Unformatted text preview: it 3
1.2 Md JUNÂ» ! ï¬rings,â k / / Prob. 3.1 - A dye test is being conducted on a particular ï¬ow ï¬eld. A ï¬ne line of dye is injected /
into the ï¬ow for 0 S t S 20 seconds. The resulting streakline at t = 20 seconds is shown in the f
ï¬gure below. The values of L in the ï¬gure indicate the length of each segment of the streakline.
The magnitude of the ï¬uid velocity (i.e., the speed) is constant, but its direction is not; That is, at
each instant all of the ï¬ow is going in the same direction with the same speed. However, at
certain times the ï¬ow has an instantaneous change in direction.
'3.) Construct the pathï¬ne for a particle of ï¬uid marked by a spot of dye released at t : 2 sec (2 seconds after the start of the injection). The pathline should cover the time period 2 s S t S 20 s. '
b) Mark the time that the particle of ï¬uid is located at signiï¬cant points along the pathline.
c) Construct the streamline through point D for t = 19 seconds. Procedure: 1) Based onthe streakline shown. deduce. what the ï¬ow directions were for the 20 3 during
Which the streakline was being formed. (Hints: When did the dye at A, B, and C leave the
injection point? What was the ï¬ow direction while the dye between A and B and between B
and C was leaving the injection point?) I 2) Once you know the ï¬ow directions for the different time periods, start with a particle at the
injection point at t : 2 s and deduce the path that it will follow. 3) Knowing the ï¬ow direction at t = 19 s, draw the streamline for part (b) of the question. Lâ} f: It 6/}; L = 3.5 units Streakline for Prob. 3.1 ...
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- Fall '08
- 2 sec, 20 seconds, Streamlines, streaklines, and pathlines, 19 seconds, streakline, 2 seconds