Brisbane, the third-largest city in Australia and the capital of Queensland, has been seriously flooded, a natural disaster not seen here since 1974. As I write this post, thousands of volunteers are helping affected people and businesses to clean up and get back on their feet.
The media has been providing extensive coverage of the disaster and its aftermath for weeks now, providing opportunities for math teachers to investigate with their students some of the statistics being quoted. This article explores one statistic in particular, the amount of water released from the Wivenhoe Dam in one day. There are many similar opportunities for the math teacher who wishes to incorporate some "real math" with relevant, interesting connections with these current events.
Brisbane Flood, 1893
Over 100 years ago, in 1893, Brisbane suffered serious flooding of the inner city and low-lying suburbs, when the Brisbane River broke its banks in February 1893 after a tropical cyclone: The 1893 flood was just one of several floods around that time, there being other floods in 1887, 1890 and two others in 1893 a fortnight after the major flood.
Brisbane Flood, 1974
In January 1974, after weeks of heavy rain, Cyclone "Wanda" developed off the Queensland coast, which then turned into a rain depression and dumped huge amounts of water onto the city and the catchment of the Brisbane River. The result was flooding of many riverside and low-lying suburbs of the city, and over 6,700 houses being flooded.
After the water had gone and city planners had a chance to analyze what caused the flood and how they might prevent a repeat of the devastating inundation of so many homes and businesses, it was decided to build a large dam upstream from Brisbane, as a flood mitigation measure. That dam is the Wivenhoe Dam: This dam, which is presently spilling huge quantities of water over the above spillway, is an impressive structure with some impressive statistics:
- Height: 50 meters
- Length: 2.3 kilometers
- Capacity: 2,640,000,000 cubic meters
- Surface Area: 109.4 square meters
- Length of Shoreline: 462 kilometers
- Catchment Area: 7.020 square kilometers
- Average Annual Rainfall: 904 millimeters
- Maximum Capacity: 225%
The 2011 Flood, Brisbane, Queensland, Australia
At the time of this article, Brisbane is slowly recovering from yet another serious flood, the peak of which was on 13 January 2011. Even though the peak of the flood was around 1 meter below the 1974 peak, this time 20,000 houses have been inundated, and the economic cost is much higher. In the media coverage of this natural disaster, Wivenhoe Dam has attracted an understandable amount of attention. Specifically, the management of the water kept behind the dam and the water released over the spillway is of great interest to the people of Brisbane. At the peak of water release, over 645,000 megaliters of water were released in one day. This is around half of the flood abatement part of the storage at Wivenhoe, which is 1,450,000 megaliters on top of the water stored for drinking and supply to Brisbane.
How Much Water is That?
Six hundred and forty-five thousand megaliters sounds like a lot - it is. But this quantity of water is very difficult to visualize. How can a teacher help students understand this quantity?
Step 1: How big is a liter?
One liter is a familiar quantity to students who buy milk in liters. It may be converted into 1,000 milliliters, or 1,000 cubic centimeters. This is the same volume of a place value thousands block, which is a 10 centimeter cube.
Ask students what would have the same volume as one liter - one liter of milk, obviously, a medium bottle of soft drink, less than one old-style house brick.
Step 2: Demonstrate a cubic meter
If you have a cubic meter kit, you can construct a cubic meter out of one-meter lengths of wood and corner connectors. How big is it, really? Students may be surprised at the size when they see an actual cubic meter. See how many students could fit into that space.
Ask students how many liters equal the volume of a cubic meter. Show them a thousands block for comparison. Students should see that the one liter block is one tenth the size of the cubic meter, in each dimension of length, width and height. Clearly, the cubic meter has a volume of 1,000 liters. What is another name for one thousand liters? The prefix for "thousand" is "kilo"; 1,000 liters = 1 kiloliter. What is the mass of a cubic meter? One liter weighs close to one kilogram (at 4 degrees C, this is its precise mass). So one cubic meter, or one kiloliter, of water has a mass of 1,000 kilograms, or one tonne! Students will probably be surprised that one cubic meter has about the same mass as a small car.
Step 3: Discuss a familiar, larger quantity
Depending on where you live, students may be familiar with household swimming pools. In Brisbane, many families have their own "backyard pool". These pools are typically around 7 or 8 meters long, 3 or 4 meters wide, and 1.5 m deep. This pool is a typical size for its type, and contains 50,000 liters, or 50 cubic meters.
Alternatively, your students may be familiar with a larger, municipal pool. An Olympic pool is 50 meters long, 25 meters wide and around 2 meters deep. Its capacity can be calculated using the formula for the volume of a rectangular prism: Volume = length x width x height = 50 m x 25 m x 2 m = 2,500 cubic meters
Some communities have domestic water collection tanks, which might be around 500 liters for a small tank, or several thousand liters for a larger one.
Ask students to compare these quantities of water with other know volumes of liquid. How many bathtubs could you fill from a domestic water tank? How many tubs of ice cream would fill a backyard pool? What would the mass of the water in a pool or tank be? How many people would be needed to lift it?
Step 4: Calculate volume of rainfall and flood flow
By continuing in the same fashion, students can calculate comparisons between familiar domestic quantities of water and the amount of water in a dam or a flood. For example, the water released from Wivenhoe Dam in one day was 645,000 megaliters. How much is this? First, some conversions:
- 645,000 ML = 645,000,000,000 L = 645,000,000,000,000 mL
We have larger units we can use in place of megaliters: one thousand megaliters is one gigaliter. So:
- 645,000 ML = 645 GL
Secondly, how much space does this take up? If we put this water into a tank, how big would it have to be? Since 1 kL = one cubic meter, we can work out that 645 GL = 645,000,000 cubic meters. If this was in a square tank one kilometer on each side, the water would be 645 meters deep - if the Empire State Building could be dropped in the tank, it would have 200 meters of water over its highest point.
- How many Olympic swimming pools would this water fill? 258,000.
- How many 5-liter ice cream buckets would this fill? 1.2 billion.
Thirdly, how much does this water weigh? Since a cubic meter of water has a mass of one tonne, 645 GL of water would have a mass of 645,000,000 tonnes. This is the mass of:
- 6,450,000 rail trucks carrying 100 tonnes each
- around 1.9 million fully-loaded jumbo jets
Finally, how much drinking water would that supply for humans? Each person should drink around 2 liters of water per day. 645 GL would supply drinking water for around:
- 320,000,000,000 people for one day - 50 times the population of earth.
To supply drinking water for the two million people of Brisbane, this amount of water would supply their drinking needs for:
- 160,000 days, or 441 years.
Of course, people use water for more than drinking, so a more realistic calculation is based on average daily water usage by Brisbane citizens - around 150 L each:
- 2150 days, or 5.8 years.
Everyday life, as every math teacher knows, is filled with authentic, real-world uses of mathematics. Students will benefit from seeing how the math of their textbooks can be brought to life through incorporation of interesting, relevant contexts from the daily news broadcast or newspaper.
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