pounds per square inch (psi) to centimeters of mercury (cmHg) 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 centimeter of mercury?

The centimeter of mercury (cmHg) is a unit of pressure equal to the pressure exerted by a one-centimeter-high column of mercury under standard conditions. It is a scaled-up form of the millimeter of mercury (torr) used in some scientific and industrial settings.

Definition

The conventional centimeter of mercury is based on a 1 cm column of mercury with a density of 13,595.1 kg/m³ under standard gravity (9.80665 m/s²):

$$1\ \text{cmHg} = 1333.22\ \text{Pa}$$

Exactly, 1 cmHg = 1333.22387415 Pa, which is ten times the millimeter of mercury (1 mmHg ≈ 133.322 Pa). This equals 10 torr under the conventional definition.

Origin and History

The unit descends directly from Torricelli's mercury barometer of 1643, where atmospheric pressure was read as the height of a mercury column. Mercury's high density makes the column compact and easy to read. The conventional value fixes mercury's density (its value at 0 °C) and standard gravity so the unit is independent of temperature and location.

Law and Notable Facts

The centimeter of mercury is not an SI unit; the SI unit of pressure is the pascal. It relates to the standard atmosphere as 1 atm = 76 cmHg exactly (by the historical 760 mmHg definition). The millimeter of mercury (mmHg), essentially identical to the torr, remains standard in medicine for blood pressure.

Real-World Examples and Conversions

• 1 cmHg = 10 mmHg (10 torr) ≈ 1.33322 kPa.
• One standard atmosphere equals exactly 76 cmHg.
• A blood pressure of 120/80 mmHg corresponds to 12/8 cmHg.
• A vacuum of 5 cmHg absolute is about 6.7 kPa, roughly 93% below atmospheric pressure.