The water in a tank is pressurized by air, and the pressure...

The water in a tank is pressurized by air, and the pressure is measured by a multifluid manometer as shown in Fig. P1-50. Determine the gage pressure of air in the tank if $h_{1}=0.2 \mathrm{m}, h_{2}=0.3 \mathrm{m},$ and $h_{3}=0.4 \mathrm{m} .$ Take the densities of water, oil, and mercury to be $1000 \mathrm{kg} / \mathrm{m}^{3}, 850 \mathrm{kg} / \mathrm{m}^{3},$ and $13,600 \mathrm{kg} / \mathrm{m}^{3},$ respectively.

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Key Concepts

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest due to the force of gravity. It is proportional to the density of the fluid, gravitational acceleration, and the height of the fluid column. This concept is pivotal in analyzing and calculating pressure drops or gains in fluid columns, such as those found in manometers.

Manometers

Manometers are devices used to measure pressures by balancing the weight of a fluid column against the pressure difference. An understanding of how different fluids contribute to pressure due to their varying densities is essential for interpreting readings from these instruments.

Multifluid Manometer Analysis

In multifluid manometers, different fluids are used in series within the same instrument, each contributing differently to the overall pressure reading. The analysis involves applying the hydrostatic pressure principle to each fluid segment, accounting for variations in density and height changes between the fluids.

Gage Pressure

Gage pressure is the pressure measurement relative to the atmospheric pressure. It represents how much a measured pressure deviates from the ambient atmospheric pressure, which is critical in practical applications where only the additional pressure is of interest.

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