Water and oil are poured into opposite sides of an open...

Water and oil are poured into opposite sides of an open U-shaped tube. The oil and water meet at the exact center of the U at the bottom of the tube. If the column of oil of density $900 \mathrm{kg} / \mathrm{m}^{3}$ is $16 \mathrm{cm}$ high on one side, how high is the water on the other side?

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Key Concepts

Fluid Density

Fluid density is a measure of the mass of a fluid per unit volume. It is a key factor in determining the hydrostatic pressure a fluid column can exert, as fluids with greater density exert more pressure at a given height than less dense fluids. Understanding density is essential for comparing how different fluids, such as water and oil, behave under the influence of gravity within the same system.

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium at any point within the fluid due to the force of gravity. It is given by the equation P = ?gh, where ? is the fluid density, g is gravitational acceleration, and h is the depth of the fluid. This principle allows us to determine the pressure at various points in a stationary fluid and is critical in analyzing systems where different fluids are subjected to gravity.

Pressure Equilibrium in Connected Vessels

In a system of connected vessels, especially those containing different fluids, pressure equilibrium dictates that the pressure at a common interface or the same horizontal level must be equal for the system to be at rest. This concept ensures that any discrepancies in pressure due to differences in density are balanced by differences in column height, enabling accurate calculations in setups like U-tube devices.

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