A U-shaped tube with a horizontal portion of
length contains a liquid. What is the difference
in height between the liquid columns in the
vertical arms (a) if the tube has an acceleration
toward the right? (b) if the tube is mounted on
a horizontal turntable rotating with an angular
speed with one of the vertical arms on the
axis of rotation?
Consider the fluid in the horizontal part of the tube. This fluid with mass
, is subject to a net force due to the pressure difference between
the ends of the tube, which is the difference between the gauge pressures
at the bottoms of the ends of the tubes. Now this difference is