= Particle-laden current with suction
{title2=$Q'=-W,\quad Q\phi'=-V\phi$}
A steady well-mixed dilute <particle-laden gravity current> above an absorbing porous bed loses carrier fluid at speed $W$ and particles at total downward speed $W+V$, where $V$ is their relative <settling velocity> magnitude. <Volume conservation> and the particle budget give $Q=Q_0-Wx$ and $\phi=(Q/Q_0)^{V/W}$ for $W>0$. The <momentum conservation> equation is $(Q^2/h+g'_0\phi h^2/2)'=-Wu$ if the withdrawn fluid carries its local horizontal <velocity>. Consequently $uu'+g'_0\phi h'+g'_0h\phi'/2=0$. At $W=0$, $\phi=e^{-Vx/Q_0}$ and the momentum flux is constant.
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