Question

A vertical cylindrical tank 6m high and 4m in diameter 2/3 full of water is rotated uniformly about its axis until on the point of overflowing. Compute the linear velocity at the circumference of the tank

Answer 1

A vertical cylindrical tank 6m high and 4m in diameter 2/3 full of water is rotated uniformly about its axis until on the point of overflowing. Compute the linear velocity at the circumference of the tank

Answer 2

The linear velocity at the circumference of the tank is 8.86 m/s.

Given:

height, h = 6 m

diameter, d = 4 m

depth of water = (2/3)*6

                         = 4 m

To Find:

The linear velocity.

Solution:

rise above water for no spilling = h - depth of water

                                                    = 6 - 4

                                                    = 2 m

rise above water = flow of water

∴ total height of paraboloid = rise + fall

                                              = 2+2

                                              = 4 m

 height of paraboloid  = v²/2g

⇒ v² = 4 x 2 x 9.81

        = 78.48

v = 8.86 m/s

Hence, The linear velocity at the circumference of the tank is 8.86 m/s.

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