Water flow duration

  • Thread starter Pzi
  • Start date
  • #1
Pzi
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Hello.

Homework Statement


There is a vertical cylinder-shaped reservoir full of water:
Height h = 18 meters
Radius R = 2 meters
If suddenly a hole appeared on the bottom (radius r = 0.25 meters) how long would it take to empty the reservoir?


Homework Equations


Probably related to Bernoulli's principle somehow someway.


The Attempt at a Solution


To be honest with you I just reposted this problem from elsewhere. Some girl tried to solve it and since I am a pure mathematician I pretty much do not have a clue about those things. Tried to google it, but without proper knowledge did not succeed.
Some kind of powerful formula and basic steps would be appreciated.

Thanks.
 

Answers and Replies

  • #2
gneill
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Bernoulli is the key. His principle gives you the speed of the water exiting the orifice, hence the flow rate and rate of change of velocity in the tank. [EDIT: I meant change of VOLUME, not change of velocity!].

Essentially, for a depth of water h above the opening, the velocity of the water will be given by [itex]\sqrt{2 g h}[/itex] .

With the flow rate and opening size you can construct the differential equation for the volume of water in the tank.
 
Last edited:
  • #3
Pzi
26
0
Bernoulli is the key. His principle gives you the speed of the water exiting the orifice, hence the flow rate and rate of change of velocity in the tank.

Essentially, for a depth of water h above the opening, the velocity of the water will be given by [itex]\sqrt{2 g h}[/itex] .

With the flow rate and opening size you can construct the differential equation for the volume of water in the tank.
So it seems that I am supposed to solve this
[PLAIN]http://img708.imageshack.us/img708/6712/eqn9284.png [Broken]

Can you confirm?
 
Last edited by a moderator:
  • #4
gneill
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20,913
2,861
Yes, that is one differential equation that fits the bill!
 

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