Hydrostatics, find length of kerosene column in U tube

AI Thread Summary
A U-shaped glass tube contains water at 12 cm on both sides, and kerosene is added to one side, causing the water level on the other side to rise by 5 cm. The density of kerosene is 870 kg/m3, and the relationship between the heights of the fluids is expressed through the equation (ρhg)1 = (ρhg)2. The initial calculations suggested a kerosene height of 19.5 cm, but the textbook answer is 11.5 cm. Clarification is needed on whether one side contains only water and the other only kerosene, as this affects the pressure calculations at the bottom of the tube. Accurate pressure determination requires considering the heights of both fluids on each side of the tube.
Ishraq Begum
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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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In the end, is one side purely water and the other purely kerosene? Make a sketch.
 
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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.
 
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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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?
 
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