Extend Prob. 3.90 to the case of the liquid motion in a frictionless U-tube whose liquid column

Question:

Extend Prob. 3.90 to the case of the liquid motion in a frictionless U-tube whose liquid column is displaced a distance Z upward and then released, as in Fig. P3.96. Neglect the short horizontal leg and combine control-volume analyses for the left and right legs to derive a single differential equation for V(t) of the liquid column.

Extend Prob. 3.90 to the case