River On A Bridge

This photo arrived in my inbox today with the following description:

Water Bridge in Germany. What a feat! Six years, 500 million euros, 918 meters long . . now this is engineering! This is a channel-bridge over the River Elbe and joins the former East and West ermany, as part of the unification project. It is located in the city of Magdeburg, near Berlin. The photo was taken on the day of inauguration.

To those who appreciate engineering projects, here's a puzzle for you armchair engineers and physicists. Did that bridge have to be designed to withstand the additional weight of ship and barge traffic, or just the weight of the water? Answer: It only needs to be designed to withstand the weight of the water! Why? A ship always displaces an amount of water that weighs the same as the ship, regardless of how heavily a ship may be loaded. Remember your high school physics, and the fly in an enclosed bottle project? Similarly, the super sensitive scale proved that it didn't make any difference whether the fly was sitting on the bottom, walking up the side, or flying around. The bottle, air, and fly were a single unit of mass and always weighed the same.

Snopes (which I wrote about here) verifies the existence of this bridge.

My husband the physicist and I were discussing the physics of this. We agreed that the bottle/fly example is a bad analogy because it is a closed system. Of course the fly/water/bottle entity will mass the same whether or not the fly is on the side of the container, or drowning in at the bottom of it's watery grave. That doesn't fit this scenario at all.

I agreed that the bridge structure would not have to account for the mass of the boat on it. The displaced water caused by the boat on the bridge would essentially run the length of the entire river so that at the point of the bridge, the displaced amount of water becomes negligible. And since the boat doesn't just drop onto the bridge from the sky, but is already in the water by the time it reaches the bridge, then there is no displacement of water when the boat enters onto the bridge.

But in a way, I noted, the bridge actually had to account for the weight of all the boats on the entire river. That is, say along that waterway there were 500 boats each massing 1000 tons. That's a total of 500,000 tons of water that will be displaced (essentially, that will rise) along the length of the river. But being a long waterway, 500,000 tons of displaced water disperses rather thinly. So again, at the point of the bridge, the difference is negligible.

Make sense? Do you agree or disagree?

This bridge, by the way, is almost a kilometer long.

Tags: bridge, physics, Germany, canal, River Elbe, unification project, Magdeburg, engineer, channel-bridge, barge