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| The crowds on the Kasr al-Nil Bridge in Cairo on Jan. 28, 2011 Photo by Peter Macdiamid/Getty Images Published in the New York Times on-line on the date above |
What does this have to do with fluid mechanics? A lot--as you can see in the picture, a large number of people are trying to squeeze from the streets into the confined space on the bridge. There is a law in fluid mechanics called "conservation of mass." In the broad street or park approaching the bridge, the number of people moving toward the bridge is given by their density times their forward velocity. You can think of it as the number of "lanes" of people moving forward times the velocity that they are moving in the lanes. On the bridge, the same law applies, but the number of lanes is greatly reduced. For a steady state, the flux of people has to be the same, which means that the people on the bridge should be moving much faster than the ones approaching the bridge.
Of course, this can't happen in a crowd, and so the bridge gets jammed--even without riot police at the far end. This situation occurs all of the time in traffic jams when the road narrows. The problem is that any slight event can cause the jam to turn into a stampede, with injuries and deaths. I was amazed, and relieved, that this seemed not to happen in Cairo. Just a few weeks ago at least 104 pilgrims were killed and another 50 injured in a stampede of pilgrims in India. Stampedes have killed people in a wide variety of venues--synagogues, theaters, meeting halls, train stations, air raid shelters, stadiums and, yes, Walmart (November 28, 2008).
And yes, this does relate to fluid mechanics--one model for traffic flow is based in river hydraulics!
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