A mercury manometer (ρ=13,600 kg / m^3) is connected to an air duct to measure the pressure insi

step 1 Atmospheric pressure is given by... Total pressure is given by atmospheric pressure plus row GH.

A mercury manometer (ρ=13,600 kg / m^3) is connected to an...

A mercury manometer $\left(\rho=13,600 \mathrm{kg} / \mathrm{m}^{3}\right)$ is connected to an air duct to measure the pressure inside. The difference in the manometer levels is $15 \mathrm{mm},$ and the atmospheric pressure is 100 kPa. $(a)$ Judging from Fig. $\mathrm{P} 1-67,$ determine if the pressure in the duct is above or below the atmospheric pressure. ( $b$ ) Determine the absolute pressure in the duct.

Key Concepts

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at rest due to the force of gravity. It is directly proportional to the density of the fluid, the acceleration due to gravity, and the vertical height (or depth) within the fluid. In practical applications, the difference in fluid heights within a manometer is used to calculate the pressure difference between two points using the hydrostatic pressure principle.

Manometer Operation

A manometer is a device that measures fluid pressure by balancing the weight of a column of liquid between two different pressure environments. The difference in height of the liquid columns, often observed in U-shaped tubes or inclined tubes, is used to determine the pressure difference between the points being measured. This device is fundamental in fluid mechanics to measure small pressure differences accurately.

Gauge Pressure vs. Absolute Pressure

Gauge pressure is the pressure relative to the ambient atmospheric pressure. When measuring with a manometer, the differential reading (linked to the fluid column height difference) provides the gauge pressure. To find the absolute pressure, which represents the total pressure including atmospheric pressure, the gauge pressure is added to the atmospheric pressure.

Pressure Measurement in Fluid Systems

This concept involves understanding how fluid properties, such as density, and the physical dimensions of the manometer (such as the height difference) interact to produce a measurable pressure difference. The calculation typically employs the hydrostatic equation to relate the height difference in the manometer to the pressure difference, allowing for practical determination of pressures in various systems.

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