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

Question

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

ehsan18 · Answer

attachment

ehsan18 · Answer

@perl

perl · Answer

I believe it is all tubes

ehsan18 · Answer

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

perl · Answer

We might be able to apply Bernoulli's principle

ehsan18 · Answer

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

perl · Answer

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 · Answer

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

ehsan18 · Answer

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 · Answer

Can we assume the tubes are open to the atmosphere

ehsan18 · Answer

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

ehsan18 · Answer

is it all the tubes?

ehsan18 · Answer

@Astrophysics @ikram002p

ehsan18 · Answer

@nincompoop

sohailiftikhar · Answer

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 · Answer

????

sohailiftikhar · Answer

are you there ????

ehsan18 · Answer

@Michele_Laino

michele_laino · Answer

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 · Answer

where A is the cross sectional area of the tube

michele_laino · Answer

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

michele_laino · Answer

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 · Answer

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

michele_laino · Answer

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

ehsan18 · Answer

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 · Answer

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

ehsan18 · Answer

Thanks guess I can close it now.

michele_laino · Answer

:)