Ehsan18 one year ago Q75. Water flowing through a tube having variable cross-sectional area is shown in the figure below.

1. Ehsan18

2. Ehsan18

@perl

3. perl

I believe it is all tubes

4. Ehsan18

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

5. perl

We might be able to apply Bernoulli's principle

6. Ehsan18

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

7. 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

8. perl

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

9. 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

10. perl

Can we assume the tubes are open to the atmosphere

11. Ehsan18

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

12. Ehsan18

is it all the tubes?

13. Ehsan18

@Astrophysics @ikram002p

14. Ehsan18

@nincompoop

15. 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 ....

16. sohailiftikhar

????

17. sohailiftikhar

are you there ????

18. Ehsan18

@Michele_Laino

19. Michele_Laino

If the motion of water is uniform, then we can apply the continuity equation: $Av = {\text{constant}}$ so we can write: ${A_1}{v_1} = {A_2}{v_2} = {A_3}{v_3}$

20. Michele_Laino

where A is the cross sectional area of the tube

21. Michele_Laino

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

22. 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

23. Michele_Laino

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

24. Michele_Laino

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

25. Ehsan18

We don't know anything about speed, probably depends upon the Area so its tube 3 most probably...what is your final answer?

26. Michele_Laino

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

27. Ehsan18

Thanks guess I can close it now.

28. Michele_Laino

:)