note 2 - (IV) FLUIDS IN MOTION Fluid motions manifest...

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(IV) FLUIDS IN MOTION Fluid motions manifest themselves in many different ways. Some can be described very easily, while others require a thorough understanding of physical laws. In engineering applications, it is important to describe the fluid motions as simply as can be justified. It is the engineer's responsibility to know which simplifying assumptions (e.g., one-dimensional, steady-state, inviscid, incompressible, etc) can be made. A. Classification of Fluid Flows 1) Uniform flow; steady flow If we look at a fluid flowing under normal circumstances - a river for example - the conditions (e.g. velocity, pressure) at one point will vary from those at another point, then we have non-uniform flow. If the conditions at one point vary as time passes, then we have unsteady flow. Under some circumstances the flow will not be as changeable as this. The following terms describe the states which are used to classify fluid flow: Uniform flow : If the flow velocity is the same magnitude and direction at every point in the flow it is said to be uniform. That is, the flow conditions DO NOT change with position . Non-uniform : If at a given instant, the velocity is not the same at every point the flow is non-uniform. Steady : A steady flow is one in which the conditions (velocity, pressure and cross-section) may differ from point to point but DO NOT change with time . Unsteady : If at any point in the fluid, the conditions change with time, the flow is described as unsteady. Combining the above we can classify any flow in to one of four types: Steady uniform flow . Conditions do not change with position in the stream or with time. An example is the flow of water in a pipe of constant diameter at constant velocity. Steady non-uniform flow . Conditions change from point to point in the stream but do not change with time. An example is flow in a tapering pipe with constant velocity at the inlet - velocity will change as you move along the length of the pipe toward the exit. Unsteady uniform flow . At a given instant in time the conditions at every point are the same, but will change with time. An example is a pipe of constant diameter connected to a pump pumping at a constant rate which is then switched off. Unsteady non-uniform flow . Every condition of the flow may change from point to point and with time at every point. An example is surface waves in an open channel. You may imagine that one class is more complex than another – steady uniform flow is by far the most simple of the four. 2) One-, two-, and three-dimensional flows A fluid flow is in general a three-dimensional, spatial and time dependent phenomenon:- (,) rt urt vrt wrt == + + G GG G G VV i j k 39
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40 ) where is the position vector, ( ,, rx y z = G ( ) i j k GGG are the unit vectors in the Cartesian coordinates, and ( are the velocity components in these directions. As defined above, the flow will be uniform if the velocity components are independent of spatial position ) uvw ( ) xyz , and will be steady if the velocity components are independent of time t .
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This note was uploaded on 09/24/2011 for the course ENGG engg1010 taught by Professor Wong during the Spring '11 term at HKU.

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note 2 - (IV) FLUIDS IN MOTION Fluid motions manifest...

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