 Ratio time change for a homogeneous fluid model

For a two-coordinate fluid model with $\dot{s}=g(n/s)$, $\dot{n}=f(n/s)$ and $s>0$, set $\kappa =n/s$ and $du/dt=1/s$. Then $d\kappa /du=f(\kappa )-\kappa g(\kappa )$ and $d\log s/du=g(\kappa )$. A bounded ratio eventually confined where $g\le -\eta <0$ makes $s$ decay exponentially in the new time. Since $dt/du=s$, the original fluid time has a finite terminal value and both coordinates tend to zero. This is a useful finite-time draining of a fluid model argument; the singular origin is treated by a stopped trajectory.