Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What does this mean? (equation for viscous flows)

  1. Mar 13, 2016 #1
    While reading a text book on viscous flows, I came across the following interpretation of an equation:

    upload_2016-3-13_13-58-32.png

    where, v is the vertical component of the free stream velocity and y is the vertical distance from the surface of a solid and Re is the reynolds number.

    Can someone please help me understand what this interpretation means?
    Thanks in advance
     
  2. jcsd
  3. Mar 15, 2016 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The funny O means 'is of the order of'
    My interpretation would be: if the reynolds number quadruples, v and y become approximately half as big

    Often the funny O is used instead of 'is proportional to' (##\propto##) if the reasoning aims to justify ignoring certain terms. But I don't know if that is true in your context.
     
  4. Mar 15, 2016 #3

    boneh3ad

    User Avatar
    Science Advisor
    Gold Member

    The order symbol expresses a concept similar to proportionality but not quite the same. It's a statement of how one function grows relative to another. In this case, ##v## and ##y## grow as ##Re^{-1/2}##. In other words, ##v## and ##y## are bounded by ##Re^{-1/2}## multiplied by some factor as they grow. This can imply proportionality but does not necessarily. Essentially, proportionality is a stronger constraint.
     
  5. Mar 15, 2016 #4
    The "O" is called "big O notation". It means "on the order of magnitude of" Your average student body size for a college campus might be O(10^4) (between 10,000 and 99,999 students), but your average classroom size might be O(10^1) (10 to 99), for example.
     
  6. Mar 26, 2016 #5
    This is called viscous flow.In this when you go upward from a fixed surface the velocity of the layer of liquid increases.At the bottom layer velocity would be zero and at top velocity of layer would be maximum.Reynold number shows that upto a specific value of Reynold number flow would be viscous and beyond that number flow would become transit and the turbulent flow.see the images below.



    noo.png imgaes2
    fluid.png image1
     

    Attached Files:

    • noo.png
      noo.png
      File size:
      6.4 KB
      Views:
      29
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: What does this mean? (equation for viscous flows)
Loading...