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PHY 232
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I have some questions about some test questions I'm working on. If you could do some 'handwaving' around these for me that would be good. I may take this test Wednesday morning depending on if I resolve these questions by then.
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Problem Number 7
What is the rate of volume flow from a faucet with cross-sectional diameter .6 cm if the pressure head is 420000 kPa?
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@& There is no significant difference in height between the pipe feeding the faucet and the outlet of the faucet. So `d(1/2 rho v^2) + `dP = 0.
`dP is the pressure head. v^2 inside the pipe is presumably negligible compared to the v^2 of the exiting water.*@
Problem Number 2
A tube 3.7 mm in diameter is run through the stopper of a sealed 8-liter container. The tube outside the container forms a U, then runs in a straight line with slope .021 with respect to horizontal. Alcohol is introduced into the tube, and fills the U, extending into the linear section of the tube. Both ends of the tube are sealed, and the air column in the linear section is originally .53 meters long. The container is slightly heated, and the alcohol column is observed to move 9 mm along the linear section of the tube. The material of which the container is constructed has coefficient of linear expansion `alpha = 81 * 10^6 / C. If the temperature of the air in the container was originally 27 Celsius, what is the new temperature?
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@& The 'pressure tube' indicates a difference in the air pressure there.
There is also a very slight difference in the vertical level of the alcohol in the tube.
The two are combined to find the presssure change within the container.
The container itself changes volume, expanding a bit. And the movement of the 'alcohol plug' in the tube increases the air volume.
You can write down an expression for the change in the volume of the air in the container, as a function of the new temperature T.
You have the information required to find the pressure change, and you can implicitly assume that the initial pressure it 1 atmosphere.
All these considerations, along with the gas law, make it possible to write down an equation whose only unknown is T.*@
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7: I know dV/dt=Av but I'm not sure how to find v with what I'm given about pressure.
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2: I've seen a lot of this kind and some make more sense than others. I can see the pieces but can't put them all together. In particular the part about the tube being/not being sealed troubles me. Does sealed mean the pressure inside the tube affects column change whereas unsealed the pressure on the outside column is atm? Where does the alcohol come from, is it in the bottle? How does alpha come into play? My guess is that it affects volume change in the bottle that in turns affects the alcohol in the column but if the tube is sealed then how much of an affect does that really have?
@& If the tube is sealed then its change in volume indicates a change in pressure.
If the tube is not sealed then the movement of the fluid in the tube is due to expansion of the gas (in this case the change in pressure due to the change in the vertical level of the fluid is more significant than if the tube is sealed, since a given movement due to expansion of the gas indicates much less pressure change than would be indicated if the tube was sealed).
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