Penn Yan flooding: conservation of mass and the physics of the flood.

Yesterday morning, New York woke up to find devastation in it’s Finger Lakes Region and Yates County. A shocking amount of rainfall has left high water marks as high as an estimated nine feet in some areas. A state of emergency has been declared and one would think that a Disaster Zone designation cannot be far behind. Events such as these seem comparatively routine in the South or along the Mississippi river delta. But even if flooding has become an increasingly common event in New York, devastation such as this feels like a new thing for our state.

Taking a step back from the human toll is helpful to understand the material damage with a bit of basic physics. Why is flood water so damaging?

At it’s most basic level, the real destructive power of water tends to come from a physical concept called the Conservation of Mass. This theory holds that, if a consistent mass of fluid is forced through a smaller channel, the water will either need to increase it’s velocity or else spread it’s mass out elsewhere to compensate. Regardless, the volume of water in movement (flux) on one side of the obstruction will be consistent with the volume of water in flux other side.

If this sounds technical and complicated, consider that everybody who waters their lawn or garden by holding their finger over the end of the garden hose is quite well aware of this effect. Instead of placidly arcing out of the hose to fall a foot in front of you, the constricted water column now sprays six or eight feet in front of you. But, if a flow of water was to go from a relatively wide channel to a narrower channel that’s still open at the top, the result would be the water running higher in the obstruction than out of it.

This silly video actually shows both effects more or less at once with a broken rubber pool. Note that, when the break happens, the water shoots out of the hole a good ten feet. But then when the pool edge falls below the water line, the water actually increases it’s height slightly to make it through the narrow channel at the top:

It also illustrates another, related characteristic of water: it’s preference for the path of least resistance. “Least resistence” does not necessarily mean “no resistance.”

In Penn Yan, we see these forces at work in pictures tweeted by Adam Chodak at 13WHAM ( @adamchodak ) of a gully that overtook the road it was supposed to protect (click for larger, clearer views):

Water’s true destructive force doesn’t just become visible when it reaches obstructions. It is created when it reaches that obstruction, as it rushes over, under, around and eventually, through the obstruction, leaving nothing in it’s wake. When you see swells in Penn Yan at 9 feet, some of those places may have been low elevation, but just as likely, they’re parts of downtown Penn Yan where the rushing water found it easier to increase it’s depth and velocity than to clear the obstruction in it’s way – which may very well have been a building.

In (simple, I promise) mathematical terms, the volume (Q) of water in “flux” – that is: moving – is equal to the height and width of the channel it’s moving through (collectively, A), times the velocity (v) at which it’s moving:

Q = vA

So if a body of water is moving 100 gallons of water a minute through a 5′ wide channel at 2′ high, the water is moving at 10 feet per minute(100 = 10(2*5) ). Constrict that channel to just two feet wide, and the water will either need to rise to 5′ high, or else increase it’s velocity to 25 feet per minute.

Every other destructive power of flood water extends from this one basic physics concept. Just two feet of relatively placid water can lift a vehicle 3000 pounds or more. As we can see, higher water and higher velocity can do a lot more damage.

By Tommy Belknap

Owner, developer, editor of DragonFlyEye.Net, Tom Belknap is also a freelance journalist for The 585 lifestyle magazine. He lives in the Rochester area with his wife and son.