A tube is sealed at both ends and contains a 0.0250-m-long portion of liquid. Th

Question

A tube is sealed at both ends and contains a 0.0250-m-long portion of liquid. The length of the tube is large compared to 0.0250 m. There is no air in the tube, and the vapor in the space above the liquid may be ignored. The tube is whirled around in a horizontal circle at a constant angular speed. The axis of the rotation passes through one end of the tube, and during the motion, the liquid collects at the other end. The pressure experienced by the liquid is the same as it would experience at the bottom of the tube, if the tube were completely filled with liquid and allowed to hang vertically. Find the angular speed (in rad/s) of the tube.

Explanation / Answer

Let P is the pressure at the bottom of the tube, if the tube were completely filled with liquid and allowed to hang vertically.

Let A is the cross sectional area.

let rho is the density of liquid.

when rotating net force acting on liquid by one end of the tube,

F = m*a

P*A = m*L*w^2

rho*g*L*A = rho*V*L*w^2

rho*g*V = rho*V*L*w^2

g = L*w^2

==> w = sqrt(g/L)

= sqrt(9.8/0.025)

= 19.8 rad/s

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