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Flow Past a Sphere

The flow past a sphere is formed by subtracting the doublet flow, equations 11.78--11.79, from the uniform flow, equations 11.72--11.73, obtaining:

 

  
Figure 11.25: The streamlines of the uniform flow of speed U superposed on the flow of a doublet for equal increments of .


The streamlines of this superposed flow, plotted in figure 11.25, are divided by the streamline , which forms the surface of a sphere, R=a. Outside this streamline, we have the flow past a sphere which is noticeably different from the plane flow past a circular cylinder shown in figure 11.15. There are two stagnation points, at .

The pressure on the surface of the sphere, , may be obtained by writing Bernoulli's equation between a point on the sphere where R=a and and a point at , where V=U and :

Notice that the minimum pressure coefficient on the surface of the sphere, at , is , compared to the much larger negative value of -3 on the circular cylinder (equation 11.63). The disturbance of the uniform flow due to the sphere is much less at this point than it is for the circular cylinder. The irrotational flow over a solid sphere exerts no drag on the sphere, the pressure distribution on the surface being symmetric about . In a viscous flow at moderate and high Reynolds numbers, the boundary layer separates from the surface and a viscous wake region develops behind the body, where the pressure is nearly . Only near the forward stagnation point, , is the flow fairly well described by the irrotational model.



Annica Warrick
Thurs July 11 16:11:48 EST 1996