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 : \(\left\lfloor . \right\rfloor \quad is\quad GIF\)


\(\bullet \) 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 .


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

This is Original .
Try More Deepanshu's Mixing of concept's.

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