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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)=0.6sqrt(2gh(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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Find the time required for a cylindrical tank of radius r and height H to empty through a round hole of area a at the bottom. The flow through the hole is according to the law v(t)=ksqrt(2gh(t)) , where v(t) and h(t) , are respectively, the velocity of flow through the hole and the height of the water level above the hole at time t , and g is the acceleration due to gravity.

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Knowledge Check

  • 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
    `sqrt3`
    B
    `sqrt2`
    C
    `(2-sqrt2)/sqrt2`
    D
    `(2-sqrt3)/sqrt3`

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