First slide

Fluid dynamics

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 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____

Moderate

Solution

Apply Bernoulli's theorem between two ends
$P_{0} + ρ \int_{3}^{5} x ω^{2} d x = P_{0} + \frac{1}{2} ρ v^{2} \Rightarrow \frac{ρ ω^{2}}{2} [5^{2} - 3^{2}] = \frac{1}{2} ρ v^{2} \Rightarrow (0.5) 2 \times 16 = v^{2} \Rightarrow v = 2 m / s$

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