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...

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!)