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Fluid Flow


A fluid can be anything which can flow; normally it is a liquid or gas. Fluids are considered as a continuous media and their motion can be described in terms of pressure, velocity, density etc. The path followed by a fluid is known as particle path. If it is parallel to the fluid velocity vector, which is termed as streamline flow. In the case of steady flow, particle paths are coincident with the stream lines.

Fluid flow rate can be defined as the volume of the fluid which is passed through given surface per unit time. It is denoted by Q. Another terms of flow rate are volumetric flow rate and volume velocity. It can be expressed mathematically.
Q = Av
Where A is the area
v is the velocity of the fluid


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Consider first of all the case of steady flow of a fluid. Fix attention on a particular point in the flow and picture a small closed curve drawn around this point in a plane perpendicular to the direction of flow. The streamlines passing through this curve will form a stream tube and if the curve is drawn small enough the velocity will be uniform over any cross section of the stream tube. Since thee is no flow across streamlines, conservation of mass requires that along the stream tube

Fluid Flow Equation

where $\rho$ is the density of the fluid, a is the cross sectional area of the stream tube and v is the velocity of the fluid in the stream tube.
This result can be stretched to cover the practical case of flow in a pipe of varying cross section provided we are content to deal only in terms of the mean velocity and ignore the actual distribution of velocity across a section of the pipe. 


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Fluid flow measurement is divided into several types, since each type requires specific consideration of such factors as accuracy requirements, cost considerations and use of the flow information to obtain the required end results. The fluid flow measurement depends on many factors such as fundamental nature of the fluid, flow characteristics etc. Certain types of meters may have special characteristics to handle some of these problems, but extra care should be exercised in evaluating such equipment to ensure successful measurement. It is also important to consider the fluid's critical temperature and critical pressure. A meter's specified accuracy is invalid if the fluid to be measured exhibits large volume changes over minor temperature and pressure changes, which is the case near critical conditions.


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Laminar and Turbulent flow:

If water is caused to flow steadily through a transparent tube and a dye is continuously injected into the water, two distinct types of flow may be observed. In the first type, the streamlines are straight and the dye remains intact. The dye is observed to spread very slightly as it is carried through the tube; this is due to molecular diffusion. The flow causes no mixing of the dye with the surrounding water. In this type of flow, known as laminar or streamline flow, elements of the fluid flow in an orderly fashion without any macroscopic intermixing with neighboring fluid. Laminar flow is observed only at low flow rates. On increasing the flow rate, a markedly different type of flow is established in which the dye streaks show a chaotic, fluctuating type of motion, known as turbulent flow. A characteristic of turbulent flow is that it promotes rapid mixing over a length scale comparable to the diameter of the tube. Consequently, the dye trace is rapidly broken up and spread throughout the flowing water. In turbulent flow, properties such as the pressure and velocity fluctuate rapidly at each location, as do the temperature and solute concentration in flows with heat and mass transfer. In both laminar and turbulent flow the velocity is zero at the wall and has a maximum value at the center line. For laminar flow the velocity profile is a parabola but for turbulent flow the profile is much flatter over most of the diameter. If the pressure drop across the length of the tube is proportional to the flow rate when the flow is laminar. When the flow is turbulent the pressure drop increases more rapidly, almost as the square of the flow rate. Turbulent flow has the advantage of promoting rapid mixing and enhances convective heat and mass transfer.
Compressible and Incompressible flow:

Generally most of the fluids are compressible to some extent. If the compressibility is very small we can call it as an incompressible fluid. Compared to liquids, gases are more compressible. In the case of pressure fluctuation in a flowing gas results the density constant provided constant temperature. If the density of a fluid is constant, the flow is explained as an incompressible flow. If the density of a gas changes, the flow is become compressible. If the pressure difference is much high, the speed of flowing gas exceeds the speed of sound. If the speed of flow is greater than the speed of sound, the flow is called supersonic flow and if the flow speed is lesser than the speed of sound, it is termed as subsonic flow.

Viscous Fluid Flow

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Viscous fluids posses internal attractive forces between the molecules hence it results a dragging force or a frictional force. This dragging force results heating hence a slight loss in mechanical energy. Viscosity is a measure of the resistance of a flowing fluid. If a fluid become viscous, it has a tendency to stick on the surface. It will affect the velocity of a flowing fluid.

Ideal Fluid Flow

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An ideal fluid is one that is frictionless and incompressible. It has zero viscosity and it cannot sustain a shear stress at any point. Although no ideal fluid actually exists, many real fluids have small viscosity and the effects of compressibility may be small. Applications include the motion of a solid through an ideal fluid are applicable with slight modification to the motion of an aircraft through the air, of a submarine through the oceans, flow through the passages of a pump or compressor or over the crest of a dam.

Fluid Flow in Pipe

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When a fluid flows through a pipe, it transfers momentum to the pipe wall. In other words the pipe wall experiences a force in the direction in which the fluid is moving. This force is best thought of as a frictional drag on the inside of the pipe wall. The frictional drag acts along the inner surface of the pipe wall and appears as a shearing stress. The fluid against the inner pipe surface experiences this shearing stress which resists the motion of the fluid. The circular pipe flow is probably the most celebrated viscous flow in the development of fluid dynamics, in view of the fundamental importance of as well as basic fluid engineering applications.

Fluid Flow In Porous Media

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The unique property of a porous medium , the one that distinguishes it from other solid bodies on the one hand and from simple conduits on the other, is its complicated pore structure. The vast majority of porous media contain an interconnected three dimensional network of capillary channels of non uniform sizes and shapes, commonly referred to as pores. Fluid flow, diffusion and electrical conduction in porous media take place within extremely complicated microscopic boundaries that make any rigorous solution of the equations of change in the capillary network practically impossible. For flow through porous porous media, one needs to relate macroscopic and measurable quantities such as the average fluid velocity, to the morphological properties of the media.