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

Pressure in the z-axis

  1. Nov 2, 2004 #1
    If you have a rectangular fluid element verticle z-axis and a horizontal x-axis, pressure is constant along the x=axis, but p=f(z) along the z-axis.

    If [tex]\frac{dP}{dz}=-density.g[/tex]

    is the integral of [tex]\frac{dP}{dz}[/tex] equal to p(z) - p(z1) = -density.g(z-z1)?
     
    Last edited: Nov 2, 2004
  2. jcsd
  3. Nov 2, 2004 #2

    Tide

    User Avatar
    Science Advisor
    Homework Helper

    That would be true only if the denisity is constant. Also, be careful with your signs on the right hand side.
     
  4. Nov 2, 2004 #3
    Assume it is a liquid and therefore (practically) incompressible.
     
  5. Nov 2, 2004 #4

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Incompressibility does not entail that the density field is constant.
     
  6. Nov 2, 2004 #5
    Density = mass / volume.

    If the volume doesn't change (incompressible), surely the mass wouldn't change?
     
  7. Nov 2, 2004 #6

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    In continuum mechanics, we use density FIELDS, rather than particle densities.

    Incompressibility entails that the density of A FLUID PARTICLE remains constant; but because the individual fluid particles may jump around in space, it does not follow that the density FIELD is constant.

    The field measures the density of whatever particle happens to be AT A FIXED POINT IN SPACE; since it may be different fluid particles which occupy that point at DIFFERENT TIMES, the density field, evaluated at that point may change in time.

    If you suppose in addition that all particles has the SAME density, then the density field will be constant.
    Get it?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Pressure in the z-axis
  1. Residue of z/cos(z)? (Replies: 15)

  2. Polar axis? (Replies: 1)

  3. Axis of a Parabola (Replies: 24)

Loading...