1. What is the Water Density vs Pressure Equation?

The water density vs pressure equation estimates how water density changes with pressure. It accounts for water's slight compressibility through the compressibility coefficient (κ).

2. How Does the Calculator Work?

The calculator uses the equation:

Where:

• \( \rho \) — Final density (kg/m³)
• \( \rho_0 \) — Initial density (kg/m³)
• \( \kappa \) — Isothermal compressibility (/Pa)
• \( \Delta P \) — Pressure change (Pa)

Explanation: The equation shows that water density increases slightly with increasing pressure, though water is generally considered nearly incompressible for most practical purposes.

3. Importance of Density-Pressure Relationship

Details: Understanding how density changes with pressure is crucial in hydraulics, oceanography, and high-pressure systems where even small density changes can be significant.

4. Using the Calculator

Tips: Enter initial density (typically 998.2 kg/m³ for water at 20°C), compressibility (4.6×10⁻¹⁰ /Pa for water), and pressure change. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this equation?
A: It's a linear approximation valid for moderate pressure changes. For extreme pressures, more complex equations are needed.

Q2: Does temperature affect this relationship?
A: Yes, both ρ₀ and κ are temperature-dependent. This calculator assumes constant temperature.

Q3: What's the typical compressibility of water?
A: About 4.6×10⁻¹⁰ /Pa at 20°C, meaning water density increases by ~0.046% per 1 MPa pressure increase.

Q4: When is this calculation important?
A: In deep ocean applications, high-pressure hydraulic systems, and precise scientific measurements where small density changes matter.

Q5: How does this compare to gases?
A: Water is much less compressible than gases - density changes are orders of magnitude smaller for the same pressure change.