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Mechanical Properties of Fluids

Applications of Bernoulli's Theorem

A circular cylinder of height h_{0}=10 {~cm} and radius r_{0}=

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Solving time: 3 mins

A circular cylinder of height $h_{0} = 10 cm$ and radius $r_{0} = 2 cm$ is opened at the top and filled with liquid. It is rotated about its vertical axis. Determine the speed of rotation so that half the area of the bottom gets exposed. $(g = 10 m / sec^{2})$ :

25 rad / s

50 rad / s

100 rad / s

200 rad / s

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Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

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William Discussed

A circular cylinder of height

h_{0} = 10 cm

and radius

r_{0} = 2 cm

is opened at the top and filled with liquid. It is rotated about its vertical axis. Determine the speed of rotation so that half the area of the bottom gets exposed.

(g = 10 m / sec^{2})

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Area of bottom

= π r_{0}^{2}

r

is the radius of the exposed bottom, then
Solution Image

π r^{2} r = \frac{1}{2} π r_{0}^{2} = \frac{r _{0}}{2}

Due to the rotation of the liquid surface profile an equation given as

y here at and at y = \frac{ω ^{2} x ^{2}}{2 g} y = H x = r_{0} y - h_{0}

x h_{0} ω = \frac{r _{0}}{2} = \frac{ω ^{2}}{2 g} (\frac{r _{0}^{2}}{2}) = 2 \frac{g h _{0}}{r _{0}} = \frac{2 10 \times 0.1}{0.02} = 100 rad / s

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Question Text	A circular cylinder of height $h_{0} = 10 cm$ and radius $r_{0} = 2 cm$ is opened at the top and filled with liquid. It is rotated about its vertical axis. Determine the speed of rotation so that half the area of the bottom gets exposed. $(g = 10 m / sec^{2})$ :
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	56

A circular cylinder of height $h_{0} = 10 cm$ and radius $r_{0} = 2 cm$ is opened at the top and filled with liquid. It is rotated about its vertical axis. Determine the speed of rotation so that half the area of the bottom gets exposed. $(g = 10 m / sec^{2})$ :

Text solutionVerified

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A circular cylinder of height h0​=10 cm and radius r0​=2 cm is opened at the top and filled with liquid. It is rotated about its vertical axis. Determine the speed of rotation so that half the area of the bottom gets exposed. (g=10 m/sec2) :

Text solutionVerified

Practice questions from Physics Galaxy Mechanics Vol 1 (Ashish Arora)

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A circular cylinder of height $h_{0} = 10 cm$ and radius $r_{0} = 2 cm$ is opened at the top and filled with liquid. It is rotated about its vertical axis. Determine the speed of rotation so that half the area of the bottom gets exposed. $(g = 10 m / sec^{2})$ :