Math in Engineering
Basics of Engineering
What is fluid mechanics?
Fluids are substances that flow, including gases and liquids. Fluid mechanics, or hydraulics, is the study of the physical behavior of these gases and liquids and their role in engineering systems. This includes the mathematics of the forces in and motion of substances, turbulence, wave propagation, and so on.
Most fluid mechanics problems in engineering are mathematically modeled using differential equations. These models can also be applied to other engineering areas, such as electromagnetism and the mechanics of solids (because solids still “move,” albeit slowly). Other fluid mechanical studies include the compressibility of substances. In most cases, liquids are considered to be incompressible and gases are considered to be compressible. But there are exceptions in some everyday engineering applications, and they can easily be explored using mathematical modeling.
Engineers also use special mathematical equations to determine certain characteristics of fluid flow, such as whether the flow is slow and smooth (laminar) or turbulent. For example, the ratio of inertia forces to viscous forces within a fluid can be expressed by what is called the Reynold’s number; laminar fluid flow can be described by the Navier-Stokes equations. For no viscosity (or an ideal flow called inviscid flow), the Bernoulli equation can be used. Finally, when the flow is zero (or static), the fluid is governed by the laws and equations of fluid statics.