At a height of 10 km ( 33000 ft ) above sea level,...

At a height of $10 \mathrm{~km}$ ( $33000 \mathrm{ft}$ ) above sea level, atmospheric pressure is about $210 \mathrm{~mm}$ of mercury. What is the net resultant normal force on a $600 \mathrm{~cm}^{2}$ window of an airplane flying at this height? Assume the pressure inside the plane is $760 \mathrm{~mm}$ of mercury. The density of mercury is $13600 \mathrm{~kg} / \mathrm{m}^{3}$.

Key Concepts

Density of Fluids in Pressure Calculations

The density of a fluid, such as mercury, plays a key role in converting measurements of height in a fluid column (like in mm Hg) to pressure in Pascals. This relationship, often derived from the hydrostatic pressure equation, is essential when linking the properties of a fluid to the pressure it exerts.

Force Calculation from Pressure

The net force on a surface due to a pressure difference is calculated by multiplying the differential pressure by the surface area over which it acts. This principle is widely applicable in physics and engineering, particularly when evaluating forces on structures such as airplane windows, where pressure differences can create substantial forces.

Pressure Differential

This concept involves recognizing that a difference in pressure on opposite sides of a surface results in a net force. In many contexts, such as in airplane cabin design, the internal pressure can be significantly higher than the external atmospheric pressure, leading to stress on the structure due to the pressure differential.

Unit Conversion

Understanding unit conversion is crucial when calculations involve different measurement systems. In pressure problems, it is often necessary to convert units like millimeters of mercury (mm Hg) to the SI unit of pressure, Pascals (Pa). Additionally, converting area from units such as square centimeters (cm²) to square meters (m²) ensures that the mathematical operations yield a result in standard SI units.

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