Water flowing in and out of a bucket

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1. The problem statement, all variables and given/known data
A cylindrical bucket is being filled with water at the rate of 2 * 10^(-3) m^3/s. The bucket itself is od diameter 1.5 m and height 2.5 m. The bucket has a small circular hole at the bottom, with diameter 3 cm. Therefore even as the bucket is being filled, there is a leakage from the bottom. At first, the water rises in the bucket. Eventually, the water stops rising when it reaches a height of h. At this point the leakage from the bottom of the bucket equals the water intake from the tap. Find this height h.


2. Relevant equations
I am not sure, we barely covered this in my class. I'm guessing A1v1 = A2v2 and Bernoulli's equation come into play somehow.


3. The attempt at a solution
I really haven't attempted it because as I stated we did really go over this so much in my class.


Thanks!
 

rl.bhat

Homework Helper
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The level of water in the bucket will stop rising when the volume of inflow is equal to A2V2.
Volume of inflow and A2 is known. Find V2.
The pressure on the top and bottom of the bucket is the same i.e. atmospheric pressure.
At the opening at the bottom V1 is almost zero. Potential energy with respect to the bottom of the bucket is ρgh. Using Bernoulli equation find h.
 

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