= One-sided constant-volume porous gravity current
{title2=$L^3=9\lambda Vt/\phi$}
A localized release of actual fluid volume $V$ per unit width on a reflecting half-line $x\geq0$ has the <Barenblatt solution> $h=[L^2-x^2]_+/(6\lambda t)$, where $L^3=9\lambda Vt/\phi$ and $\lambda=k\Delta\rho g/(\phi\mu)$. The <mass conservation> normalization is $\phi\int_0^Lh\,dx=V$. Zero slope at the reflecting boundary gives zero <Darcy flux>. For symmetric spreading on the full line, the same formula has $L^3=9\lambda Vt/(2\phi)$ when $V$ denotes the total released volume. A finite initial patch is not determined by volume alone; this exact source profile has a concentrated initial release.
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