First slide

Fluid statics

Question

A given shaped glass tube having uniform cross-section is filled with water and is mounted on a rotatable shaft as shown in Fig. 12.52. If the tube is rotated with a constant angular velocity $ω$ then :

Moderate

A

water levels in both A and B go up
B

water level in section A goes up and that in B comes down
C

water level in section A comes down and that in B it goes up
D

water levels remain same in both sections

Solution

$ρ$ =density
A = cross-section area
$[{ρgh}_{A} - ρg (3 h - h_{A} - h_{B})] A = (ρAL) ω^{2} (\frac{L}{2}) 2 h_{A} + h_{B} - 3 h = \frac{ω^{2} L^{2}}{2 g} . . . . (1) ρg [h_{B} + 3 h + h_{A} + h_{B}] A = [ρA (2 L)] ω^{2} (\frac{2 L}{2}) 2 h_{B} + h_{A} - 3 h = \frac{2 ω^{2} L^{2}}{g} . . . . . (2) From eqns . (1) and (2) h_{A} = h - \frac{ω^{2} L^{2}}{3 g}, h_{B} = h + \frac{11 ω^{2} L^{2}}{6 g} \Rightarrow Water level in section B goes up and in section A comes down .$

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