PATHLINE, STREAKLINE, STREAMLINES AND VELOCITY PROFILES

PATHLINE, STREAKLINE, STREAMLINES AND VELOCITY PROFILESDr Uditha RatnayakeRoom 1F.102Tel Ext 5255uditha.ratnayake@itb.edu.bn1Fluid in MotionWhen a fluid flows around bodies such as aircraft the shape of the boundaries, the externally applied forces and the fluid properties cause the velocities of the fluid particles to vary from point to point throughout the flow field.The geometry of the motion of fluid particles in space and time is known as the kinematics of the fluid motionIn order to make fluids work for us efficiently we need to understand the kinematics

2Two ways to look at a fluidWhile moving with the flowWhile being stationary3Lagrangian & Eulerian ViewLagrangianVelocity depends on the position vectorConsiders individual fluid particlesTherefore to view a fluid field, equations for all particles must be solved Eg. Observer does not see changes with time if he stands on a boat sailing in sea. Relative to boat water flow pattern does not change

EulerianVelocity of a particle depends on both space and time This can be used to describe the particles moving past a specific point in spaceMajority of fluid analysis use this methodEg. Observer see changes happening with time. When the boat moves waves and flow in front of him changes4Flow VisualizationLet us take the Eulerian view of the flowWe can:Look at the path taken by a particleLook at the particles which goes through a specific pointSpeed and direction of the flow

We draw lines on a flow to indicate each of the above observations and they are called Flow Patterns5One, Two or Three-dimensional FlowIn general, all fluids flow three-dimensionally, with pressures and velocities and other flow properties varying in all directions.In many cases the greatest changes only occur in two directions or even only in one.In these cases changes in the other direction can be effectively ignored making analysis much more simple.

61-D FlowFlow is one dimensional if the flow parameters (such as velocity, pressure, depth etc.) at a given instant in time only vary in the direction of flow and not across the cross-section. The parameter vary in time but still not across the cross-section.An example of one-dimensional flow is the flow in a pipe. There are parameter changes across 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 usually applied.72-D & 3-D FlowFlow is two-dimensional if it can be assumed that the flow parameters vary in the direction of flow and in one direction at right angles to this direction. Usually in the horizontal direction. Example is the flow over a airfoilFlow is three-dimensional if the flow parameters vary in all three direction of flow with same degree of severity.All real problems are 3-D. But analysis is complicated and time consuming.

8Back to Flow VisualisationBasic requirement to study the kinematics of fluid flow is to visualize the flow patternsWe look at three different flow patternsPathlinesStreaklinesStreamlines9PathlineThe pathline of a uid element is simply the path it takes through space as time passes. An example of a pathline is the trajectory taken by one pu of smoke which is carried by the wind.

t0t1t2t310Equation of a pathline11StreaklineAll fluid particles which pass through a particular point P are said to form the streakline of point P. An example of a streakline is the continuous line of smoke emitted by a chimney

12Equation of a streaklineA streakline is formed by a series of particles each with its own pathline. The equation is obtained by the series of pathline equations with same initial position and different T0 values.Point in the FluidPathline AParticle APathline BParticle BStreakline13StreamlineThis is the line drawn through fluid particles which have same velocity so that always the velocity direction is tangential to the line.

It is also important to recognize that the position of streamlines can change with time14Some things to know about streamlines Because the fluid is moving in the same direction as the streamlines, fluid can not cross a streamline.Streamlines can not cross each other. If they were to cross this would indicate two different velocities at the same point. This is not physically possible.The above point implies that any particles of fluid starting on one streamline will stay on that same streamline throughout the fluid.15Equation of a streamline16StreamtubesA 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 streamtube.In a two-dimensional flow, we have a streamtube which is flat (in the plane of the paper).

17StreamtubeThe "walls" of a streamtube are made of streamlines.As we have seen above, fluid cannot flow across a streamline, so fluid cannot cross a streamtube wall.The streamtube can often be viewed as a solid walled pipe.But a streamtube is not a pipe - it differs because the "wall" can move with the fluid.

18Steady and unsteady flows19Uniform and Non-uniform flow20Flow characteristicIn a uniform steady flow:

The PathlineStreaklineStreamline Coincide and form a single line21Mean flow velocity & dischargeLet the dischrge through a given flow cross section be QThenQ = A x VmWhere, Vm is the mean velocity.

The actual velocity within the cross section varies from point to point.22Typical velocity profileThe velocity adjacent to a boundary or a wall is always zero as there is no shear.In a pipe the typical velocity profile is; The mean velocity Um and the maximum velocity Umax are different.The profile has a symmetrical parabolic shape

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