What happens if in each branch we have immiscible liquids of different densities like water and oil?
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We have liquid A with density dA and liquid B with density dB.
In the visual we fix density dA, but the density of liquid B can be varied.
For the density at point O to be the same as the density at point R,
the heights of the liquid in the two branches must be different:

If liquid B is more dense than liquid A, height hB should be less than height hA and in a proportion determined by the densities.
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