The Suez Canal — How Ships Float

Suez Canal

I read about the recent incident in the Suez Canal with the container ship, Ever Given.

I started thinking about the support of floating ships.

With a relatively narrow canal, it was easier to imagine the mechanics.

Archimedes

Recall Archimedes Principle — we simply say a floating object displaces its weight in water.

Let’s look at this from the viewpoint of the water

Now, in a salt water canal, place a large ship noting the water level before and after placement. The rise in water level multiplied by the area of water surface gives the volume of water displaced. The rise in water level increases the pressure on the floor of the canal.

Maybe the rise in water level is very small — let’s say 1 inch; so the water pressure is increased by only about 63.93 PSF / 12 inches = approximately 5.33 pounds per square foot (*) — but this pressure increase is over the ENTIRE canal floor area.

Ever Given

For the Ever Given, at a listed displacement of approximately 266,000 tons = 532,000,000 pounds, the 1 inch water level rise would occur over an area of approximately 99,900,000 square feet = 3.58 square miles.

Let’s look at this from the viewpoint of the ocean

Now consider the same ship in the ocean.

The water level increases by a very small fraction of an inch but the increase in water level is over the ENTIRE ocean surface. Therefore, the increase in sea floor pressure is over the ENTIRE ocean floor.

Conclusion

And we conclude that any object floating in the ocean is supported by an increase in pressure on the ENTIRE ocean floor.

Of course, the surface area of the world’s oceans is huge — 139.7 million square miles — the Ever Given displacement would result in a ocean floor pressure increase of only (3.58 square miles / 139,700,000 square miles) * 5.32 PSF = 136E-9 PSF = 3.8 pounds per square mile!

The rise in ocean level would be (3.58 square miles / 139,700,000 square miles) * 1 inch = 26.3E-9 inches = 26 billionths of an inch!

Open question: When such a ship is launched, how long does it take for the entire ocean level to rise?

(*) REFERENCE:

Fresh water weight = approximately 62.43 pounds per cubic foot (SG = 1)
Sea water weight = approximately 63.93 pounds per cubic foot (SG = 1.024)

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