Iguazu Falls Trip: Paraguay (2/3)

This is the second post of three regarding our trip to Iguazu Falls.
Iguazu falls at the intersection of 3 countries: Brazil, Argentina, and Paraguay. I've already described our brief trip to Argentina. For the second day, we took a brief trip into Paraguay to check it out.

The main attraction to Paraguay is the Itaipu Dam. This is the second largest hydroelectric dam, in size, in the world, second only to the Three Gorges Dam in China. However, the annual energy output of Itaipu is the largest. In 2008, the produced a record 94.7 terrawatt-hours which is comparable to the amount of electricity the entire planet uses in two days.

The Itaipu Dam in Paraguay

The Itaipu Dam is a joint effort between Paraguay and Brazil. There are 20 turbines split evenly between the two nations. Interestingly, Paraguay uses 220V/50 Hz for its electricity while Brazil uses 110V/60Hz.

A broader view of the Itaipu Dam. The foreground shows the discharge channels, which open (but don't generate electricity) if the water level is too high.

Paraguay used to own the territory of Parana, where the Iguazu Falls are located. However, they were landlocked and, according to our tour guide, wanted access to the sea. In 1864, war broke out as Paraguay invaded Brazil and Argentina in order to reach Uruguay. Uruguay was a small nation, easily conquered and with access to the ocean. However, the three nations formed a Triple Alliance and soundly beat Paraguay. Paraguay now no longer controls the falls and lost a lot of territory as a result of the war.

A satellite view (from Google Earth) of Itaipu Dam. The discharge channels are partially open. Up to 40 times the Iguazu Falls rate can pass through these channels.

We were given tons of facts on the dam. The most repeated one being that all the iron and steel used in its production would amount to 380 Eiffel Towers. The one that caused us to be skeptical though, was that the amount of water passing through 2 of its tubes (see photo) is the same as that of the Iguazu Falls. That seemed far too impressive to be true. So like good scientists, we set out to check it with some quick order-of-magnitude calculations.

These 10-meter diameter tubes channel the water to turbines about 50-meters below that generate electricity

We can calculate the velocity water, or anything really, would reach given an initial height of about 100-m with:

mgh = 1/2 mv^2

The mass cancels, and we can ignore the factor of 2. Between friends, g is 10 m/s^2, so we have v^2~1000 or v~30m/s.

The rate of water is just the velocity times the cross-sectional area. We were told the diameter of the tubes were 10-m (internal) so we have a rate of (3*25)*30 ~ 2200 cubic meters/second. This is likely to be off by a factor of a few, but certainly accurate within a factor of 10. In comparison, Iguazu Falls has an average flow rate of about 1800 cubic meters/second so a statement like "the amount of water in the Iguazu Falls falls through two of these tubes each second" is a perfectly believable statement. Considering there are 20 tubes, we can see that the Rio Paraná has 10 times the flow of the Rio Iguazu.

The location of Itaipu Dam with respect to the 3 countries and Iguazu Falls. Red arrows indicate the direction of the water's flow. The Paraná River, which runs south from the dam, divides Paraguay-Brazil and Paraguay-Argentina. The Iguazu River, which flows west and joins the Paraná, divides Argentina-Brazil.

After the brief excursion to the dam, we went shopping. None of us really were up for it, but apparently the rest of the tour group would die if they couldn't shop. At least we got a look at the city, but we were not impressed:

The streets of Ciudad del Este, in Paraguay

We were warned of the blatant corruption of police officers and the streets were so crowded and full of people trying to sell you stuff or run you over with their bikes that we spent most of the time indoors.

Here's a brief video of the Itaipu Dam. Not as impressive as my Iguazu Falls video, but here you go: