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Water level in tank

  • Thread starter vissh
  • Start date
  • #1
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hellO :D

Homework Statement


(Q)A large cylindrical tank has a hole of area A at its bottom.Water is poured in the tank by a tube of equal cross-sectional area "A" ejecting water at the speed "v".
<a>Water level in the tank will keep on rising
<b>No water can be stored in the tank
<c>The water level will rise to a height v2/(2g) and then stop.
<d>The water level will oscillate


Homework Equations


Hmm.. Bernoulli's equation [-->Speed of Efflux] and equation of continuity.


The Attempt at a Solution


hmm I think that as soon as some water is poured through the tube , all that water will flow out of the tank . And thus no water can be stored.
But the answer is <c>
Can anyone help me out >:D
Thanks for reading ^.^
 

Answers and Replies

  • #2
1,384
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hmm I think that as soon as some water is poured through the tube , all that water will flow out of the tank . And thus no water can be stored.
On what basis do you think that? Try to arrive at the result theoretically (in terms of the relevant equations you wrote above)
 
  • #3
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Start by writing an equation for the rate of change of water in the tank.


i.e. [tex]\frac{dW}{dt} = W_e - W_l[/tex]

where W is the amount of water in the tank, We is the amount of water entering the tank, and Wl is the amount of water leaving the tank.
 
  • #4
1,384
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Start by writing an equation for the rate of change of water in the tank.


i.e. [tex]\frac{dW}{dt} = W_e - W_l[/tex]

where W is the amount of water in the tank, We is the amount of water entering the tank, and Wl is the amount of water leaving the tank.
How do you solve by this method? I am interested in knowing it.
 
  • #5
50
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How do you solve by this method? I am interested in knowing it.
We is the rate of water entering the tank; it is equal to the velocity of water entering the tank times the cross-sectional area.

Wl is the rate of water leaving the tank; it is equal to the velocity of water leaving the tank times the cross-sectional area. So you start this with bernouli's equation in order to find the velocity leaving the tank, and multiply it by A.

When the tank is in equilibrium, the rate of change of the water level will be zero. In other words, We-Wl=0
 
  • #6
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Thanks both of you :)
--->But i still have problem ~.O
I can't decide from questions language whether the tank had initially a water level or not.
To me its appears to be Empty initially.So, as the pipe pours in some water , that water will spread out on tank's large bottom and there "will not" be any water level .
>Rate of water entering = Av
>But How i apply the Bernouuli's equation in this to find out the velocity of out going fluid ??
Can you guide me more :)
Thanks for reading ^.^
 
  • #8
82
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Hehe I know that law :)
But i can't see how to use it in this problem .As i wrote in previous post, i can't see any water level in the tank.
And also i can't see that equation of continuity can be used here with the rate of water flowing from the tube and rate of water from the hole. As much i know, the equation of continuity is used in a "Tube of flow" And water from the tube to hole isn't appearing to me in a tube of flow.
Can u explain ^.^
 
  • #9
50
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Don't think of the start of this problem, think of the problem when the tank is at equilibrium. If the tank is to be in equilibrium, the velocity of water entering times the cross sectional area of the entranceway is equal to the velocity of water leaving times the cross sectional area of the exitway.

Assume the tank has some height of water, h.

Torricelli's Law gives you the velocity of water exiting the tank.

Solve for h.
 
  • #10
82
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Thanks again :)
Ok if i think like that i get the answer ^.^
But can we tell the velocity of fluid [using equation of continuity and bernoulli's equation]flowing out from hole if we start from the instant the tank is "empty" and then, the water is poured in ?? Oo[Not from the instant when water is in equilibrium]
Just a bit curious :)
 
  • #12
surface tension and position of hole and inflow water positon is required to carry out a full analysis via finite element analysis, if you want to leave that part then focus on the governing equationsat a particular height h.
by the way , even if the inflow pipe is directed towards the hole, due to surface tesion effects and stream widening,some water will always be accumulating in the tank and this is the worst case scenario to think of.
 
  • #13
82
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Thankuuu ^.^
 

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