A horizontally oriented tube AB of length l rotates with a constant angular velocity about a stationary vertical axis OO' passing through the end

A horizontally oriented tube AB of length l rotates with a constant angular velocity ω about a stationary vertical axis OO' passing through the end A (Fig. 1.86). The tube is filled with an ideal fluid. The end A of the tube is open, the closed end B has a very small orifice. Find the velocity of the fluid relative to the tube as a function of the column "height" h.

Fig. 1.86.