Find the gauge and absolute pressures in the balloon and...

Find the gauge and absolute pressures in the balloon and peanut jar shown in Figure 11.19, assuming the manometer connected to the balloon uses water whereas the manometer connected to the jar contains mercury. Express in units of centimeters of water for the balloon and millimeters of mercury for the jar, taking $h=0.0500 \mathrm{m}$ for each.

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at equilibrium due to the force of gravity. In practice, it is calculated as the product of the liquid’s density, gravitational acceleration, and the height of the fluid column. This concept is fundamental in understanding fluid statics, calculating pressure differences in manometers, and converting height measurements into pressure units.

Manometer Principle

A manometer is an instrument used to measure pressure based on the height of a liquid column. The working principle relies on the hydrostatic balance where differences in liquid column heights correspond to differences in pressure. Manometers can use different fluids, such as water or mercury, and the choice of fluid affects the sensitivity and unit conversion of the measurement, linking the pressure difference to the height difference according to the liquid's density.

Gauge Pressure

Gauge pressure is the pressure measured relative to an ambient atmospheric pressure. It represents the difference between the internal pressure of a system and the external atmospheric pressure, and is commonly used in devices like manometers to assess whether the pressure inside a container is above or below the ambient condition. This concept helps in understanding forces exerted on the container walls and is critical for designing pressure vessels.

Absolute Pressure

Absolute pressure is the total pressure within a system measured relative to a perfect vacuum. It is obtained by adding the atmospheric pressure to the gauge pressure. This measurement is essential in many practical applications where knowing the total pressure acting on or within a system is necessary for accurate analysis and design, especially in fluid mechanics and thermodynamics.

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