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### Course: AP®︎/College Physics 2>Unit 1

Lesson 1: Density and Pressure

# Finding height of fluid in a barometer

Using our understanding of fluid pressure to figure out the height of a column of mercury. Created by Sal Khan.

## Want to join the conversation?

• I don't understand why the mercury should be going up the test tube. I understand there is no atmosphere acting on it, but there is also no force dragging it up. Please help! :|
• The atmosphere outside the whole system is pushing down on the mercury in the bowl, and that pressure is distributed evenly throughout the mercury in the bowl. As there is no atmosphere in the test tube (its a vacuum), there is no pressure inside the test tube to push down on the mercury below it. The mercury therefore gets pushed up the test tube due to the pressure being exerted on the whole bowl of mercury, and the lack of pressure pushing back from within the tube. It is only because of the vacuum that the mercury goes up the tube, if that was just a regular test tube you pulled out of a drawer (with no vacuum), this wouldn't work. This is at least how I picture it.
• I thought standard measurement was 760 mm Hg= 1 atm. Here you got 770 mm Hg?
• Yes it is 760mm. The mistake is coming from the atm conversion to Pa.
1atm is 101325Pa not 103000Pa.
• Q 1: Will the vacuum of the test tube try to raise / suck the Hg into it? If so, do we have to compensate for an added force upward? I can see that if it were not a vacuum, it would be pushing the Hg out of the tube.
Q 2: Since we are dealing with a vacuum in the tube, do we have to deal with the Hg trying to evaporate and creating a gas in the available vacuum? I think this would yield some inaccurate measurements since you can't measure the pressure contribution of the gas via height.
• Q1: This is an incredibly common misconception. A complete vacuum cannot exert any pressure whatsoever. It has no density, so it's pressure (given by P = (rho)*g*h) must be zero. It is the difference in pressures that would drive the mercury to be "sucked into" the space occupied by the vacuum. If the pressure on one side is 0 atm, and the other is 1 atm, then higher pressure (in this case 1 atm) will generate a force to push the mercury to the lower-pressure side (0 atm).

Q2: This is pretty interesting. However, if you consult a phase diagram for mercury, you'll notice that mercury is does some weird things at low and high pressures. So, the short answer is yes, it would create a problem, but no, we don't worry about that here.
• So does the cross-sectional area of the test tube not matter when determining how high the mercury will rise? I would think this would have to be accounted for.
• Nope, it does not matter. The mercury will stop rising when its weight inside the tube equals the force being exerted by the atmospheric pressure on the same area (the cross sectional area of the test tube). So, when weight of liquid inside tube equals force of atmosphere inside tube:

Weight of liquid in tube = density*Area*Height*g
Force of atmosphere = AtmPressure*Area of tube

If you equal the two you get: density*Area*Height*g = AtmPressure*Area
The Areas are the same so they cancel each other out, leaving you with the equation Sal used: density*h*g = AtmPressure

Hope it helped.
• Since the portion above the mercury is a vacuum, how is it that the mercury stops climbing up the tube? The pressure of 1 atmosphere must exist at the top and push upwards, correct?
• To understand why it stop you need to understand what a vacuum is. Try to think in terms of forces. First "Vacuums" don't suck things up, or cause things to move by exerting forces because they are vacuums - they are a space of nothing. The reason that things seem to be "sucked" up or "pulled" by the vacuum is because other forces are pushing said things in towards the vacuum. Why are they pushing things towards the vacuum, because there is nothing pushing back from the vacuum. Now to your question, if nothing is pushing back then why doesn't it go all the way up? Nothing is pushing back rather gravity is pulling down. Make a free-body-diagram on the column of mercury, you will find that the at that height up the tube, the pressure dude to gravity pulling the column of mercury down is equal to the pressure pushing it up due to the atmosphere at the bottom of the tube. I hope this helps (^-^)/ Forgive me if I'm wrong!
• I Didnt Understand the 1atm at France Paris?

I know that 1 atm is an approx. value, But in France does it have the correct measurment?

(Thank You!)
• The standard atmosphere (atm) is equal to 101325 Pascal. This value was meant to represent the mean atmospheric pressure at mean sea level at the latitude of Paris.
• Does this also mean that the height of the mercury in the bowl from its deepest point to the point where the pressure was equal is also going to be 0.77 meters, since the pressure is the same, the density and the gravitational force?
• No, the 1 atmosphere of pressure that was used to calulate the height of the mercury was at the surface of the mercury in the bowl so the height is measured from there.

If you used the pressure at the deepest part of the bowl you would get a height of 0.77 + the depth of the bowl.
• If both water faucets upstairs and downstairs were turned fully on, will more water come out of the downstairs faucet? Why?
• This is a great question! I'm not sure entirely what the answer would be, and maybe someone with more knowledge of fluid mechanics could correct me, but I don't see how more water would come out of a downstairs faucet as I'd imagine the entire system is under relatively constant pressure. If there was a difference, I think it would be minimal.
(1 vote)
• Does the Atmospheric pressure acting on our body at inside home and outside home is different? I mean that when we are inside the is only a few meters of air column up to the ceiling. So, the pressure must be smaller that outside pressure!