pounds per square inch (psi) to millimeters of mercury (mmHg) conversion

What is pounds per square inch?

Pounds per square inch (psi) is a unit of pressure that's commonly used, especially in the United States. Understanding what it represents and how it's derived helps to grasp its significance in various applications.

Definition of Pounds per Square Inch (psi)

Pounds per square inch (psi) is a unit of pressure defined as the amount of force in pounds (lbs) exerted on an area of one square inch ($in^2$).

$$Pressure (psi) = \frac{Force (lbs)}{Area (in^2)}$$

How psi is Formed

Psi is derived by dividing the force applied, measured in pounds, by the area over which that force is distributed, measured in square inches. It's a direct measure of force intensity. For example, 10 psi means that a force of 10 pounds is acting on every square inch of the surface.

Applications and Examples of psi

• Tire Pressure: Car tires are typically inflated to 30-35 psi. This ensures optimal contact with the road, fuel efficiency, and tire wear.

• Compressed Air Systems: Air compressors used in workshops and industries often operate at pressures of 90-120 psi to power tools and equipment.

• Hydraulic Systems: Hydraulic systems in heavy machinery (like excavators and cranes) can operate at thousands of psi to generate the immense force needed for lifting and moving heavy loads. Pressures can range from 3,000 to 5,000 psi or even higher.

• Water Pressure: Standard household water pressure is usually around 40-60 psi.

• Scuba Diving Tanks: Scuba tanks are filled with compressed air to pressures of around 3,000 psi to allow divers to breathe underwater for extended periods.

Pascal's Law and Pressure Distribution

Pascal's Law is relevant to understanding pressure in fluids (liquids and gases). Blaise Pascal was a French mathematician, physicist, and philosopher. Pascal's Law states that pressure applied to a confined fluid is transmitted equally in all directions throughout the fluid. This principle is fundamental to hydraulics and pneumatic systems where pressure is used to transmit force. Pascal's Law can be summarized as:

A change in pressure at any point in a confined fluid is transmitted undiminished to all points in the fluid.

More formally:

$$\Delta P = \rho g \Delta h$$

Where:

• $\Delta P$ is the hydrostatic pressure difference (in Pascals or psi)
• $\rho$ is the fluid density (in $kg/m^3$ or $lbs/in^3$)
• $g$ is the acceleration due to gravity (approximately $9.81 m/s^2$ or $32.2 ft/s^2$)
• $\Delta h$ is the height difference (in meters or inches)

For more information, you can refer to this excellent explanation of Pascal's Law at NASA

What is millimeters of mercury?

Millimeters of mercury (mmHg) is a unit of pressure, often used in medicine (especially blood pressure) and meteorology. It represents the pressure exerted by a column of mercury one millimeter high at a standard temperature. Let's delve into its definition, history, and applications.

Definition and Formation

Millimeters of mercury (mmHg) is a manometric unit of pressure. Specifically, it's the pressure exerted at the base of a column of mercury exactly 1 millimeter high when the density of mercury is 13,595.1 kg/m³ and the local acceleration of gravity is exactly 9.80665 m/s². It's not an SI unit, but it is accepted for use with the SI.

While not an official SI unit (Pascal is the SI unit for pressure), mmHg remains widely used due to its historical significance and practical applications, especially in fields like medicine.

History and Torricelli's Experiment

The unit originates from Evangelista Torricelli's experiments in the 17th century. Torricelli, an Italian physicist and mathematician, invented the mercury barometer in 1643. He filled a glass tube with mercury and inverted it into a dish of mercury. The mercury column would fall, leaving a vacuum at the top, and the height of the column was proportional to the atmospheric pressure. This led to the standardized measurement of pressure using the height of a mercury column. Read more about it in Britannica.

Relation to Other Units

• Pascal (Pa): The SI unit of pressure. 1 mmHg is approximately equal to 133.322 Pascals.

  $$1 \, mmHg \approx 133.322 \, Pa$$

• Atmosphere (atm): A standard unit of pressure. 1 atm is equal to 760 mmHg.

  $$1 \, atm = 760 \, mmHg$$

• Torr: Named after Torricelli, 1 Torr is very close to 1 mmHg. For most practical purposes, they are considered equivalent.

  $$1 \, Torr \approx 1 \, mmHg$$

Real-World Examples and Applications

• Blood Pressure: In medicine, blood pressure is commonly measured in mmHg. For example, a blood pressure reading of 120/80 mmHg indicates a systolic pressure of 120 mmHg and a diastolic pressure of 80 mmHg. The first number represents the pressure in the arteries when the heart beats (systolic pressure) and the second number represents the pressure in the arteries between beats (diastolic pressure).

• Atmospheric Pressure: Meteorologists often use mmHg to report atmospheric pressure. Standard atmospheric pressure at sea level is 760 mmHg. Changes in atmospheric pressure are often precursors to changes in weather.

• Vacuum Gauges: Many vacuum gauges, particularly older or specialized instruments, display pressure in mmHg. Low pressures in vacuum systems, such as those used in scientific experiments or manufacturing processes, are often expressed in mmHg or fractions thereof (e.g., milliTorr, which is approximately 1/1000 of a mmHg).

• Aircraft Altimeters: Aircraft altimeters use atmospheric pressure to determine altitude. While the actual scale on the altimeter might be in feet or meters, the underlying pressure measurement is often related to mmHg.

Important Considerations

While mmHg is widely used, it's essential to be aware of its limitations:

• Temperature Dependence: The density of mercury varies with temperature, so precise measurements require temperature corrections.
• Local Gravity: Although standardized, the local acceleration due to gravity can vary slightly depending on location, potentially affecting accuracy.