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Canal

by Derek Rush (Submitted: 04/28/2003)

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CANAL

This model illustrates the well known conundrum about the operation of the Panama Canal.

It hinges upon the fact that for a canal to operate there must be water available, or made available by pumping, at the upper levels of the system.
The Panama Canal includes in its upper middle stretches a large lake that inevitably supplies water to the
locks at either end of the system. In presenting the puzzle it is usual to pass over the manner in which
this lake maintains its level, e.g. by feeder streams or rainfall etc.

The puzzle is often put to small sailboat enthusiasts, (many do, or at least dream of making transit through the canal), in the form of the suggestion that a 30 foot sailboat uses as much of the upper lakes waters as a 20,000 ton ship in passing through the canal. This can lead to heated argument at the bar of the sailing club.
Although the algebra to solve the conundrum is not difficult it is best attempted with the aid of a diagram.
Hence Netlogo is an eminently suitable medium:

To make the animation manageable the system is compressed into two locks and one upper lake; also we allow
the vessels to wrap back to the start, (round Cape Horn), rather than disappearing.
Two vessels are available to pass through the canal, a rowing boat and a big boat.

TO OPERATE:

EACH TIME press SETUP followed by the choice of BOAT.

NOTICE:

When a vessel reaches the top of a lock the water that has been added to the lock does not include the displacement volume of the vessel; but when a vessel moves into the lake, water equal to this volume is
lost by the lake and moves into the lock; also when a vessel leaves the lake and enters a lock the lake
regains the lost water from the lock.
THUS IT FOLLOWS THAT the volume of water lost by the lake when a vessel transits the canal is independent
of the vessels displacement.
This is confirmed by running the model for two sizes of vessel.

NOTE: It would be USUAL for transits by several vessels to be made simultaneously in both directions and seldom if ever would a lock operate empty of a vessel; but this does not change the result.

The author Derek Rush may be contacted by Email at derekrush@beeb.net March 2003.

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