= Inertial dam-break current in a triangular valley
{title2=$X\propto g^{2/5}(W/\lambda)^{1/5}t^{4/5}$}
In a horizontal prismatic V-shaped valley with section area $A=\lambda h^2$, a fixed-volume high-Reynolds-number <gravity-current box model> has $h=(W/(\lambda X))^{1/2}$ and front speed $\dot X=\operatorname{Fr}\sqrt{gh}$. Integrating gives $X=[5\operatorname{Fr}\sqrt g(W/\lambda)^{1/4}t/4]^{4/5}$ after the initial release scale is neglected. This is an inertial closure, distinct from the viscous <V-shaped channel gravity current>, whose exponent is different.
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