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  4. A horizontal oriented tube AB of length 5 m rotates with a constant angular velocity 0.5 rad / s about a stationary vertical axis OO ' passing through the end A. The tube is filled with ideal fluid. The end of the tube is open, the closed end B has a very small orifice. The velocity with which the liquid comes out from the hole (in m / s ) is:

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Q. A horizontal oriented tube AB of length 5 $m$ rotates with a constant angular velocity $0.5 rad / s$ about a stationary vertical axis $OO$ ' passing through the end $A$. The tube is filled with ideal fluid. The end of the tube is open, the closed end $B$ has a very small orifice. The velocity with which the liquid comes out from the hole (in $m / s$ ) is:Physics Question Image

Mechanical Properties of Fluids

Solution:

Apply Bernoullie theorem between two ends
$P_{0}+\rho \int\limits_{3}^{5} x \omega^{2} d x=P_{0}+\frac{1}{2} \rho v^{2} $
$\Rightarrow \frac{\rho \omega^{2}}{2}\left[5^{2}-3^{2}\right]=\frac{1}{2} \rho v^{2}$
$\Rightarrow (0.5) / 12 \times 16= v ^{2}$
$ \Rightarrow v =2 m / s$