U-Shaped Tube Pressure Problem

In summary, a U-shaped tube containing mercury is open to the air on both ends. When water is poured into the left arm, the water column is 10 cm deep. The question asks for the distance that the mercury in the right arm rises from its initial position. Using the equations for pressure and density, the correct answer is x/2. This is because the water causes the mercury on the left side to go down, and the mercury on the right side to go up by the same amount. Therefore, the difference in heights between the new level on the right and the original level on the right is half of the calculated value for x.
  • #1
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Homework Statement


A U shaped tube, open to the air on both ends, contains mercury. Water is poured into the left arm until the water column is 10 cm deep. How far upward from its intitial position does the mercury in the right arm rise?


Homework Equations





The Attempt at a Solution



h is the height of mercury on the left side of the tube
x is the distance that the mercury moves up

101300 Pa + (1000kg/m^3)(9.80)(.10m) + (13600kg/m^3)(9.80)h= 101300 Pa + (13,600kg/m^3)(9.80)(h+x)

980 + 133280h = 133280h + 133280x
980=133280x
x= .00735m = .735cm I'm not sure if I did this correctly--this answer seems quite small
 
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  • #2
Hi bcjochim07,

It looks to me like you are answering the wrong question. In your equation x is the distance the top of the mercury is above the bottom of the water on the other side. However, they are asking for how much the mercury rose up above where it was before the water was poured in.
 
  • #3
101300 Pa + (1000kg/m^3)(9.80)(.10m) = 101300 Pa + (13,600kg/m^3)(9.80)(x)

finally,

result: x/2


hint: you don't need to write the same pressure both side. draw a horizontal line from top of the lowest height side of most bottom liquid. And calculate the pressures for only the upper side of line which you draw.
ejhgmh.jpg
 
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  • #4
What did you mean by x/2? I got the same number for x using your equation that I did mine. I really didn't need to put the h in.
 
  • #5
x in your equation is the distance above the bottom of the water (where the purple line is in volcano's post). Pouring in the water pushes the mercury level down on the left side, and up on the right side. You found the difference in heights between the mercury levels on the left and right side; they want the difference in height between the new level on the right and the original level on the right.
 
  • #6
If I try to visualize how it was before the water was added, I would just distributed the mercury evenly, so would I divide my answer by two then?
 
  • #7
How much down(x/2), so much up(x/2) both sides. Think this, if one side down 10cm, how much rise other side? What is the distance difference between both sides?
 

1. What is the U-Shaped Tube Pressure Problem?

The U-Shaped Tube Pressure Problem is a scientific experiment that demonstrates the principles of fluid pressure. It involves a U-shaped tube filled with a liquid and two different heights of liquid on each side of the tube. The pressure at the bottom of the tube is measured to determine the difference in pressure between the two sides.

2. How does the U-Shaped Tube Pressure Problem work?

The U-Shaped Tube Pressure Problem works by using the principles of hydrostatics, which is the study of fluids at rest. The liquid in the tube exerts pressure on the bottom of the tube, and this pressure is transmitted equally throughout the liquid. This causes the liquid to rise to different heights on each side of the tube, depending on the pressure exerted by the liquid.

3. What is the purpose of the U-Shaped Tube Pressure Problem?

The U-Shaped Tube Pressure Problem is used to demonstrate the relationship between the height of a liquid and the pressure it exerts. It is also used to show how liquids will seek their own level due to the equal distribution of pressure throughout the liquid.

4. What are some real-life applications of the U-Shaped Tube Pressure Problem?

The U-Shaped Tube Pressure Problem has many real-life applications, including in the design of hydraulic systems, such as car brakes and elevators. It is also used in the design of water distribution systems and in medical devices, such as blood pressure cuffs.

5. Can the U-Shaped Tube Pressure Problem be used to measure the pressure of gases?

No, the U-Shaped Tube Pressure Problem can only be used to measure the pressure of liquids. This is because gases are compressible, while liquids are not. The pressure exerted by gases would vary depending on the volume of the container, making it difficult to accurately measure the pressure using this method.

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