Draining a Container
Question: Consider a container with area and height
. A small hole of
is put into the bottom of the container. How much time
does it take to drain the container? Assume
.
We will show:
Applicable Ideas:
Continuity Equation
There is no accumulation in the amount of fluid anywhere in the container.
Bernoulli Equation
The statement of conservation of energy for the fluid. Applying this to the problem, where is atmospheric pressure:
Sidenote: If , then
and we have
. This is Torricelli’s law where the speed of the fluid emerging from the bottom of the container is equal to the speed it would have attained falling through a distance
.
Here we can use that fact to write:
The negative sign is introduced because the water is leaving the container.
Bonus Question: Consider a hemispherical container of radius . A small hole of radius
is put into the bottom of the container. How much time
does it take to drain the container? Assume
.
We will show:
We will apply the continuity equation and Bernoulli’s equation just like before.
From the Bernoulli equation:
We will approximate because
holds most of the time.
You must be logged in to post a comment.