Hydrostatics, find length of kerosene column in U tube

In summary, the conversation discusses a scenario where a glass tube is bent into a U shape and water is poured into it. The water stands at 12 cm on each side and kerosene is slowly added to one side until the water on the other side raises by 5 cm. The question is what is the length of the kerosene column. The attempt at a solution involves using the equation (ρhg)1 = (ρhg)2 with given values, but the textbook answer is different. A sketch is made to clarify the scenario and it is determined that one side has 17 cm of water and the other has only 7 cm with h cm of kerosene above it. The pressure at the bottom is then
  • #1
Ishraq Begum
13
3

Homework Statement


A glass tube is bent into a U shape. Water is poured into the tube until it sands 12 cm high on each side. Kerosene (density = 870 kg/m3) is added slowly to one side until water on the other side raises 5 cm. What is the length of kerosene column?

Homework Equations


(ρhg)1 = (ρhg)2

The Attempt at a Solution


Taking h1 = 17 cm
then h2 = (17 ⋅ 1000) / 870
so, h2 = 19.5
but the answer in the textbook is given as 11.5
 
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  • #2
In the end, is one side purely water and the other purely kerosene? Make a sketch.
 
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  • #3
gneill said:
In the end, is one side purely water and the other purely kerosene? Make a sketch.
https://ibb.co/iVWqXR
It is something like this.
 
  • #4
Ishraq Begum said:
https://ibb.co/iVWqXR
upload_2018-1-12_10-43-17.png

It is something like this.
Okay, and do your calculations reflect that scenario?
 

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  • upload_2018-1-12_10-43-17.png
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  • #5
There are 17 cm of water on one side, and only 7 cm of water on the other side, with h cm of kerosene above the water on that side. What is the pressure at the bottom, as determined by the heights of the fluids on the two sides sides?
 

1. How does hydrostatics affect the length of a kerosene column in a U-tube?

Hydrostatics is the study of fluids at rest and the pressure exerted by these fluids. In the case of a U-tube filled with kerosene, the height of the kerosene column is determined by the balance of pressure at the two ends of the tube. This means that the length of the kerosene column will be affected by changes in pressure or height on either side of the tube.

2. What factors influence the length of the kerosene column in a U-tube?

The length of the kerosene column in a U-tube is determined by the density of kerosene, the height difference between the two sides of the tube, and the atmospheric pressure. These factors all contribute to the overall pressure exerted on the kerosene and therefore affect its height in the tube.

3. How can the length of the kerosene column in a U-tube be calculated?

The length of the kerosene column in a U-tube can be calculated using the equation P1ρ1h1 = P2ρ2h2, where P is pressure, ρ is density, and h is height. This equation takes into account the pressure and height on both sides of the tube to determine the length of the kerosene column.

4. Can the length of the kerosene column change over time?

Yes, the length of the kerosene column in a U-tube can change over time due to changes in atmospheric pressure or changes in the density of the kerosene. For example, if the temperature increases, the kerosene will expand and the length of the column will increase.

5. How is the length of the kerosene column affected by the shape of the U-tube?

The shape of the U-tube does not affect the length of the kerosene column. As long as the tube is closed and there are no leaks, the pressure and height on both sides of the tube will remain the same, resulting in a consistent length for the kerosene column.

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