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!