C and β = 0.00020/°C, we can calculate the density of the fresh water as follows:
ρ = 1000 kg/m³ [1 – 0.00020/°C(20°C – 4°C)]
ρ = 998 kg/m³
Example 2: Density of Fresh Water at 10 Meters Depth
A pipe is used to transport fresh water from a reservoir at 10 meters depth to a treatment plant at the surface. What is the density of the fresh water at the pipe inlet?
At a depth of 10 meters in fresh water, the pressure is approximately 0.1 MPa. Using the formula above, with T_0 = 4°C and β = 0.00020/°C, we can calculate the density of the fresh water as follows:
ρ = 1000 kg/m³ [1 – 0.00020/°C(T – 4°C) + 0.00001/MPa(0.1 MPa)]
ρ = 1000.02 kg/m³
Numerical Problem 1: Mass of 10 Liters of Fresh Water at 10°C
A tank is filled with fresh water at 10°C. What is the mass of 10 liters of the fresh water?
First, we need to calculate the density of the fresh water at 10°C using the formula above:
ρ = 1000 kg/m³ [1 – 0.00020/°C(10°C – 4°C)]
ρ = 999.8 kg/m³
Then, we can calculate the mass of 10 liters of the fresh water as follows:
mass = density x volume
mass = 999.8 kg/m³ x 0.01 m³
mass = 9.998 kg
Numerical Problem 2: Change in Density of Fresh Water from Reservoir to Pipe Inlet
A pipe is used to transport fresh water from a reservoir at 20 meters depth to a treatment plant at the surface. What is the change in density of the fresh water as it rises from the bottom of the reservoir to the pipe inlet?
At a depth of 20 meters in fresh water, the pressure is approximately 0.2 MPa. Using the formula above, with T_0 = 4°C and β = 0.00020/°C, we can calculate the density of the fresh water at the bottom of the reservoir as follows:
ρ_bottom = 1000 kg/m³ [1 – 0.00020/°C(T – 4°C) + 0.00001/MPa(0.2 MPa)]
ρ_bottom = 1000.04 kg/m³
At the pipe inlet, the pressure is approximately 0.1 MPa, and the temperature is the same as at the bottom of the reservoir. Using the formula above, we can calculate the density of the fresh water at the pipe inlet as follows:
ρ_inlet = 1000 kg/m³ [1 – 0.00020/°C(T – 4°C) + 0.00001/MPa(0.1 MPa)]
ρ_inlet = 1000.02 kg/m³
Therefore, the change in density of the fresh water as it rises from the bottom of the reservoir to the pipe inlet is:
Δρ = ρ_bottom – ρ_inlet
Δρ = 1000.04 kg/m³ – 1000.02 kg/m³
Δρ = 0.02 kg/m³
Figures, Data Points, and Measurements
The following figure shows the density of fresh water as a function of temperature at atmospheric pressure:
The following table shows the density of fresh water at various temperatures and pressures:
| Temperature (°C) | Pressure (MPa) | Density (kg/m³) |
|---|---|---|
| 0 | 0.1 | 999.87 |
| 4 | 0.1 | 1000.00 |
| 10 | 0.1 | 999.70 |
| 20 | 0.1 | 998.20 |
| 4 | 0.2 | 1000.13 |
| 10 | 0.2 | 1000.03 |
| 20 | 0.2 | 999.13 |
References
- Measurable Goals Guidance for Phase II Small MS4s
- Water Quality Data Pathfinder | Earthdata – NASA
- “Freshwater” in the Ocean is Not a Useful Parameter in Climate …
- Monitoring Networks and Identification of Data Gaps Best Management Practices
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