1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Pressure of liquid given radius, help please!

  1. Aug 11, 2012 #1
    A test tube filled with water is being spun around in an ultracentrifuge with angular velocity. The test tube is lying along a radius and the free surface of the water is at radius r(o).

    Show that the pressure at radius r within the test tube is:

    p = .5(p)(angular velocity)^2(r^(2) -r(o)^2)

    where p is the density of the water. Ignore gravity and atmospheric pressure.

    p = p - g(density)(height)

    gravity or centripetal acceleration, a= r(angular velocity)^2

    height or depth of water, h = r- r(o)

    this only gets me to p= p + density*r*angular velocity^2(r-r(0))

    I'm not sure where the rest comes from!
  2. jcsd
  3. Aug 11, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    At any depth 'below' the surface, the pressure has to provide enough force to accelerate all the fluid 'above' it. Hint: Set up an integral.
  4. Aug 11, 2012 #3
    Doc Al, I'm not sure I understand what I should be taking the integral of. Could you explain further?
  5. Aug 11, 2012 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Write an expression for the net force on an infinitesimal slice (thickness dr) of the fluid in the tube; then integrate from r(0) to r to find the total force, and then the pressure, at any point along the tube.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook