A U-tube contains two fluids with densities ρ1 = 1070 kg/m3 and ρ2 = 595 kg/m3 as sketched below. What is the difference d in the heights of the top surfaces of the two fluids?

I would need to see the sketch to know where the interface of the two materials is located.

To find the difference d in the heights of the top surfaces of the two fluids, you can use the concept of pressure difference.

The pressure at any point in a fluid column depends on the density of the fluid and the height of the column. The pressure difference between two points in a fluid column is given by the formula ΔP = ρgh, where ΔP is the pressure difference, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height difference between the two points.

In this case, the two fluids in the U-tube have different densities, ρ1 = 1070 kg/m3 and ρ2 = 595 kg/m3. The pressure at the top surfaces of the two fluids are atmospheric pressure, which is the same on both sides of the U-tube.

Since the pressure at the top surfaces of the fluids are the same, the pressure difference between the top surfaces is zero. Therefore, the height difference, d, can be calculated using the formula ΔP = ρgh.

0 = (ρ1 - ρ2)gh

Solving for d:
d = 0 / ((ρ1 - ρ2)g)
= 0

So, the difference in the heights of the top surfaces of the two fluids, d, is zero.