Elementary concept of the uniform flow
Introduction: Uniform Flow, Steady Flow: It is possible - and useful - to classify the type of flow which is being examined into small number of groups. If we look at a fluid flowing under normal circumstances - a river for example - the conditions at one point will vary from those at another point (e.g. different velocity) 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. He following terms describes 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 fluid it is said to be uniform.
- non-uniform: If at a given instant, the velocity is not the same at every point the flow is non-uniform.(In practice, by this definition, every fluid that flows near a solid boundary will be non-uniform – as the fluid at the boundary must take the speed of the boundary, usually zero. However if the size and shape of the of the cross-section of the stream of fluid is constant the flow is considered 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. (In practice there are always slight variations in velocity and pressure, but if the average values are constant, the flow is considered steady.
Compressible or Incompressible: All fluids are compressible - even water - their density will change as pressure changes. Under steady conditions, and provided that the changes in pressure are small, it is usually possible to simplify analysis of the flow by assuming it is incompressible and has constant density. As you will appreciate, liquids are quite difficult to compress - so under most steady conditions they are treated as incompressible. In some unsteady conditions very high pressure differences can occur and it is necessary to take these into account even for liquids. Gasses, on the contrary, are very easily compressed, it is essential in most cases to treat these as compressible, taking changes in pressure into account.
Three-dimensional flow: Although in general all fluids flow three-dimensionally, with pressures and velocities and other flowproperties varying in all directions, in many cases the greatest changes only occur in two directions oreven only in one. In these cases changes in the other direction can be effectively ignored making analysismuch simpler.Flow is one dimensional if the flow parameters (such as velocity, pressure, depth etc.) at a given instant intime only vary in the direction of flow and not across the cross-section. The flow may be unsteady, in thiscase the parameter vary in time but still not across the cross-section. An example of one-dimensional flowis the flow in a pipe. Note that since flow must be zero at the pipe wall - yet non-zero in the center – thereis a difference of parameters across the cross-section. Should this be treated as two-dimensional flow?Possibly - but it is only necessary if very high accuracy is required. A correction factor is then usuallyapplied.
Streamlines and stream tubes: In analyzing fluid flow it is useful to visualize the flow pattern. This can be done by drawing lines joining points of equal velocity - velocity contours. These lines are known as streamlines. Here is a simple example of the streamlines around a cross-section of an aircraft wing shaped body: When fluid is flowing past a solid boundary, e.g. the surface of an aero foil or the wall of a pipe, fluid obviously does not flow into or out of the surface. So very close to a boundary wall the flow direction must be parallel to the boundary.
At all points the direction of the streamline is the direction of the fluid velocity: this is how they are defined. Close to the wall the velocity is parallel to the wall so the streamline is also parallel to the wall. It is also important to recognize that the position of streamlines can change with time - this is the case in unsteady flow. In steady flow, the position of streamlines does not change.
A useful technique in fluid flow analysis is to consider only a part of the total fluid in isolation from the rest. This can be done by imagining a tubular surface formed by streamlines along which the fluid flows. This tubular surface is known as a stream tube.