1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fluid Mechanics and order of magnitude calculation

  1. Feb 16, 2014 #1
    Hi

    In my lecture notes we making some calculations and all terms [itex]\mathcal O(M^3)[/itex] are to be thrown away. Here M is the Mach number. Now, there is the expression (u denotes the velocity):
    [tex]
    uu\partial_t \rho \approx \rho_0 uu\nabla u
    [/tex]
    which in my notes are thrown away because they claim it is [itex]\mathcal O(M^3)[/itex]. But is it really true, I mean the derivative of u will not necessarily be on the same order as Ma, right?
     
  2. jcsd
  3. Feb 17, 2014 #2

    olivermsun

    User Avatar
    Science Advisor

    That's right. The gradient also contains a length scale in each direction. In many cases one simply asserts on physical grounds that du/dx is same order as u (so the flow is sufficiently "smooth") or that there is some characteristic length scale of order one. Does the problem assume M << 1 and also no viscous effects?
     
  4. Feb 17, 2014 #3

    boneh3ad

    User Avatar
    Science Advisor
    Gold Member

    I'd also postulate that there is some more complicated order-of-magnitude analysis that can be done here a la that done in deriving Prandtl's boundary layer equations, but it would be difficult to carry that out without more information from the OP on what assumptions were made and what the physical situation is.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Fluid Mechanics and order of magnitude calculation
  1. Order of magnitude (Replies: 3)

  2. Order of magnitude (Replies: 10)

  3. Orders of Magnitude. (Replies: 3)

  4. Fluid mechanics (Replies: 4)

Loading...