Catastrophic Streamlines

My sister is teacher at a local elementary school. Recently, I tried to pack some ideas of mathematical modelling into a two-hours guided tour for nine-year-olds.

As you may remember, in June 2013, Linz was hit by one of the worst Danube floods in history with a water depth of 9.30 metres (compared to average 4 metres).

The question I asked was “During the flooding, how many litres of water were flowing below the Danube bridges in Linz per second?”

I am convinced that interested children can tackle such a problem if someone gives them advice and helps them in sorting the orders of magnitude. At least my sister’s pupils were able to do so.

Boat in dangerous situation below the historic Eisenbahnbrücke.

(Source: Landespolizeidirektion Oberösterreich)

View from the Nibelungenbrücke downstream with

Brucknerhaus and Museum Lentos in the left half.

(Photo by Günter Auzinger) 

View from the Nibelungenbrücke upstream with

the castle of Linz in the right upper corner.

(Photo by Günter Auzinger)

The current post does not contain the solution of the Linz flooding problem. This is to inspire you to think about it yourself: Which information do I need?  What simplifications can be made to obtain still reasonable results? Can I verify my result qualitatively and quantitatively? Which tools from a household (bathtub?, loaf pan?) can be used to have an even more colourful demonstration?
Next week on Mathematics Wednesday: Streamlines and skateboarding.