:with Application to Measurement of the Velocity of Subterranean Water by the Single Boring Method
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概要
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A theoretical study is made on the viscous flow past a cylindrical hole (radius <I>R</I><SUB>0</SUB>) bored inside an otherwise unbounded homogeneous porous media (permeability <I>K</I>). This situation occurs, for example, in measurement of the subterranean water flow by means of the single boring method. The fluid far from the hole is assumed to be a uniform constant velocity <I>U</I><SUB>∞</SUB>, and the entire flow field is obtained by matching a solution of the Stokes equation inside the hole with that of the generalized Darcy's equation in the porous region. In general, the effect of the hole increases with the value of ζ<SUB>0</SUB> (=<I>R</I><SUB>0</SUB>/<I>√k</I>).When ζ<SUB>0</SUB> is much greater than unity, which corresponds to the case for underground water flow, the velocity at the center of the hole becomes 3U<SUB>∞</SUB>, while the volume flux fiowing into the hole from upstream-side becomes twice, in comparison with that flowing into the same region in the absence of the hole. The present results show many differences from those obtained on the assumption that the hole region is a porous media of infinitely high permeability.
- 社団法人 日本流体力学会の論文