The U-tube manometer shown in Fig. P 2.36 has two fluids,...

The U-tube manometer shown in Fig. $P 2.36$ has two fluids, water and oil $(S=0.80) .$ Find the height difference between the free water surface and the free oil surface with no applied pressure difference.

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Key Concepts

Specific Gravity

Specific gravity is a dimensionless quantity that expresses the ratio of the density of a fluid to a reference density, typically that of water. It is used to determine the actual density of a fluid when compared to water, which is essential when working with fluids of differing densities in hydrostatic systems such as mixed-fluid manometers.

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at rest due to the force of gravity. It is calculated as the product of the fluid’s density, gravitational acceleration, and the height of the fluid column. In U-tube manometers, this concept is central because the pressure difference in the fluid columns is related directly to the differences in heights and densities of the fluids.

Manometer Principle

A manometer is a device used to measure pressure differences by using columns of fluid in equilibrium. In its operation, it relies on the principle that the pressure at the same horizontal level in a continuous fluid must be the same, which allows for the determination of pressure differences by measuring the difference in heights of fluid columns. This principle is applied to relate the height differences of fluids with different densities in a U-tube.

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