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.

Question

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 A 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.

Question figure

TestHub · Accepted Answer

Apply Bernoullie theorem between two ends

$P_{0} + ρ \int_{3}^{5} x ω^{2} dx = P_{0} + \frac{1}{2} ρ v^{2}; \frac{ρ ω ^{2}}{2} [5^{2} - 3^{2}] = \frac{1}{2} ρ v^{2} \Rightarrow (0.5)^{2} \times 16 = v^{2} \Rightarrow v = 2 m / s$

Physics - Fluid Question with Solution | TestHub

Doubts & Discussion