Principles of Fluid Mechanics

 BASIC PRINCIPLES OF FLUID:-

The application of the principles of fluid dynamics to the flow of air in underground openings. Airflow is induced from the atmosphere, through the intake opening, underground airways, return opening, and back to the atmosphere again by differential pressure between intake and return openings of the mine. This pressure differential is usually very small, in the order of 2 to 3% in most cases, when compared to the absolute pressure of the system. Therefore, volume and density changes are neglected without serious loss of accuracy or validity. Airflow in mines is also generally treated as steady-state, turbulent, and incompressible. However, in situations where the pressure, temperatures, and humidity changes are large and air conditioning processes are involved, calculations must incorporate the compressibility effect of air.

Definition of A Fluid:-

A fluid may be defined broadly as a substance that deforms continuously when subjected to shear stress. This fluid can be made to flow if it is acted upon by a source of energy. This can be made clear by assuming the fluid being consisted of layers parallel to each other and letting a force act upon one of the layers in a direction parallel to its plane. This force divided by the area of the layer is called shear stress. As long as this shear stress is applied the layer will continue to move relative to its neighboring layers. If the neighboring layers offer no resistance to the movement of fluid, this fluid is said to be frictionless fluid or ideal fluid. (Practically speaking, ideal fluids do not exist in nature, but in many practical problems the resistance is either small or is not important, therefore can be ignored.) Fluid is always a continuous medium and there cannot be voids in it. The properties of a fluid, e.g., density, may, however, vary from place to place in the fluid.

Turbulent and Laminar Flows:-

In a flowing fluid, each particle changes its position with a certain velocity. The magnitudes and directions of the velocities of all particles may vary with position as well as with time. Streamline is used to illustrate this very concept. Imagine a pipe of circular cross-section containing fluid such as water. For flow to occur without slippage, then the various layers must move at different velocities. The fluid layer adjacent to the pipe wall is virtually stationary, while the layers further out move at increasing higher velocities until a maximum velocity is attained at the center.

streamline:-

A streamline is an imaginary line in a fluid, the tangent to which gives the direction of the flow velocity at that position, as shown in Figure, where the distance between two streamlines is an inverse measure of the magnitude of the velocity. If the streamlines are smoothly curved and almost parallel to each

other, as illustrated in Figure, the flow is known as streamlined flow or laminar flow . On the other hand, if the streamlines are arranged haphazardly as illustrated  the flow is known as turbulent flow .

 

 

It was recognized earlier on that the type of flow depended upon the velocity and viscosity of the fluid. It was not until the 1880s this relationship was mathematically expressed in terms of the ratio of inertial and viscous forces by Professor Osborne Reynolds through many experiments and dimension analysis,

NRe = r D V m r is the fluid density; n = m/r, is kinematic viscosity; m is absolute viscosity; D is diameter of conduit; V is velocity Reynolds number (NRe ) is a dimensionless number.

If this number is less than 2000, viscous forces prevail and the flow will be laminar. The condition of the flow is less well defined for this number beyond 2000 for which turbulence starts to occur. It has been common practice to regard the flow as turbulent when Reynolds number is larger than 4000,

Laminar flow – for NRe < 2,000

Turbulent flow – for NRe > 4,000

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