Ehsan18
  • Ehsan18
Q75. Water flowing through a tube having variable cross-sectional area is shown in the figure below.
Physics
schrodinger
  • schrodinger
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Ehsan18
  • Ehsan18
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Ehsan18
  • Ehsan18
perl
  • perl
I believe it is all tubes

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Ehsan18
  • Ehsan18
Yeah I think the same, but can you back it up?
perl
  • perl
We might be able to apply Bernoulli's principle
Ehsan18
  • Ehsan18
Could you please apply it and tell me how it looks like..
perl
  • perl
I am reading this. http://physics.stackexchange.com/questions/799/why-does-the-water-level-equalize-in-a-series-of-tubes It has something to do with the pressure being constant
perl
  • perl
That article deals with static water, it might be different when you have flowing water
Ehsan18
  • Ehsan18
It is, because when the water is static, it has a property to maintain a certain level, its used in hydraulics too...but when it comes to flowing liquid its Bernoulli equation
perl
  • perl
Can we assume the tubes are open to the atmosphere
Ehsan18
  • Ehsan18
yes maybe, I think its tube 3 according to eq. of continuity A1v1=A2v2 A=area. v=velocity
Ehsan18
  • Ehsan18
is it all the tubes?
Ehsan18
  • Ehsan18
Ehsan18
  • Ehsan18
sohailiftikhar
  • sohailiftikhar
its tube III because here speed is slow than other and hence pressure is high due to which goes up to its maximum level ....
sohailiftikhar
  • sohailiftikhar
????
sohailiftikhar
  • sohailiftikhar
are you there ????
Ehsan18
  • Ehsan18
Michele_Laino
  • Michele_Laino
If the motion of water is uniform, then we can apply the continuity equation: \[Av = {\text{constant}}\] so we can write: \[{A_1}{v_1} = {A_2}{v_2} = {A_3}{v_3}\]
Michele_Laino
  • Michele_Laino
where A is the cross sectional area of the tube
Michele_Laino
  • Michele_Laino
so we have the minimum value of the speed at section #3
Michele_Laino
  • Michele_Laino
next we have to consider the Theorem of Bernoulli: \[z + \frac{P}{\gamma } + \frac{{{v^2}}}{{2g}} = const\] where P is the pressure, and \gamma is the specific weight of the water
Michele_Laino
  • Michele_Laino
so the pressure P is maximum at the section where the speed v is minimum. What can you conclude?
Michele_Laino
  • Michele_Laino
more precisely, the quantity: \[\frac{P}{\gamma }\] is called the "groundwater level"
Ehsan18
  • Ehsan18
We don't know anything about speed, probably depends upon the Area so its tube 3 most probably...what is your final answer?
Michele_Laino
  • Michele_Laino
yes! at the tube #3 the pressure is the highest and so it is the level reached by water
Ehsan18
  • Ehsan18
Thanks guess I can close it now.
Michele_Laino
  • Michele_Laino
:)

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