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## Wednesday, December 14, 2011

### Fluid Flow and its classification

Fluid Flow :

 Types of flow of fluid
Motion of a fluid subjected to unbalanced  forces or stresses. The motion continues as long as unbalanced forces are applied. For example, in the pouring of water from a pitcher the water velocity is very high over the lip, moderately high approaching the lip, and very low near the bottom of the pitcher. The unbalanced force is gravity, that is, the weight of the tilted water particles near the surface. The flow continues as long as water is available and the pitcher remains tilted.

A fluid may be a liquid, vapor, or gas. The term vapor denotes a gaseous substance interacting with its own liquid phase, for example, steam above water. If this phase interaction is not important, the vapor is simply termed a gas.

### Classification of Fluid Flow – Based on Flow Pattern

Fluid flow can be very smooth, calm, and regular, but generally the flow of a fluid is not so disciplined- it becomes a vagabond and starts flowing in random patterns. What are different flow patterns, how are flows classified, and what are the fluid paths in those patterns?

While studying the motion of a rigid body we do not have to bother about the relative motion of the particles of the rigid body as they are very firmly fixed to each other and move as a whole. But for the study of the motion of fluids, things are not so simple because the fluid particles are attached with each other with very weak forces. There are various relative motions and a lot of possibilities for relative motion between the fluid particles.

To make things somewhat simple or for making the flow analysis feasible, fluid flow is visualized as a composition of fluid elements. These elements are defined by using certain similarities or patterns and mathematics is applied to them to study fluid flow comprehensively.

Rotational or Irrotational Flow

To classify any flow as Rotational or Irrotational the angular motion of the fluid elements is analyzed. If the angle between the two intersecting lines of the boundary of the fluid element changes while moving in the flow, then the flow is a Rotational Flow. But if the fluid element rotates as a whole and there is no change in angles between the boundary lines then the flow cannot be Rotational Flow, so it is Irrotational Flow.

This means that there should be some deformation in the fluid element in a Rotational Flow. Such deformation of the fluid element or the shear strain is necessarily caused by tangential forces or shear stresses. Shear stresses are caused by viscosity, thus the flow of viscous fluids is rotational. But this does not mean that the flow of non-viscous or ideal fluid is always irrotational. The flow of ideal fluids can be rotational by external work or heat interaction.

Laminar or Turbulent Flow

Laminar Flow

The flow of a fluid moving with a moderate speed has fluid layers moving past other layers as if some sheets are moving over other layers. Such flow of fluids is called Laminar Flow.

In Laminar Flow viscous shear stresses act between these layers of the fluid which defines the velocity distribution among these layers of flow. In Laminar Flows the shear stresses are defined by Newton's equation for shear stress.
 Illustration of flows in a pipe

Turbulent Flow

As the flow speed of the otherwise calm layers increases, these smoothly moving layers start moving randomly, and with further increase in flow velocity, the flow of fluid particles becomes completely random and no such laminar layers exist any more. Shear stresses in the Turbulent Flow are more than those in Laminar Flow.

A dimensionless parameter, Reynolds Number, is defined as the ratio of inertial and viscous force to characterize these two types of flow patterns. With increase in flow velocity the initial forces increase so the Reynolds Number. For moderate flows the Reynolds Number is below 2000 and for Turbulent Flows it is well above 2300. For the transition region between the two types the Reynolds Number varies between 2000-4000.

### Classification of Fluid Flow

When a fluid flows past a point or through a path different parameters associated with the flow of the fluid vary in different patterns. In this article we will study classification of fluid flow in different types according to the conditional variations of the flow parameters with space and time.

When a fluid flows past a point or through a path different parameters associated with the flow of the fluid, certain parameters vary and others may remain constant.

The two basic parameters of any fluid flow are velocity of the fluid particle or element and the pressure of the fluid at the point under consideration. The flow of fluids can be classified in different patterns based on the variation of the flow parameters with time and distance. The benefit of characterizing the fluid flow as certain patterns helps in analyzing it under the appropriate solution paradigm.

Classification Based on Variation with Time

The classification of the fluid flow based on the variation of the fluid flow parameters with time characterizes the flow in two categories, steady and unsteady flow. If the flow parameters, such as velocity, pressure, density and discharge do not vary with time or are independent of time then the flow is steady. If the flow parameters vary with time then the flow is categorized as unsteady.

In real conditions it is very rare to have such flows with parameters exactly constant with time. The parameters usually vary with time but variation is within a small range such as the average of particular parameter is constant for certain duration of time.

Classification Based on Variation with Space

The other classification criterion for the fluid flow is based on the variation of the flow parameters with distance or space. It characterizes the flow as uniform or non-uniform. The fluid flow is a uniform flow if the flow parameters remain constant with distance along the flow path. And the fluid flow is non-uniform if the flow parameters vary and are different at different points on the flow path.

For a uniform flow, by its definition, the area of the cross section of the flow should remain constant. So a fitting example of the uniform flow is the flow of a liquid thorough a pipeline of constant diameter. And contrary to this the flow through a pipeline of variable diameter would be necessarily non-uniform.

### Flow Types and Examples

A steady flow can be uniform or non-uniform and similarly an unsteady flow can also be uniform or non-uniform. For a steady flow discharge is constant with time and for a uniform flow the area of cross section of the fluid flow is constant through the flow path.

Examples of Different Flow Types

Steady and Uniform Flow: Flow through a pipeline of constant diameter with a discharge constant with time.

Steady and Non-Uniform Flow: Fixed discharge flow through a tapering pipe. Water flow through a river with a constant discharge is also a good example of such flow as the span of river generally varies with distance and amount of water flow in river is constant.

Unsteady and Uniform Flow: A flow through pipeline of constant cross section with sudden changes in fluid discharge or pressure.

Unsteady and Non-Uniform Flow: Pressure surges in a flow through a pipe of variable cross section. A practical example can be the water flow in the network of canals during water release.

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