Problem 6 - Applied Physics

Question

A barometer in the Rocky Mountains reads \(516 \mathrm{~mm}\) of mercury. Find this pressure (a) in \(\mathrm{kPa}\) and \((\mathrm{b})\) in \(\mathrm{lb} / \mathrm{in}^{2}\).

Step-by-Step Solution

Answer

The pressure is 68.81 kPa and 9.98 psi.

Step 1: Understand the Problem

We are given a barometric pressure reading of 516 mmHg. We need to convert this pressure into two different units: first into kilopascals (kPa) and then into pounds per square inch (psi).

Step 2: Convert mmHg to kPa

Pressure in mmHg can be converted to kPa using the conversion factor: 1 mmHg = 0.133322 kPa.\[\text{Pressure in kPa} = 516 \text{ mmHg} \times 0.133322 \frac{\text{kPa}}{\text{mmHg}}\]Calculate the multiplication to find the pressure in kPa.

Step 3: Calculate Pressure in kPa

Perform the multiplication:\[516 \times 0.133322 = 68.809512 \text{ kPa}\]Thus, the pressure is approximately 68.81 kPa.

Step 4: Convert mmHg to psi

Pressure in mmHg can also be converted to psi using the conversion factor: 1 mmHg = 0.0193368 psi.\[\text{Pressure in psi} = 516 \text{ mmHg} \times 0.0193368 \frac{\text{lb/in}^2}{\text{mmHg}}\]Multiply to find the pressure in psi.

Step 5: Calculate Pressure in psi

Perform the multiplication:\[516 \times 0.0193368 = 9.9797568 \text{ psi}\]The pressure is approximately 9.98 psi.

Key Concepts

Barometric Pressure

Barometric pressure is a fundamental concept in meteorology. It refers to the amount of atmospheric pressure exerted by the weight of air above a specific point on Earth's surface. Typically measured using a barometer, it can provide essential information, such as weather forecasting and altitude determination. To measure this pressure, traditional barometers often utilize liquid mercury, which is where the term "mmHg" (millimeters of mercury) comes from. For instance, a reading of 516 mmHg indicates that the atmospheric pressure can support a column of mercury that is 516 millimeters high. Understanding how barometric pressure works helps you comprehend how different regions experience varying atmospheric conditions, affecting everything from weather patterns to the functioning of your body at different altitudes.

Unit Conversion

Unit conversion is vital in scientific calculations to ensure consistent and accurate results across various systems of measurement. In the realm of pressure, converting units means changing the measurement from one scale to another—like moving from millimeters of mercury (mmHg) to kilopascals (kPa) or pounds per square inch (psi). When tackling a conversion problem:

• Identify the original measurement and its unit.
• Find the appropriate conversion factor that links the original unit to the desired unit.
• Multiply the original measurement by the conversion factor to obtain the result in the new unit.

For example, converting 516 mmHg to kilopascals involves using the conversion factor 1 mmHg = 0.133322 kPa.

Kilopascal

A kilopascal (kPa) is a metric unit for measuring pressure and is part of the International System of Units (SI). Used commonly in many scientific and engineering applications, it provides a precise measure of pressure in terms of energy per unit volume. Here's why kilopascals can be significant:

• They allow for easy comparison and conversion in scientific equations.
• Offer precise measurement useful in atmospheric studies and applied sciences.
• Preferred in many countries adopting the metric system for consistency.

To convert 516 mmHg to kPa, multiply by 0.133322 to get approximately 68.81 kPa. This conversion provides a standardized measurement that is globally understood by professionals and academics alike.

Pounds per Square Inch

Pounds per square inch (psi) is another common unit for pressure, especially in engineering contexts within the United States and other countries that use the imperial system. Psi measures the force exerted on an area of one square inch. It's frequently used for tire pressure, hydraulic systems, and more. Understanding psi includes:

• Recognizing its application in mechanical and engineering settings.
• Converting to and from psi when using different measurement systems.
• Using psi for practical, everyday applications like inflating tires or checking water pressure.

For example, converting 516 mmHg to psi involves multiplying by 0.0193368, yielding approximately 9.98 psi, which shows the pressure in terms suitable for many practical applications.