Height of oil of above water U cylinders

[coldsteel]

An open U shaped tube is initially partially filled with water (ρ=1000 kg/m^3). A 10 cm high column of oil (ρ=800 kg/m^3) is poured into the right side of the tube. What is the height of the oil above the water?



I set the water and oil equal to each other. (800)(10)(9.8)=(1000)(H)(9.8)



Using that equation I solved for H to get 8 cm. I then took 10cm the height of oil - the 8 cm from the water to get 2cm. Is this correct?

 

[haruspex]

Yes, that's the right logic.

 

[coldsteel]

so 2cm is the correct answer?

 

[haruspex]

so 2cm is the correct answer?

Yes.

 

[Nickie]

Yes, your method and answer are correct. By setting the pressures of the water and oil equal to each other, you are using the principle of hydrostatic equilibrium to determine the height of the oil above the water. Your calculation shows that the height of the oil above the water is 2 cm. This means that the oil is floating on top of the water, with a height difference of 2 cm between the two liquids. This is a common phenomenon in liquids with different densities, where the less dense liquid will sit on top of the more dense liquid.