At sea level, average atmospheric pressure is about 14.7 pounds per square inch (psi)

/ Exams & Certification / By

At sea level, average atmospheric pressure is about 14.7 pounds per square inch (psi). At altitude, pressure decreases. As the pressure decreases, there are fewer air molecules in a given volume. Therefore, baseballs fly farther at Coors Field in Denver (elevation = 5280 feet) than at sea level, and it is very difficult to breathe on Mt. Everest (elevation = 29,035 feet). Create a spreadsheet that allows a user to input an elevation between
0 and 50,000 feet and estimates the atmospheric pressure based on Table P2.19. Use linear interpolation to estimate values between the data points shown in the table. If a value of less than 0 or greater than 50,000 feet is entered, then “Out of Range” should be displayed in the spreadsheet.

The correct answer and explanation is:

To create a spreadsheet that estimates the atmospheric pressure based on the elevation, we can follow a few steps. Here’s an overview of how to set it up, including linear interpolation for pressure estimation.

Steps to Create the Spreadsheet:

  1. Data Table Setup: You will first need a table with known elevations and corresponding atmospheric pressures. The data for atmospheric pressure at different elevations is typically available from atmospheric tables like Table P2.19, which lists pressure in relation to elevation. For the sake of this example, here’s a small sample of the table (you would need to expand this based on actual data from the source you are using): Elevation (ft) Pressure (psi) 0 14.7 1,000 14.2 5,000 12.5 10,000 11.0 20,000 8.0 30,000 4.8 50,000 1.5
  2. Linear Interpolation: To estimate the pressure at any given elevation, you can use the linear interpolation formula: P(x)=P1+(P2−P1E2−E1)⋅(x−E1)P(x) = P_1 + \left( \frac{{P_2 – P_1}}{{E_2 – E_1}} \right) \cdot (x – E_1) Where:
    • P(x)P(x) is the atmospheric pressure at the desired elevation.
    • P1P_1 and P2P_2 are the pressures at the two known points closest to the desired elevation.
    • E1E_1 and E2E_2 are the elevations of those two points.
    • xx is the input elevation between E1E_1 and E2E_2.
    This formula assumes that the relationship between elevation and pressure is linear between two adjacent data points.
  3. Handling Input Outside the Table Range: If the user enters an elevation that is less than 0 feet or greater than 50,000 feet, you should display “Out of Range”. You can use an IF statement to check for this condition. Example formula for the pressure (assuming user input is in cell A2 and the elevation data is in cells B2:B7 and C2:C7): =IF(OR(A2<0, A2>50000), "Out of Range", (C2 + (C3 - C2) / (B3 - B2) * (A2 - B2))) In this formula:
    • A2 is the elevation the user inputs.
    • B2:B7 is the list of elevations.
    • C2:C7 is the corresponding list of pressures.
    The formula checks if the input is within the acceptable range (0 to 50,000 feet). If not, it displays “Out of Range”. Otherwise, it performs linear interpolation based on the known data points.

Explanation:

  • Interpolation: Linear interpolation is used because it provides an estimate between two known values. It assumes that the change in atmospheric pressure between two data points is approximately linear.
  • Handling Out of Range Values: By setting conditions in the formula, the spreadsheet can give an error message (“Out of Range”) if the input exceeds the bounds of 0 to 50,000 feet.
  • User Input: The user can simply enter an elevation between 0 and 50,000 feet, and the spreadsheet will compute the corresponding atmospheric pressure.

Explanation:

Atmospheric pressure decreases with altitude, meaning that at higher elevations, the air becomes thinner, and it is harder to breathe. The relationship between pressure and elevation is not perfectly linear, but for practical purposes, a linear approximation is often used. By creating a spreadsheet that uses linear interpolation, we can estimate the atmospheric pressure at any elevation between 0 and 50,000 feet based on the known pressure values at specific elevations.

To perform linear interpolation, the difference in pressure between two known data points is divided by the difference in elevation, and then this ratio is multiplied by the difference between the target elevation and the lower known elevation. This gives an estimate of the pressure at the target elevation.

The spreadsheet uses IF statements to ensure that the input elevation is within the valid range of 0 to 50,000 feet. If the input is out of range, the spreadsheet will display “Out of Range” to inform the user. If the input is valid, the formula computes the interpolated pressure. This setup allows users to input any elevation within the specified range and get an estimated pressure value in real time.

This method is especially useful for environments like Coors Field in Denver or Mt. Everest, where the atmospheric pressure significantly impacts the performance of activities like sports or climbing. By having a tool like this, individuals can better understand how pressure changes with elevation and make necessary adjustments for their needs, such as equipment calibration or physical conditioning.

Related Posts

Scroll to Top