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There is a beaker with two liquids placed above another. The beaker has a hole at bottom. So can I use Bernoulli equation across the interface of liquids.

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The bernoulli equation can be used only on a single ideal fluid at a time, since changing the density of the fluid while using the equation is wrong.
But you can still use them separately with the two fluids, while using bernoulli equation to find the pressure at the interface of the liquid. And since the interface is this, you can give the argument that pressure just above and just below the interfsce is approximately equal, and this will help you find the pressure at any point in the second fluid.

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