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A hemi-spherical tank of radius 2 m is i...

A hemi-spherical tank of radius 2 m is initially full of water and has an outlet of `12c m^2` cross-sectional area at the bottom. The outlet is opened at some instant. The flow through the outlet is according to the law `v(t)=sqrt(0. 62gh(t)),` where `v(t)` and `h(t)` are, respectively, the velocity of the flow through the outlet and the height of water level above the outlet and the height of water level above the outlet at time `t ,` and `g` is the acceleration due to gravity. Find the time it takes to empty the tank.

Text Solution

Verified by Experts

The correct Answer is:
`t=(7xx10^(5))/(135sqrtg)`
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Knowledge Check

  • The outlets in yom home provide ·

    A
    direct current
    B
    alternating current
    C
    electric discharge
    D
    static electricity

  • The reaction in the Kipp's apparatus stops when the outlet is closed from the top because

    A
    the acid becomes weak
    B
    gas starts coming out
    C
    gas pressure breaks the contact between FeS and the acid
    D
    protective film is formed on FeS

  • A tank full of water has a small hole at the bottom. If one-fourth of the tank is emptied in t_(1) seconds and the remaining three-fourths of the tank is emptied in t_(2) seconds. Then the ratio (t_(1))/(t_(2)) is

    A
    `sqrt(3)`
    B
    `sqrt(2)`
    C
    `(1)/(sqrt(2))`
    D
    `(2)/(sqrt(3))-1`

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