Leaky bucket

Classical Mechanics Level 4

A bucket is lying on the ground with water up to the brim. It is lifted and a hole is made in it, right at the bottom, through which the water can escape. Find the time taken to empty the bucket (in seconds).

Height of the bucket $=30 \ \text{cm}$

Area of the bucket $=60 \ \text{cm}^2$

Area of the hole $= 10 \ \text{cm}^2$

$\text{g}=9.8 \ \text{m}/\text{s}^2$

The answer is 1.463850109.

1 solution

Ronak Agarwal
Aug 8, 2014

At any time let the water level in the bucket be h

Then according to torricelli's law we have :

${ v }_{ efflux }=\sqrt { 2gh }$

Also by conservation of mass of water we have

${ A }_{ hole }{ v }_{ efflux }={ A }_{ bucket }(\frac { -dh }{ \quad dt } )$

Finally we have :

$\int _{ 0 }^{ t }{ \frac { -{ A }_{ hole } }{ { A }_{ bucket } } \sqrt { 2g } dt } =\int _{ h }^{ 0 }{ \frac { dh }{ \sqrt { h } } }$

Solving we have $t=\frac { { A }_{ bucket } }{ { A }_{ hole } } \sqrt { \frac { 2h }{ g } }$

Put the values to get $\boxed { t=1.484\quad sec }$

Shouldn't we consider the area of holes and use the equation ${ v }_{ efflux }=\sqrt { \frac { 2gh }{ 1-\frac { { A }^{ 2 } }{ { a }^{ 2 } } } }$ where $A$ =Area of bucket and $a$ =area of hole.

Anandhu Raj - 6 years ago

ans would come the same i guess !! i tried that too

A Former Brilliant Member - 6 years ago

Yes..Just asked.

Anandhu Raj - 6 years ago

Leaky bucket

The answer is 1.463850109.

1 solution

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