Pressure-drag flow numerical results

Figure 2. Numerical results for drag/pressure flow.

The solution to this equation is more difficult than the solution to Eq. 7.194. The case of pure pressure flow was first solved by Boussinesq [130] in 1868. The solution to the combined drag and pressure flow was first published in 1922 [98] the authorship of this publication remains a question. Since the 1922 publication, numerous workers have presented solutions to this problem. Meskat [131] reviewed various solutions and demonstrated that they were equivalent. The velocity profile resulting from the drag flow can be written as ... 

For laminar flows, the laminar sublayer fills the entire cross section. Thus, the effect of wall drag is influenced to a greater extent by the shape of the cross section. For many noncircular conduits with laminar flows, either theoretical analyses (similar to the Hagen-Poiseuille equation) or numerical analyses for the pressure-flow relation have been conducted. The results can be expressed in dimensionless form as... 

Dandy and Dwyer [30] computed numerically the three-dimensional flow around a sphere in shear flow from the continuity and Navier-Stokes equations. The sphere was not allowed to move or rotate. The drag, lift, and heat flux of the sphere was determined. The drag and lift forces were computed over the surface of the sphere from (5.8) to (5.13), respectively. They examined the two contributions to the lift force, the pressure contribution and the viscous contribution. While the viscous contribution always was positive, the pressure contribution would change sign over the surface of the sphere. The pressure contribution to the lift was found to be negative for most of the Reynolds numbers and shear rates that were examined. The total lift was always found to be positive, and the results agreed well with those of Saffman [105, 106]. 

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