Question

How can pressure units like millimeters of mercury, centimeters of water, and inches of mercury be converted into units like newtons per meter squared without using a table of pressure conversion factors?

a) By using specific gravity.
b) By using Archimedes' principle.
c) By using Boyle's law.
d) By using the equation P = F/A.

Answer 1

To convert pressure units like mmHg, cmH2O, and inHg to N/m², multiply the height of the liquid column by the liquid's density and by the acceleration due to gravity, then perform the appropriate unit conversions.

Step-by-step explanation:

To convert pressure units like millimeters of mercury (mmHg), centimeters of water (cmH2O), and inches of mercury (inHg) into newtons per meter squared (N/m²), we use the equation P = F/A, where P is pressure, F is force, and A is area. This equation takes into account the gravitational force exerted by the column of liquid (whether mercury or water) and the area over which it acts. To calculate the pressure in N/m², we need to multiply the height of the liquid column by the density of the liquid (for mercury or water) and by the acceleration due to gravity (g = 9.81 m/s²).

For example, if we had a pressure of 760 mmHg, we would calculate the pressure as follows:

• Convert the height into meters: 760 mm * (1 m / 1000 mm) = 0.76 m.
• Multiply the height by the density of mercury (≈ 13.6 g/cm³ or 13600 kg/m³) and the acceleration due to gravity (g = 9.81 m/s²); 0.76 m * 13600 kg/m³ * 9.81 m/s².
• Perform the calculation to get the result in N/m²: 0.76 m * 13600 kg/m³ * 9.81 m/s² = 101325 N/m².

Similarly, this process can be applied to convert pressures in cmH2O or inHg to N/m² by using the respective densities of water and mercury and their respective heights.