Correct statement about siphon used to empty water tank

[songoku]

Homework Statement

Siphon is used to empty tank A. For each statement, check whether it is true or false
(i) At maximum height, the pressure is zero
(ii) According to Bernoulli, for siphon to work well, position of B can be higher than A but must lower than position of water surface at tank.
(iii) Pressure A is equal to pressure B to make the siphon work
(iv) Velocity of water is greater at B than at the maximum height of the siphon

Relevant Equations

Bernoulli Equation

Continuity Equation

Hydrostatic Pressure

The answer to this question is statements (i) and (ii) are correct.

(i) I don't understand why this is corect. By "at maximum height", I assume at the highest position of the siphon, but why the pressure is zero?

(ii) I think this is correct because conservation of energy. If B is higher than the water surface, the gravitational potential energy of the water is not enough to push the water through the siphon

(iii) This is wrong because pressure at A is higher than B

(iv) This is wrong because, assuming the siphon has constant area, then by continuity equation the speed at B is the same as speed of water everywhere inside the siphon

Why (i) is correct and are my reasoning for other statements correct?

Thanks

 

[jbriggs444]

(i) I don't understand why this is corect. By "at maximum height", I assume at the highest position of the siphon, but why the pressure is zero?

I dislike this question. It is full of ambiguities.

It appears that by "at maximum height" they mean the maximum height to which the top of the siphon could have been adjusted. At that height the [absolute] pressure in the fluid would be zero. Any higher and the fluid would spontaneously cavitate/boil and the siphon would stop working.

(ii) I think this is correct because conservation of energy. If B is higher than the water surface, the gravitational potential energy of the water is not enough to push the water through the siphon

I agree with your reasoning.

However, I maintain that (ii) is false for a different reason. If B is higher than A then the tank cannot be completely emptied. We were told that the siphon "is used to empty tank A". If the siphon does not empty the tank then it cannot be said to "work well".

If one has practical experience with siphons then a minimum criterion for "works well" is that the fluid velocity in the tube should be greater than the rate at which air bubbles can rise in the fluid. So that any air that would otherwise accumulate at the top of the siphon is swept harmlessly away.

(iii) This is wrong because pressure at A is higher than B

(iv) This is wrong because, assuming the siphon has constant area, then by continuity equation the speed at B is the same as speed of water everywhere inside the siphon

Yes. Agreed on both counts.

 

[Chestermiller]

I dislike this question. It is full of ambiguities.

It appears that by "at maximum height" they mean the maximum height to which the top of the siphon could have been adjusted. At that height the [absolute] pressure in the fluid would be zero. Any higher and the fluid would spontaneously cavitate/boil and the siphon would stop working.

At the maximum hight of the siphon, when cavitation occurs, the absolute pressure is not zero, It is equal to the vapor pressure of the liquid.

 

[Lnewqban]

Because the reasons explained above, statement (i) is only approximately correct.

Please, see:
https://www.aps.org/archives/publications/apsnews/201210/physicshistory.cfm

 

[songoku]

Because the reasons explained above, statement (i) is only approximately correct.

Please, see:
https://www.aps.org/archives/publications/apsnews/201210/physicshistory.cfm

Approximately correct because the absolute pressure will be zero only at 0 K?

Thanks

 

[jbriggs444]

Approximately correct because the absolute pressure will be zero only at 0 K?

[Water] siphons stop working at about 0 C.

 

[Lnewqban]

Approximately correct because the absolute pressure will be zero only at 0 K?

Thanks

Because molecules of the liquid will be jumping into the gas space as long as they have extra energy to do so.
Those jumps will increase if the pressure of the gas decreases and/or the temperature of the liquid increases.
Each substance shows a different dependence rate on pressure and temperature.
For each temperature, there is a pressure at which the same number of molecules jump in each direction (liquid to vapor-gas mix / vapor-gas mix to liquid).

Please, see:
https://en.wikipedia.org/wiki/Vapour_pressure_of_water

https://en.wikipedia.org/wiki/Vapor

 

[Gavran]

(i) I don't understand why this is corect. By "at maximum height", I assume at the highest position of the siphon, but why the pressure is zero?

https://en.wikipedia.org/wiki/Siphon#Maximum_height

 

[songoku]

Because molecules of the liquid will be jumping into the gas space as long as they have extra energy to do so.
Those jumps will increase if the pressure of the gas decreases and/or the temperature of the liquid increases.
Each substance shows a different dependence rate on pressure and temperature.
For each temperature, there is a pressure at which the same number of molecules jump in each direction (liquid to vapor-gas mix / vapor-gas mix to liquid).

Please, see:
https://en.wikipedia.org/wiki/Vapour_pressure_of_water

https://en.wikipedia.org/wiki/Vapor

In the first link there are several formulas for the pressure but I don't think using any of those formulas can result in P to be zero so can you elaborate more why the statement (i) is approximately correct?

https://en.wikipedia.org/wiki/Siphon#Maximum_height

When deriving the equation, the pressure at max height is taken to be zero. But there is also statement "This means that the height of the intermediate high point is limited by pressure along the streamline being always greater than zero".

Does this mean that zero pressure can't be achieved and this is just an idealized situation (only in theory)?

And from equation of "general height of siphon" to equation of "maximum height of siphon", the velocity o the fluid is taken to be zero so at max height the fluid does not move?

Thanks

 

[jbriggs444]

In the first link there are several formulas for the pressure but I don't think using any of those formulas can result in P to be zero so can you elaborate more why the statement (i) is approximately correct?

At room temperature the saturated vapor pressure of water is about 3% of an atmosphere. Whether this counts as "approximately zero" depends on how large an approximation error you are willing to accept.

One atmosphere is about 10 meters (or 30 feet) of water. The vapor pressure of water is about 31 centimeters (or one foot) of water.

So another way of asking your question would be whether a 31 cm error on the maximum height of a ten meter siphon would be acceptable.

If we chilled the water to zero C then the vapor pressure would be down to 0.6 percent of an atmosphere. Then the question is whether a 6 cm error on a ten meter siphon would be acceptable.

Or we could consider the vapor pressure of mercury at room temperature. That is between one and two microns of hg. We routinely accept that the vapor pressure in the "vacuum" in a mercury barometer is zero and do not try to compensate for the error.

View attachment 366643

When deriving the equation, the pressure at max height is taken to be zero. But there is also statement "This means that the height of the intermediate high point is limited by pressure along the streamline being always greater than zero".

Does this mean that zero pressure can't be achieved and this is just an idealized situation (only in theory)?

It depends on what you mean.

Much effort is spent in the lab to evacuate containers to obtain better and better vacuums. Perfect vacuums are not practically achievable. However, negative absolute water pressures are possible if the tubing is clean and the fluid is free from nucleation sites. Water coheres.

One usually does not want to consider such things in an introductory exercise like this one.

 

[Gavran]

Does this mean that zero pressure can't be achieved and this is just an idealized situation (only in theory)?

Yes it does and this holds in theory. There is not an idealized situation in theory when P_B=0 and the syphon works.
h_B=P_atm/(ρg)-v_B²/(2g) is the height of the syphon which can not be reached because at that height P_B=0 and the syphon will “break”. This value limits the height of the syphon.

The same holds for h_B,max=P_atm/(ρg) except that in this case there is one more restriction v_B=0. When v_B=0 the syphon also “breaks”.