Fluids flows can be characterized by many different aspects. Some aspects are simply defined properties of the fluid while others are much more qualitative.
Viscosity
Viscosity is a well known property that defines fluid. Viscosity is typically thought of as how easily a fluid a flow, more viscous fluids require greater force to move. Therefore it is not a surprise that fluids can be characterized by their viscosity. We can think of the viscous effect and friction between a fluid and surface as one and the same for a fluid flow. Viscosity is defined for Newtonian fluids (such as air and water) as the coefficient that relates stress and strain in a fluid:
\tau_{xy}=\mu\dfrac{du}{dy}
Viscosity is sensitive to temperature and pressure but is typically relatively constant for most applications with small temperature fluctuations.
Fluid flows can be classified into two types regarding viscosity:
- Viscous: Viscosity is non-negligible and must be accounted for.
- Inviscid: Viscosity is negligible and assumed to be zero.
Compressibility
Density is related to momentum and energy in fluid flows, taking the place of mass in Newton’s second law. An increase in density for a fluid flow at the same speed will yield in increase in momentum and energy.
Flows can be classified in two ways regarding density:
- Compressible: Density is a function of location and time: \rho=\hat{\rho} (x,y,z,t).
- Incompressible: Density is constant throughout the entire flow field, both spatially and temporally.
Internal and External Flows
The way in which a flow is constrained by a solid surface is one important way to classify flows.
- Internal Flow: Flow completely enclosed by a solid. e.g. flow though a pipe or nozzle.
- External Flow: Flow over a body immersed in a fluid. e.g. flow over an airplane wing (airfoil).
- Open-Channel Flow: Flow in a channel which is exposed to a free surface (zero shear). e.g. flow of a river.
Turbulence
Turbulence is a difficult flow characteristic to define. Typically turbulence is thought of as some kind of randomness or measure of chaos occurring in a flow. As opposed to turbulence, laminar flows are very ordered, where flow is characterized as have smooth, parallel layers. Whether a flow is turbulent or laminar is typically defined by the Reynold’s number of the flow:
Re=\dfrac{\rho VL}{\mu}
Where V and L are some characteristic velocity and length scale for the given flow type. Typically a critical Reynold’s number exists for different flow types which signals the transition from laminar to turbulent flow. Reynold’s numbers below this critical number will be classified as laminar and above this critical number will be classified as turbulent.
For pipe flow the critical number is usually taken to be around 2300. The characteristic length scale for pipe flow is the pipe inner diameter, and the characteristic velocity is the average fluid velocity through the pipe at a given cross-section.