
Water is a liquid substance exhibiting fluid dynamics, quantum effects, and crowd simulation properties.Water (H₂O) is a polar compound with a bond angle of about 104.5°. Oxygen pulls electrons, acquiring a partial negative charge, while hydrogens become positive. The resulting hydrogen bonds create a dynamic network, making water an excellent solvent for many substances. Water reaches its maximum density at 4 °C, not at freezing; this leads to convective mixing, preventing water bodies from freezing solid.
In antiquity, water was considered one of the primary elements. In 1781, Henry Cavendish synthesized water; Lavoisier named its components hydrogen and oxygen. Gay-Lussac and Humboldt determined the volume ratio 2:1. In the 20th century, X-ray diffraction and neutron scattering revealed the structure of water and ice; high-pressure ice phases were discovered by Percy Bridgman. Quantum chemical models of hydrogen bonding were developed by John Pople.
The hydrogen bond in water has a partially covalent character (~10%) and energy of about 20 kJ/mol. Its directionality and saturation ensure a local tetrahedral structure, which makes ice have a more open packing and lower density. Upon melting, some bonds break, but short-range order persists. When heated from 0 to 4 °C, residual ordering collapses, increasing density. Quantum effects (proton tunneling) are important for the properties of heavy water and some ice phases.
A universal solvent for chemical reactions, heat carrier in cooling and heating systems, basis of biological fluids, key factor in Earth's climate system.
Hot water sometimes freezes faster than cold water — the mysterious Mpemba effect, for which there is still no clear explanation.
| \mathcal{M} | variable | Mach number — mach number |
| v | variable | flow velocity — velocity metre per second |
| c_s | variable | local speed of sound — speed of sound metre per second |


















