Examkracker Fluid Pressure Question

[rowjimmy]

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(Note h is the depth of the fluid in the container and d is the height of the siphon from ground level.)

Question 561: If h is 5m and d is 10m, and the siphon is closed at the end that is not submerged, what is the absolute pressure at the top of the siphon?

A. -.5 atm
B. 0 atm
C. .5 atm
D. 1 atm

Answer is C, .5 atm.



Why is the P=pg(h-d) pressure subtracted from the atmospheric pressure? If pascal's principle states that pressure applied to an enclosed fluid is applied at all points in the fluid then why wouldn't the pressure at the top of the siphon equal the pressure at the bottom of the siphon plus the atmospheric pressure?

 

[ljc]

Because pressure is a function relative to the exposed surface. So since the exposed surface is 5 meters BELOW the top of the siphon, you must subtract the pressure.

Another way to look at it:
Pressure at the exposed surface is 1atm. As you move down, you are stacking water molecules on top, so pressure must go up. If you were to move up, you are essentially unstacking water molecules, so pressure must go down.

Edit: In regards to pascals principle -- that's really just saying you can't compress a fluid. If you stack fluid on top, pressure (weight) will increase, in the same way it would increase on top of you if you were to stack bricks on yourself while laying down. But if someone were to push you up, the bricks would move up too - the movement of you+bricks (analogous to fluid) is uniform, despite differences in pressure (weight).

 

[rowjimmy]

Thanks! I figured that was the answer but in the lecture book it said that it's impossible to have negative pressure so I was hesitant to subtract a pressure value from atmospheric pressure because that implies that there is negative pressure. But, in this case I'm assuming that you can subtract pressure because the question is essentially asking for the pressure relative to a certain point, thus the pressure d-h meters high will be "negative" relative to the surface of the fluid.

Another aspect that confused me was that if one end of the siphon was closed off then wouldn't the siphon actually break and the water in the tube towards the left would flow back into the tank and the fluid towards the right would stay in place due to the closed end. So I actually thought of this scenario occuring and assumed that the pressure would be equal to atmospheric pressure because at exactly the top of the siphon there'd be no fluid. But I guess it really isn't beneficial to overthink a question like that!

 

[ljc]

Thanks! I figured that was the answer but in the lecture book it said that it's impossible to have negative pressure so I was hesitant to subtract a pressure value from atmospheric pressure because that implies that there is negative pressure. But, in this case I'm assuming that you can subtract pressure because the question is essentially asking for the pressure relative to a certain point, thus the pressure d-h meters high will be "negative" relative to the surface of the fluid.

You bring up a good point here. You are correct in saying that you can't have negative pressure, but this is absolute pressure. Gauge pressure can be negative, which is just pressure relative to atmospheric.
You got me thinking though, what if the siphon had been 100 meters tall? Wouldn't that imply negative absolute pressure at the top, since at 5 meters it has decreased by half? Now my assumption is that this couldn't happen -- that as soon as you got to the point where you would cross into negative territory, the pressure exerted by the column of fluid would be too great on the water tank and would increase the water level there.

Therefore, I'd take a guess that the highest you could potentially have a siphon above a surface of water would be 10m (since this is equivalent to one atmosphere of pressure). In such a case, pressure at the top of the siphon would be zero. Though someone more knowledgeable is welcome to confirm/correct me.

 

[milski]

Therefore, I'd take a guess that the highest you could potentially have a siphon above a surface of water would be 10m (since this is equivalent to one atmosphere of pressure). In such a case, pressure at the top of the siphon would be zero. Though someone more knowledgeable is welcome to confirm/correct me.

That's right. It's the same situation as a barometer. Once the syphon is high enough for the pressure to drop to zero you'll get vacuum on top of the syphon and it will stop working.

A small technicality - it's not even vacuum, it's just the vapor pressure of the fluid at that temperature. For water at room temp it won't make significant difference.