Finite-blade side-drainage pile
= Finite-blade side-drainage pile
{title2=$h(0^+,y)=[126(\alpha^2-y^2)]^{1/7}$}
A long blade with negligible under-blade leakage diverts incoming fluid laterally. A deep-pile profile $h^3=9[x_N(y)-x]$ and integrated flux conservation give $d(\int h^4dx)/dy=-12y$, hence $x_N=[126(\alpha^2-y^2)]^{3/7}/9$. This leading approximation excludes the nose and blade-tip transition regions.