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Primary dependent variable is fluid velocity vector V = V ( r ); where r is the position vector.
If V is known then pressure and forces can be determined.
Consideration of the velocity field alone is referred to as flow field kinematics in distinction from flow field dynamics (force considerations).
Fluid mechanics and especially flow kinematics is a geometric subject and if one has a good understanding of the flow geometry then one knows a great deal about the solution to a fluid mechanics problem.
Flow Past A Turbine Blade Uniform Flow Particle p at time t 1 Particle p at time t 2
Velocity: Lagrangian and Eulerian Viewpoints There are two approaches to analyzing the velocity field: Lagrangian and Eulerian Lagrangian: keep track of individual fluids particles. Apply Newton’s second law for each individual particle! Say particle p is at position r 1 (t 1 ) and at position r 2 (t 2 ) then,
Of course the motion of one particle is insufficient to describe the flow field. So the motion of all particles must be considered simultaneously which would be a very difficult task. Also, spatial gradients are not given directly. Thus, the Lagrangian approach is only used in special circumstances.
Eularian Approach Eulerian: focus attention on a fixed point in space. In general, where, u = u(x,y,z,t), v = v(x,y,z,t), w = w(x,y,z,t)
This approach is by far the most useful since we are usually interested in the flow field in some region and not the history of individual particles. This is similar to description of A Control Volume. We need to apply newton Second law to a Control Volume.
Velocity vector can be expressed in any coordinate system; e.g., polar or spherical coordinates.
Recall that such coordinates are called orthogonal curvilinear coordinates.
The coordinate system is selected such that it is convenient for describing the problem at hand (boundary geometry or streamlines).
Fluid Dynamics of Coal Preparation & Supply BY P M V Subbarao Associate Professor Mechanical Engineering Department I I T Delhi Aerodynamics a means of Transportation ……
Major Components of Coal Fired Steam Generator
Schematic of typical coal pulverized system A Inlet Duct; B Bowl Orifice; C Grinding Mill; D Transfer Duct to Exhauster; E Fan Exit Duct.
Velocity through various regions of the mill during steady operation
Cyclone-type classifier. Axial and radial gas velocity components
The same principles that govern the design of gas-solid separators, e.g. cyclones, apply to the design of classifiers.
Solid separator types have been used preferentially as classifiers in mill circuits:
centrifugal cyclone-type and gas path deflection, or
The distributions of the radial and axial gas velocity in an experimental cyclone precipitator are shown in Figures.
The flow pattern is further characterized by theoretical distributions of the tangential velocity and pressure, the paths of elements of fluid per unit time, and by the streamlines in the exit tube of the cyclone.