Fluid Mechanics seventh edition by Frank M. White · Problem 2.14

The key to this problem is hydrostatic pressure balance: pressure must be equal at any given horizontal level within a connected fluid system. Start by identifying a reference level (usually the interface between two liquids) and write pressure equations on both sides of the system, accounting for the weight of each liquid column. Since the liquids have different densities, equal heights don't mean equal pressures—you'll need to use $P = \rho g h$ for each column and set pressures equal at a common depth to solve for the unknown heights.

The key to this problem is hydrostatic pressure balance: pressure must be equal at any given horizontal level within a connected fluid system. Start by identifying a reference level (usually the interface between two liquids) and write pressure equations on both sides of the system, accounting for the weight of each liquid column. Since the liquids have different densities, equal heights don't mean equal pressures—you'll need to use $P = \rho g h$ for each column and set pressures equal at a common depth to solve for the unknown heights.