Re: Tank Draining Problem

From: Gordo (gordo20878_at_hotmail.com)
Date: 06/07/04 

Date: Mon, 07 Jun 2004 12:17:42 GMT

David Moran <ktulwxwatcher@hotmail.com> wrote:
> "Virgil" <ITSnetNOTcom/virgil@COMCAST.com> wrote in message
> news:ITSnetNOTcom/virgil-C82D8D.20425706062004@[63.218.45.211]...
>> In article <2ihrauFn7pknU1@uni-berlin.de>,
>> "David Moran" <ktulwxwatcher@hotmail.com> wrote:
>>
>>> Hi all, I am working on a problem that I just can't seem to work
>>> out.
>>>
>>> The problem reads: At time t=0 the bottom plug (at the vertex) of
>>> a full conical tank of water 16 ft high is removed. After 1 hour,
>>> the water in the tank is 9 ft deep. When will the tank be empty?
>>>
>>> I know that my initial conditions are f(0)=16 and f(1)=9 and I
>>> think that the volume of a cone will probably be part of it too,
>>> but I just can't see how to set the Differential Equation up. Any
>>> help would be greatly appreciated.
>>>
>>> Dave
>>>
>>>
>>
>> I suspect that you are meant to assume that the rate of flow through
>> the drain is proportional to the pressure at the bottom of the tank
>> , which, of course, will be proportional to the depth of the water.
>>
>> Have you tried to do the problem using this assumption?
>
> The only equation that the book gives is Torricelli's Law.

The potential energy of a small mass m of fluid at the top (height h) must
match the kinetic energy of the same mass of fluid exiting at the bottom:
mgh=mv^2/2, where v is velocity, g is gravity.
Hence, ideal v = sqrt(2gh) [Torricelli's theorem]

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