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

Flow rate is calculated using only the parallel velocity

  1. Jul 25, 2014 #1
    So flow rate is calculated using only the parallel velocity to the area vector. Why is this? How can I mathematically prove this? Namely, how do I prove any perpendicular component of the velocity vector is not contributing to any volume output? I know this is the result of the dot product; I want to know why the dot product is valid reasoning for this scenario.

    thanks.
     
  2. jcsd
  3. Jul 25, 2014 #2

    Nathanael

    User Avatar
    Homework Helper

    If the entire velocity were perpendicular, what would be the flow rate?
     
  4. Jul 26, 2014 #3
    Consider the definition of the volumetric flow rate

    [itex]\dot{V}[/itex]=[itex]\frac{dV}{dt}[/itex]

    say

    [itex]V=\vec{A} \cdot \vec{x}[/itex]

    substitution yields

    [itex]\dot{V}=\vec{A}\cdot\frac{d\vec{x}}{dt}=\vec{A}\cdot\vec{v}[/itex]

    where [itex]\vec{v}=\frac{d\vec{x}}{dt}[/itex] and [itex]A[/itex] materially conserved
     
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: Flow rate is calculated using only the parallel velocity
  1. Flow rate calculation (Replies: 3)

Loading...