## Introduction

Fluid Flow is a part of fluid mechanics and deals with fluid dynamics. Fluids such as gases and liquids in motion is called as fluid flow. Motion of a fluid subjected to unbalanced forces. This motion continues as long as unbalanced forces are applied.

For example, if you are pouring a water from a mug, the velocity of water is very high over the lip, moderately high approaching the lip, and very low at the bottom of the mug. The unbalanced force is gravity, and the flow continues as long as water is available and the mug is tilted.

## Types of flow

Fluid flow can be characterized in the following two types. This characterization is based on the industrial application of fluid flow and is mostly under consideration nowadays.

### Laminar flow:

Laminar flow occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface. Laminar flow is a flow regime characterized by high momentum diffusion and low momentum convection.

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### Turbulent flow

One important characteristics of a turbulent flow is that the velocity and pressure may be steady or remain constant at a point, but still may exhibit irregular fluctuations over the mean or average value. The fluid elements which carry out fluctuations both in the direction of main flow and at right angles to flow are not individual molecules but rather are lumps of fluid of varying sizes known as eddies. The fluctuating components may be a few percent of the mean value, but it is the controlling factor in describing the flow. A turbulent fluid flow is then characterized as the main flow stream super-imposed with localized rotational eddies, where motion are three dimensional, unstable, and random. Turbulent eddies have a wide range of sizes or length scales. These eddies form continuously and disintegrate within few oscillation periods, and hence have very small time scales. In general, the frequencies of the unsteadiness and the size of the scales of motion span several orders of magnitude.

The governing equations for fluid flow for a general linear Newtonian viscous fluid are Navier-Stokes equations given by the following set of equations:

Where u_{i} and u_{j} are the mean velocities of water, P is the pressure, ρ is the density of the fluid and µ is the dynamic viscosity.

In principle, the time dependent three dimensional Navier-Stokes equations can fully describe all the physics of a given turbulent flow. This is due to the fact that turbulence is continuous process which consist of continuous spectrum of scales ranging from the largest one associated with the largest eddy to the smallest scales associated with the smallest eddy, referred as Kolmogorov micro-scale, a concept brought by the theory of turbulence statistics. These eddies overlap in space, larger one carrying the smaller ones. The process can be characterized as a cascading process by which the turbulence dissipates its kinetic energy from the larger eddies to the smaller eddies through vortex stretching. The energy is finally dissipated into heat through the action of molecular viscosity in the smallest eddies. These larger eddies randomly stretch the vortex elements that compress the smaller eddies cascading energy to them. The cascading process give rise to the important features such as apparent stresses and enhanced diffusivity, which are several orders of magnitude larger than those in corresponding laminar flows.

The scales of motion or wave lengths usually extend all the way from a maximum size comparable to the characteristic length of the flow channel to a minimum scale corresponding to the smallest eddy fixed by the viscous dissipation. The range of these scales or the ratio of minimum to maximum wave lengths varies with characteristic flow parameter such as Reynolds number of the flow.

#### References

Computational Fluid Dynamics Analysis of Turbulent Flow

Pradip Majumdar Department of Mechanical Engineering, Northern Illinois University, Illinois U.S.A