Pressure and Height in Liquids: A Container with Different Diameter Tubes

In summary, the problem involves a container with two tubes, one wider (A) and one narrower (B). The diameter of tube A is four times that of tube B. Mercury is poured into the container, followed by water into tube B. The height of the water in tube B is 70 cm. The questions are: a) how much does the mercury in tube A rise, b) how much does the mercury in tube B fall, and c) if water is poured into tube A, what is the difference in height between the mercury levels in the two tubes? The equations P=hρg and the concept of pressure being unaffected by shape are relevant, but no calculations are needed. The solution is that the heights of the
  • #1
jasonlaiyh
3
0

Homework Statement


A container consists of two tubes, tube A which is wider and tube B which is narrower. The diameter of a tube A is four times that of tube B. Some mercury is poured into the container first and then water is added into the thin tube until it reaches a depth of 70 cm.

a) By how much does the mercury in the big tube rise?

b) By how much does the mercury in the thin tube fall?

c) If the water is poured into the wide tube, what is the difference in height of the mercury level between the narrow tube and the wide tube?



Homework Equations


P=hρg
(though I think no calculations are needed)


The Attempt at a Solution


I really have no idea on how to do this, but I'm guessing that the heights are the same since the pressure is the same?
Please help! This is my own revision and not a homework because my physics paper for my o-level is coming next week.
 
Last edited:
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  • #2
Is the situation a U-tube manometer with a diameter change?
 
  • #3
It's as stated a container with diameter change.
What I understand is that the pressure is not affected by shape.
So the heights should be equal, right?
The problem is I don't know how to get the length.
 

1. What is pressure in liquids?

Pressure in liquids refers to the force per unit area that is exerted by a liquid on its container or any object immersed in it. It is caused by the weight of the liquid and is measured in units of force per unit area, such as pounds per square inch (psi) or pascals (Pa).

2. How is pressure in liquids different from pressure in gases?

The main difference between pressure in liquids and pressure in gases is that liquids are virtually incompressible, meaning they cannot be easily compressed or squeezed into a smaller volume. This is due to the strong intermolecular forces between liquid particles. On the other hand, gases are highly compressible, meaning they can easily change their volume when subjected to pressure.

3. What factors affect pressure in liquids?

The pressure in a liquid is affected by the depth or height of the liquid, the density of the liquid, and the acceleration due to gravity. In a closed container, the pressure is also affected by the volume of the liquid and the temperature.

4. How does pressure in liquids change with depth?

According to Pascal's principle, the pressure in a liquid increases with depth. This is because the weight of the liquid above exerts a force on the liquid below, causing an increase in pressure. The increase in pressure is directly proportional to the depth of the liquid.

5. What is the practical application of pressure in liquids?

Pressure in liquids has many practical applications, such as in hydraulic systems and hydraulic brakes used in vehicles. It is also used in measuring devices like barometers and manometers, and in industries that involve the transfer of liquids, such as pumping and irrigation systems.

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