Problem 1.324

A horizontally oriented tube $A B$ of length $l$ rotates with a constant angular velocity $\omega$ about a stationary vertical axis $O O^{\prime}$ 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" $h .$