Let A Be The Cross Sectional Area Of Your U Tube And L Be The Length Of The Port
Let A be the cross-sectional area of your U-tube and L be the length of the portion of the tube that is filled
with fluid. (The total volume of fluid in the tube is thus V= LA .) Show that if the fluid levels are displaced
from equilibrium by “±z ” (see Fig. 1), the increased weight of fluid on one side of the tube compared to the
other is: F=−ρ(hA)g=−2ρAgz,
(where ρ is the density of the fluid and “h ” is the instantaneous height difference between the fluid levels. This
excess weight on one side of the system is what causes the entire volume of liquid in the U-tube to oscillate!)