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:

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: (A) 1 m / s (B)  2 m/s  (C)  4 m/s (D)  3 m / s

Tardigrade Admin · Accepted Answer

Apply Bernoullie theorem between two ends P0+ρ ∫ limits35 x ω2 d x=P0+(1/2) ρ v2 ⇒ (ρ ω2/2)[52-32]=(1/2) ρ v2 ⇒ (0.5) / 12 × 16= v 2 ⇒ v =2 m / s

$1 m / s$

$2 m / s$

$4 m / s$

$3 m / s$

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

1m/s

2m/s

4m/s

3m/s

Apply Bernoullie theorem between two ends P0​+ρ3∫5​xω2dx=P0​+21​ρv2 ⇒2ρω2​[52−32]=21​ρv2 ⇒(0.5)/12×16=v2 ⇒v=2m/s

$1 m / s$

$2 m / s$

$4 m / s$

$3 m / s$

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