# Water Bucket out of the world !

Consider an water Bucket (known as " Balti " in Indian language ) which is half filled. It has a shape of an frustum (refer to figure). It has upper radius 'b' and lower radius 'a' and Hight H. It is hanging on a fixed support and initially kept open in atmosphere ( in presence of air having Heat capacity ' C ' ).

Now this bucket is tightly Packed at the top at time t=0 , and instantly (at t=0) a small hole of cross sectional area $${ A }_{ hole }$$ is made at the centre of the base of this hanging bucket , so that water is starts coming out. Then Find the Time Interval ( T ) in which water level fall's half of it's initial hight . (Means Final Hight Becomes H/4 from bottom. )

Report Answer as : $$\left\lfloor T \right\rfloor$$

Here : $$\left\lfloor . \right\rfloor \quad is\quad GIF$$

Assumptions

$$\bullet$$ Assume that whole atmosphere is made of Ideal Helium gas (Mono atomic)

$$\bullet$$ In whole Event, this Ideal Gas has constant Heat capacity $$C=2R$$ J/mole/k where 'R' is universal gas constant.

$$\bullet$$ Neglect Heat capacity and thermal expansion of Liquid and Bucket . Neglect Viscosity , surface Tension.

$$\bullet$$ You may Use wolfram alpha for calculation .

Details

$$\displaystyle{a=1m,\quad b=2m,\quad H=1m,\quad { A }_{ hole }=0.01{ m }^{ 2 },\\ { \rho }_{ w }={ 10 }^{ 3 }kg/{ m }^{ 3 },\quad { P }_{ atm }={ 10 }^{ 5 }N/m,\quad g=10m/{ s }^{ 2 }}$$

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