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Water Bridge

Check it out, a water bridge:

Amazing… I got this in an email that read:

Even after you see it, it is still hard to believe. 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 Germany, 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.

The explanation at the bottom about the weight of the ships is misleading. The conclusion itself is correct, but water displacement is not enough to explain it.
First, to demonstrate the flaw in the writer’s argument, consider the following experiment: Close the bridge on both ends so it doesn’t connect to the nearby rivers. Drop a ship onto the bridge. The bridge must now support the weight of the water plus that of the ship. The fact that the water is displaced doesn’t matter here, as long as it doesn’t get spilled.

Now for the water bridge. Fact: The water pressure depends only on the depth at which you’re measuring. It does not depend on the objects submerged in the water.

When you put a boat in the water the water rises by a negligible amount, because the surface area of the water (including the rivers) is so enormous compared to that of the ship. For all practical purposes, the water level doesn’t change. Therefore the water depth at the bridge stays the same, and no additional force is exerted on it.

Here’s another way of looking at it: When you put something in water, its weight is distributed evenly across the bottom. So the ship’s weight is distributed acroos the bridge + the adjoining rivers + the bottom of the ocean. The area of the bridge’s bottom and sides is negligible compared to the total area supporting, and hence it doesn’t feel the additional weight of the boat.