pounds per square inch (psi) to technical atmospheres (at) 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 the technical atmosphere?

The technical atmosphere (at) is a non-SI unit of pressure equal to one kilogram-force per square centimeter. It was widely used in engineering, especially in Europe, before the pascal became standard.

Definition

The technical atmosphere is defined as the pressure of one kilogram-force acting on one square centimeter:

$$1\ \text{at} = 98066.5\ \text{Pa}$$

This equals exactly 1 kgf/cm² (98,066.5 Pa), because standard gravity is 9.80665 m/s². It is close to, but distinct from, the standard atmosphere (atm = 101,325 Pa) and the bar (100,000 Pa).

Origin and History

The technical atmosphere arose from the gravitational metric system of units, which used the kilogram-force rather than the newton. Expressing pressure as kilogram-force per square centimeter was intuitive for engineers weighing loads, and the unit became common in mechanical and hydraulic engineering, boilers, and pneumatics through much of the 20th century.

Law and Notable Facts

The technical atmosphere is not part of the SI and its use is discouraged in favor of the pascal or bar. It is easily confused with the standard atmosphere; the two differ by about 3.3%. Gauge and absolute variants were often written "atü" (gauge) and "ata" (absolute) in German-language engineering.

Real-World Examples and Conversions

• 1 at = 1 kgf/cm² = 98.0665 kPa ≈ 0.9678 atm.
• 1 at ≈ 14.223 psi, close to but slightly below the 14.696 psi of one standard atmosphere.
• A pressure of 10 at (about 981 kPa) is a common rating benchmark for industrial hydraulic components.
• 1 at ≈ 0.980665 bar, so the bar and technical atmosphere differ by under 2%.