Problem 5.16

# Problem 5.16 - compared to the no-friction case The...

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Problem 5.16 [Difficulty: 5] Discussion: Refer back to the discussion of streamlines, pathlines, and streaklines in Section 2-2. Because the sprinkler jet oscillates, this is an unsteady flow. Therefore pathlines and streaklines need not coincide. A pathline is a line tracing the path of an individual fluid particle. The path of each particle is determined by the jet angle and the speed at which the particle leaves the jet. Once a particle leaves the jet it is subject to gravity and drag forces. If aerodynamic drag were negligible, the path of each particle would be parabolic. The horizontal speed of the particle would remain constant throughout its trajectory. The vertical speed would be slowed by gravity until reaching peak height, and then it would become increasingly negative until the particle strikes the ground. The effect of aerodynamic drag is to reduce the particle speed. With drag the particle will not rise as high vertically nor travel as far horizontally. At each instant the particle trajectory will be lower and closer to the jet
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Unformatted text preview: compared to the no-friction case. The trajectory after the particle reaches its peak height will be steeper than in the no-friction case. A streamline is a line drawn in the flow that is tangent everywhere to the velocity vectors of the fluid motion. It is difficult to visualize the streamlines for an unsteady flow field because they move laterally. However, the streamline pattern may be drawn at an instant. A streakline is the locus of the present locations of fluid particles that passed a reference point at previous times. As an example, choose the exit of a jet as the reference point. Imagine marking particles that pass the jet exit at a given instant and at uniform time intervals later. The first particle will travel farthest from the jet exit and on the lowest trajectory; the last particle will be located right at the jet exit. The curve joining the present positions of the particles will resemble a spiral whose radius increases with distance from the jet opening....
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