In a solid, shear stress is a function of strain, but in a fluid, shear stress is a function of strain rate. A consequence of this behavior is Pascal's law which describes the role of pressure in characterizing a fluid's state.
Depending on the relationship between shear stress, and the rate of strain and its derivatives, fluids can be characterized as one of the following:
- Newtonian fluids : where stress is directly proportional to rate of strain
- Non-Newtonian fluids : where stress is not proportional to rate of strain, its higher powers and derivatives.
The behavior of fluids can be described by the Navier–Stokes equations—a set of partial differential equations which are based on:
- continuity (conservation of mass),
- conservation of linear momentum,
- conservation of angular momentum,
- conservation of energy.
The study of fluids is fluid mechanics, which is subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion.
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