Ideal/Real Fluid
An ideal fluid is a fluid that that experiences no viscous forces. This property of inviscid fluids allow them to flow along walls without an velocity decay due to skin friction, and also eliminates drag on adjacent lamina due to velocity gradients. This in turn means that ideal fluids do not form turbulent vortices as these flow past obstructions. Ideal fluids can be thought of as body of tiny frictionless particles, capable of supporting pressures at normal incidence but unaffected by shearing stresses. Ideal fluids are strictly a theoretical conception, but are sometime useful in modeling real-world situations where viscous forces can be neglected to a reasonable approximation.
Viscous fluids more commonly found in practical situation are called real fluids, and though their analysis is a great deal more complex due to the addition of viscous forces, they are use in a far broader range of applications.
Laminar/Turbulent Flow
Laminar flow is the movement of fluid in thin parallel layers who slide one over the other much like sheets of paper. Each layer experiences strong viscous forces from adjacent layers and these forces have a damping effect on disruptions in the flow so that flow downstream of an obstacle quickly returns to its undisturbed state. Turbulent flow is the highly random and chaotic flow that occurs at high Reynolds numbers characterized by the formation of eddies and vortices of various sizes. Unlike laminar flow, in which fluid behavior is determined primarily by viscous forces, flow behavior in turbulent flow is determined by inertial forces. Calculating fluid behavior in turbulent flow is often very difficult, as the Navier-Stokes equations that must be used are very complex. These equations relate the pressure, density, temperature and velocity of a fluid through the use of rate of stress and strain tensors, and the result is a set of five coupled differential equations (an additional equation of state is also needed in order to find a solution). In all but the simplest of cases, these equations are extremely difficult to solve analytically, and most solutions must be found through approximations and the use of high speed computers.
Fluid Viscosity
Viscosity is often defined as a measure of how resistive a fluid is to flow or deformation. Viscosity can be likened somewhat to friction experienced by solid objects, but unlike the frictional forces between solids, viscous forces are independent of pressure. Viscosity is ultimately caused by cohesive intermolecular forces, and can be expressed mathematically as the ratio of shearing stress on a fluid to its velocity gradient. Viscosity can be observed in a number of common liquids. For example, maple syrup has a higher viscosity than water and so flows more slowly. Gases also experience viscous forces and these forces increase as the temperature of the gas increases. This is due to the fact that as temperature increases, so does the kinetic energy of the molecules and so there is an increase in rate of intermolecular collisions. To a good approximation, the viscosity of a gas goes as the square root of its temperature.
Skin Friction Drag
Skin friction drag is the component of the total drag, also called parasitic or profile drag, experienced by a body in a fluid flow due directly to frictional forces between the fluid and the surface of the body. Assuming no boundary layer separation occurs, skin friction is the sole source of friction.
Reynolds Number
Osborne Reynolds first introduced the dimensionless constant that bears his name in his 1883, in a paper he published in the Philosophical Transactions of the Royal Society. The paper, “An Experimental Investigation Of The Circumstances Which Determine Whether Motion Of Water Shall Be Direct Or Sinuous And Of The Law Of Resistance In Parallel Channels”, detailed the findings of his experimental work. Using an apparatus that allowed his to inject a small stream of dye into fluid flowing through a glass tube and using a manometer to determine flow velocities, Reynolds noticed that at lower flow velocities, the stream of dye remained intact but at higher velocities the coherent stream began to diffuse. He also noted that the diffused dye could be reformed into a stream if the velocity was decreased. Reynolds found that there was a critical velocity, which he termed the upper critical velocity, at which the turbulent flow developed and a lower critical velocity at which turbulent flow became laminar. Velocities located between these two points were classified as lying in the transition region.
The Reynolds number itself is a dimensionless constant used to distinguish laminar from turbulent flow in a pipe or channel or sometime around an immersed object, with lower values corresponding to laminar flow and higher ones to turbulent flow. The Reynolds number is calculated using mean velocity, pipe diameter, density, and viscosity, and is valid for any fluid. The Reynolds number is also dependent upon the geometry of the pipe, as well as the roughness of the walls. Analysis of the Reynolds number using the dimensionless forms of the Navier Stokes equations reveals that the Reynolds number is really a ratio of inertial forces to vicious forces. As of yet, no successful analytic methods for determining Reynolds numbers have been developed due largely to the difficulty associated with predicting turbulent flow, and so Reynolds numbers for flow through pipes or around immersed objects must be determined experimentally.
Boundary Layers
Boundary layers are regions of fluid located immediately adjacent to an immersed object or wall in which flow velocities are governed by viscous forces. Drag forces and most of the heat exchange experienced by the object are due to fluid in this region. Boundary layers typically begin as a very thin region of laminar flow that thickens with increasing Reynolds numbers and then gradually transitions to a turbulent layer flowing over a viscous sublayer. Flow outside of the boundary layer is independent of Reynolds number criteria.
