How could we know the direction and pattern of streamline? EXAMPLE 4-9 Determina

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How could we know the direction and pattern of streamline? EXAMPLE 4-9 Determination of Rotationality of a Line Sink A simple two-dimensional velocity field called a line sink is often used to simulate fluid being sucked into a line along the z axis. Suppose the volume flow rate per unit length along the zaxis, VIL, is known, where Vis a nega- tive quantity. In two dimensions in the r6-plane, Line sink: and , 0 Draw several streamlines of the flow and calculate the vorticity. Is this flow rotational or irrotational? SOLUTION Streamlines of the given flow field are to be sketched and the rotationality of the flow is to be determined. Analysis Since there is only radial flow and no tangential flow, we know immediately that all streamlines must be rays into the origin. Several stream- linoe aro ckotchod in Fig. 1-52. Tho vorticity is calculated from Eq. 1-33 Streamlines FIGURE 4 52 Streamlines in the ro-plane for the case of a line sink. rr a0 Since the vorticity vector is everywhere zero, this flow field is irrotational. Discussion Many practical flow fields involving suction, such as flow into inlets and hoods, can be approximated quite accurately by assuming irrota- tional flow (Heinsohn and Cimbala, 2003).

Explanation / Answer

Most professional wind visualizations show wind speed and direction using a glyph called a wind barb in a grid pattern. Research into flow visualization has suggested that streamlines better represent flow patterns but these methods lack a key property-unlike the wind barb, they do not accurately convey the wind speed. With the goal of improving the perception of wind patterns, and at least equaling the quantitative quality of wind barbs, we designed two variations on the wind barb and designed a new quantitative glyph. All of our new designs space glyph elements along equally spaced streamlines. To evaluate these designs, we used a North American mesoscale forecast model. We tested the ability of subjects to determine direction and speed using two different densities each of three new designs as well as the classic wind barb. A second experiment evaluated how effectively each of the designs represented wind patterns. The results showed that the new design is superior to the classic, but they also showed that the classic barb can be redesigned and substantially improved. We suggest that flow patterns with integrated glyphs may have widespread application in flow visualization.

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