Question

A “U” shaped tube (with a constant radius) is filled with water and oil as shown. The water is a height h1 = 0.39 m above the bottom of the tube on the left sideof the tube and a height h2 = 0.14 m above the bottom of the tube on the right side of the tube. The oil is a height h3 = 0.32 m above the water. Around the tubethe atmospheric pressure is PA = 101300 Pa. Water has a density of 1000 kg/m3.
1)What is the absolute pressure in the water at the bottom of the tube?

2)What is the absolute pressure in the water right at the oil-water interface?

3)What is the density of the oil?

Now the oil is replaced with a height h₃ = 0.32 m of glycerin which has a density of 1261 kg/m³.Assume the glycerin does not mix withthe water and the total volume of water is the same as before.

4) Now what is the absolute pressure in the water at the interface between the water and glycerin?
5)How much higher is the top of the water in the tube compared to the glycerin?(labeled d in the diagram)

6)What is the absolute pressure in the water at the very bottom of the tube?

Answer 1

Let Po be atmospheric pressure and let p be the pressure at the bottom of the tube.The densities of the two fluids are pwater and poil(which is less thanwater).For each fluid we have
P = Po + pwater * g * hwater
P = Po + poil * g * hoil
Since the pressure P at the bottom of the tube is the same for both fluids,we set these two expressions equal to each other and solve for hoil in terms ofhwater.The result is
hoil = pwater/poil * hwater
Sine oil is less dense than water,the ratio pwater/poil is greater than unity and hoil is greater than hwater.This result makes sense:a greater height ofloe density oil is needed to produce the same pressure P at the bottom of the tube.