Tag: continuity equation

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    When the Mediterranean Dried Up

    Geological evidence shows that millions of years ago, the Mediterranean Sea nearly dried out. In fluid mechanics, we’d describe this problem using one of our fundamental equations: conservation of mass, also known as continuity.

    Imagine a volume containing the entire Mediterranean. To describe the amount of sea water in that volume, you need to keep track of two major quantities: how much water is flowing into the volume and how much is leaving it. For the prehistoric (as well as today’s) Mediterranean, the sources feeding the sea are 1) an inflow from the Atlantic through the Strait of Gibraltar; 2) inflows from rivers; and 3) rainfall. Water is lost primarily to evaporation.

    As explained in the video, the Mediterranean’s dry spell was heralded by tectonic changes that sealed the Strait of Gibraltar, depriving it of its largest source of inflow. At the same time, warmer temperatures and less rainfall reduced influx from rivers and the atmosphere while increasing evaporation rates. The result? Water levels in the Mediterranean dropped by hundreds of meters, creating massive salt deposits, wiping out native marine life, and allowing mass migration by land-dwelling animals. Eventually, though, the Strait re-opened, creating what might have been a massive flood. (Video and image credits: PBS Eons)

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    Crash Course Fluids

    Crash Course Physics returns to the subject of fluids with their video on fluid dynamics. They stick with ideal fluids (i.e. incompressible, inviscid, laminar flows) for simplicity and cover some of the basics by discussing conservation of mass (also called continuity) and a simple form of Bernoulli’s equation. Despite keeping things basic, the video does a nice job introducing these topics; I especially like that they explain Bernoulli’s equation as a form of conservation of energy. Sometimes it’s easy to let the terminology in fluid dynamics mask the fact that the equations we use are just alternative forms of the classical equations for conserving mass, momentum, and energy. As with their fluids at rest video, the information is densely packed, so expect to pause and rewind. (Video credit: Crash Course)

  • Physics Tattoos

    Physics Tattoos

    This is a man with great commitment to fluid dynamics. He writes:

    This, on my leg, is the incompressible form of the conservation of mass equation in a fluid, also known as the continuity equation. When people ask what it means, I say it defines flow. Sometimes I say it means you should have studied more physics, but that is only when I am feeling like being funny. What it means in more detail is that, for an incompressible fluid, the partial derivative of the velocity of the fluid in the three spatial dimensions must sum to zero. It therefore concisely states the fundamental nature of a fluid. #

    (via physicsphysics)