1. Not finding help here? Sign up for a free 30min 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!

Newtonian fluid mechanics: Navier-Stokes equation

  1. Feb 21, 2015 #1
    1. The problem statement, all variables and given/known data
    woot.png

    2. Relevant equations
    Navier-Stokes

    3. The attempt at a solution
    Not really trying to solve a problem, trying to understand what is going on in my textbook. So look at the stuff in red first. I see where all that is coming from, it's clear to me. However, the stuff in green indicates that in the example case the right side of the equation should be zero, instead they throw in the stuff in blue out of the blue. What exactly happened here that they totally missed to explain?!
     
  2. jcsd
  3. Feb 21, 2015 #2
    Are you familiar with the material derivative, d/dt? It is defined as:
    $$\frac{d}{dt}=\frac{\partial}{\partial t}+u\frac{\partial}{\partial x}+v\frac{\partial}{\partial y}+w\frac{\partial}{\partial z}$$
    The material derivative of u is equal to the x-component of the fluid acceleration.
    $$\frac{du}{dt}=a_x=\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}$$

    Chet
     
  4. Feb 21, 2015 #3
    Okay yeah I remember that from class. Thanks.

    I'm still slightly confused though. How am I supposed to know if it's a material derivative of just a regular derivative? What exactly makes it a material derivative? If I take the expression "at face value" then u does NOT depend on t and it equal zero.
    Thanks again!
     
  5. Feb 21, 2015 #4
    It's all a matter of the terminology your textbook or professor uses. Some fluids textbooks use d/dt and others use D/Dt. Of course, if you are familiar with the NS equations, you know to look for that.

    Chet
     
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: Newtonian fluid mechanics: Navier-Stokes equation
  1. Newtonian Mechanics (Replies: 2)

Loading...