Introduction

Any material that flows in response to an applied stress is a fluid. Although solids acquire a finite deformation or strain upon being stressed, fluids deform continuously under the action of applied forces. In solids, stresses are related to strains; in fluids, stresses are related to rates of strain. Strains in solids are a consequence of spatial variations or gradients in the displacements of elements from their equilibrium positions. Strain rates in fluids are a result of gradients in the velocities or rates of displacement of fluid elements. Velocity gradients are equivalent to strain rates, so stresses in fluids are related to velocity gradients. The equation connecting stresses with velocity gradients in a fluid is known as the rheological law for the fluid. The simplest fluid, and as a consequence the one most often studied, is the Newtonian or linear fluid, in which the rate of strain or velocity gradient is directly proportional to the applied stress; the constant of proportionality is known as the viscosity. We deal only with Newtonian viscous fluids throughout this chapter. Non-Newtonian fluid behavior is discussed in Chapter 7. Fluid mechanics is the science of fluid motion. It uses the basic principles of mass, momentum, and energy conservation together with the rheological or constitutive law for the fluid to describe how the fluid moves under an applied force.

Many problems involving fluid mechanics arise in geodynamics. Obvious examples involve flows of groundwater and magma.