Examkrackers Fluid Pressure 559

[rowjimmy]

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What is the approximate maximum height d at which the siphon will be capable of draining the water tower nearly completely?

A. 1m
B. 10m
C. 100m
D. There is no maximum height.

The answer is 10m but I was wondering is this 10m above the surface of the water or 10m is the length of d altogether? The explanation states that Patmos=(roh)gy where y is the height from the surface of the liquid to the top of the siphon. Wouldn't this mean that at the surface of the liquid the atmospheric pressure is zero since y=0? But at the surface of a liquid Patm=1atm so I can't seem to make sense of this equation. It also says that at a greater height than h (which is the surface level of the fluid) the absolute pressure would be lower than zero which is impossible. This makes me assume that the answer refers to 10m as the length of d and anything above the surface would contribute to negative pressure.

I understand that 10 meters of water creates 1atm of pressure so at 10 meters the pressure would equal atmospheric pressure but if pressure is scalar and doesnt have direction then how can you say that 10 meters of water counteracts or "goes against" the atmospheric pressure. Intuitively it makes sense but when I try to make logical sense using equations and the fact that pressure is scalar it's not as easy.

Also, why doesn't the hydrostatic pressure in the fluid container contribute to the siphon pressure? One would think Patm+(roh g h) would equal the pressure in the siphon?

 

[rowjimmy]

What is milski taking the day off or something?

 

[milski]

I have to go to class occasionally. 😛

10 m is from the top of the surface to the horizontal part of the syphon. You need d to be long enough so that the right bottom of the syphon is lower than the surface of the water. After that it does not matter how much lower that point is.

The atmospheric pressure is ρgy where y is the top of the water in a syphon/closed tube where there is vacuum above the liquid. For a point in the syphon exactly at the surface level you should have the same pressure as a point on the surface of the fluid. For the point on the surface, P is Patm. For the point inside the pressure is ρgy. Since they have to be the same, ρgy=Patm. That's valid only at the maximum level of fluid in the syphon. Obviously you're not going to lower the atmospheric pressure by lowering the syphon.

At heights greater than that the pressure inside the syphon/closed tube is 0. Or if you want to be completely precise, it's the vapor pressure of the fluid in the syphon.

Patm+(roh g h) - h here is height from the top of the surface. If some part of the syphon is below the surface, the pressure there will be higher than atmospheric, it will be exactly atmospheric at the surface and lower than that higher in the syphon.

 

[rowjimmy]

I have to go to class occasionally. 😛

10 m is from the top of the surface to the horizontal part of the syphon. You need d to be long enough so that the right bottom of the syphon is lower than the surface of the water. After that it does not matter how much lower that point is.

The atmospheric pressure is ρgy where y is the top of the water in a syphon/closed tube where there is vacuum above the liquid. For a point in the syphon exactly at the surface level you should have the same pressure as a point on the surface of the fluid. For the point on the surface, P is Patm. For the point inside the pressure is ρgy. Since they have to be the same, ρgy=Patm. That's valid only at the maximum level of fluid in the syphon. Obviously you're not going to lower the atmospheric pressure by lowering the syphon.

At heights greater than that the pressure inside the syphon/closed tube is 0. Or if you want to be completely precise, it's the vapor pressure of the fluid in the syphon.

Patm+(roh g h) - h here is height from the top of the surface. If some part of the syphon is below the surface, the pressure there will be higher than atmospheric, it will be exactly atmospheric at the surface and lower than that higher in the syphon.

Ok I think I get it so the absolute pressure in the siphon at the surface level when y=-10 meters (relative to surface) is Pabs=0=Patm+ ρgy=101000-101000 so Patm= ρgy. So up until y=-10 the Pabs kept decreasing and decreasing until it reached the point where Patm= ρgy. What confused me is that the question asked for the height d but they also used d to diagram the entire vertical length of the siphon so it made it seem like the length of the entire siphon (including under the water) can only be 10m which didn't really make sense because the length of the siphon will vary depending on the body of water its submerged in.

 

[milski]

Ok I think I get it so the absolute pressure in the siphon at the surface level when y=-10 meters (relative to surface) is Pabs=0=Patm+ ρgy=101000-101000 so Patm= ρgy. So up until y=-10 the Pabs kept decreasing and decreasing until it reached the point where Patm= ρgy. What confused me is that the question asked for the height d but they also used d to diagram the entire vertical length of the siphon so it made it seem like the length of the entire siphon (including under the water) can only be 10m which didn't really make sense because the length of the siphon will vary depending on the body of water its submerged in.

Yes, that's it. In what you describe y is positive down and negative up, right?

The length under the water does not really matter.

 

[rowjimmy]

Yup, thanks.