Q75. Water flowing through a tube having variable cross-sectional area is shown
in the figure below.

- Ehsan18

Q75. Water flowing through a tube having variable cross-sectional area is shown
in the figure below.

- schrodinger

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- Ehsan18

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- Ehsan18

- perl

I believe it is all tubes

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## More answers

- Ehsan18

Yeah I think the same, but can you back it up?

- perl

We might be able to apply Bernoulli's principle

- Ehsan18

Could you please apply it and tell me how it looks like..

- 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

That article deals with static water, it might be different when you have flowing water

- 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

Can we assume the tubes are open to the atmosphere

- Ehsan18

yes maybe,
I think its tube 3
according to eq. of continuity
A1v1=A2v2
A=area.
v=velocity

- Ehsan18

is it all the tubes?

- Ehsan18

- Ehsan18

- 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

are you there ????

- Ehsan18

- 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

where A is the cross sectional area of the tube

- Michele_Laino

so we have the minimum value of the speed at section #3

- 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

so the pressure P is maximum at the section where the speed v is minimum. What can you conclude?

- Michele_Laino

more precisely, the quantity:
\[\frac{P}{\gamma }\]
is called the "groundwater level"

- 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

yes! at the tube #3 the pressure is the highest and so it is the level reached by water

- Ehsan18

Thanks guess I can close it now.

- Michele_Laino

:)

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