Engineering
Physics
Statics
Question

Cylindrical vessel with a fluid rotates around the axis of symmetry with an angular velocity of w. Normally on a same horizontal level, pressure is same but here the pressure on the bottom near the vessel wall is more than the pressure at the center. Here ω = 5 rad/s, ℓ = 1m, r = 0.1 mm, R = 2 m.
                    
By the side wall of the vessel we tied a massless inextensible string of length ℓ. To this string we tie a balloon of radius r. During the rotation of the cylinder, the thread makes an angle a with the wall. 

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Linked Question 1

What is the angle of inclination of the liquid to the horizontal at the points lying at a distance of r = 5 cm from the axis?

tan–1  (12)

tan–1 (14)

tan–1 (116)

tan–1 (18)

Solution
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y=ω2x22g

dydx=ω2xg=18=tanθ

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Linked Question 2

The Buoyant force on the balloon is in direction

Solution
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no solution 

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Linked Question 3

The angle α is given by 

tan α = 2.5    

tan α = 1.25 (2 + sin α)

tan α = 2.5 (2  cos α)

tan α = 2.5 (2 – sin α)

Solution
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T sin α = mω2 (R – l sin α)/α                
T cos a = mg/α 
tanα=ω2(Rlsinα)g=2.5(2sinα)

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