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 - Water flowing through a pipe

  1. Mar 3, 2013 #1
    1. The problem statement, all variables and given/known data
    JOOi9xN.png

    3. The attempt at a solution
    I am interested in why my method is flawed:
    ufZsUTx.jpg

    Alright I know how to do this problem. Essentially you solve mass flow rate = rho * double integral of u dA. HOWEVER, I decided to do this differently. I know that I can solve for the average u from the equation mass flow rate = rho * u_avg * A. I also know that the average u is just the integral of u over the integral of 1. I tried this and I get 1.528 m/s which is clearly not one of the answers. Why does my method not work?
     
  2. jcsd
  3. Mar 3, 2013 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    In the expression: ##\dot{m} = \rho u_{avg}A##,
    ##u_{avg}## needs to be the average over the cross-sectional area of the pipe, not the average over the radius.
     
  4. Mar 3, 2013 #3
    Hmmm, according to the equation doesn't u only depend on r? In other words u is constant for some circular ring r = k?
     
  5. Mar 3, 2013 #4

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Consider two intervals of radius, one near the center of the pipe and one out at the edge. Suppose the interval dr is the same for both. There are more patches of area in the same interval dr out near the edge. So, the value of the velocity out at the edge contributes more to the average over the cross–section than the value near the center.
     

    Attached Files:

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: Fluid mechanics - Water flowing through a pipe
  1. Fluid Flow in a pipe (Replies: 3)

Loading...