Water Density Calculator: Temperature and Salinity

What is Water Density?

Water density is a measure of the mass of water per unit volume. It varies with temperature and salinity, which are crucial factors in oceanography, climate studies, and many industrial processes. Understanding water density is essential for predicting ocean currents, stratification, and the behavior of marine ecosystems.

Formula

The density of seawater is calculated using the UNESCO 1983 (EOS 80) equation of state:

\[ \rho = \rho_0 + AS + BS^{3/2} + CS^2 \]

Where:

• \( \rho \) is the density of seawater (kg/m³)
• \( \rho_0 \) is the density of pure water at the given temperature
• \( S \) is the salinity (PSU - Practical Salinity Unit)
• \( A \), \( B \), and \( C \) are temperature-dependent coefficients

Calculation Steps

Let's calculate the density of seawater at 20°C with a salinity of 35 PSU:

1. Calculate \( \rho_0 \) (density of pure water at 20°C): \[ \rho_0 = 998.2071 \text{ kg/m³} \]
2. Calculate coefficients \( A \), \( B \), and \( C \) at 20°C: \[ A = 0.824493 \] \[ B = -0.0040899 \] \[ C = 0.000076438 \]
3. Apply the formula: \[ \rho = 998.2071 + (0.824493 \times 35) + (-0.0040899 \times 35^{3/2}) + (0.000076438 \times 35^2) \]
4. Perform the final calculation: \[ \rho \approx 1024.7639 \text{ kg/m³} \]

Example and Visual Representation

Let's visualize how water density changes with temperature and salinity:

This graph illustrates:

• The relationship between temperature and density for fresh water (red curve) and seawater (green curve)
• As temperature increases, water density generally decreases
• Seawater is denser than fresh water at the same temperature due to dissolved salts
• The density of water reaches its maximum at about 4°C for fresh water (a phenomenon known as the density anomaly of water)