I'm wondering how the propagation rate of surface level in a liquid relates to various factors, such as viscosity / density / gravity / geometry of container, when there is a point source or sink adding to / removing from that liquid.
Suppose I have a large pool of water, roughly 1km in area and not too squashed in dimensions (say, ratio of max widths / min width < 1.5), and I turn on a pump at one point, withdrawing 1 m³ per second (1000 L / s) from it. Over the long term the pool of water will drop at 0.001 mm/sec = 3.6mm / hour. How long will it take for the whole surface of the water to be decreasing within, say, 10% of this rate? How does this relate to the area and earth's gravity $g$ and the properties of water? What if it's a more viscous fluid?
I would have thought it relates highly with speed of sound in the liquid, but then I'm thinking about honey, and how it's much slower to equalize surface level if you perturb it, even though the speed of sound in honey isn't much different from the speed of sound in water (higher than water, apparently!)
