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Figure 10. Drag Coefficients of Elliptical Cylinders with Varying Eccentricities [Data from Lindsey (1938) and Delany and Sorensen (1953)]

The constants a and b were found to be 0.97379 and 0.73456, respectively. Since the constant a is close to unity and since the eccentricity function should equal unity when the blockage element is circular, the constant a was set to unity. The eccentricity function with a set to unity is not a true regression curve, but the eccentricity function represents the trend of the data. The resulting eccentricity function, e073456 , is also shown in Figure 10.

The circular-blockage-element drag function, equation (8), was then multiplied by the eccentricity function to yield an ellipsoidal-blockage-element drag function, shown in equation (17).

The above function increases without bound as the eccentricity increases. As the eccentricity increases, the roughness elements are expected to experience drag similar to and limited by the drag of a flat plate perpendicular to the flow. Janna (1993) reports that the drag coefficient of a flat plate perpendicular to the flow will have a drag coefficient of 1.8 for Reynolds numbers above 60,000. The eccentricity of an ellipse that results in a drag coefficient of 1.8 for a Reynolds number of 60,000 is 4.46. For eccentricities greater than 4.46, the blockages are expected to act like flat plates perpendicular to the flow as described by equation (18).

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