pascals (Pa) to centimeters of water (cmH2O) conversion

What is pascals?

Pascal (Pa) is the SI unit of pressure, defined as the force of one newton acting on an area of one square meter. This section will delve into the definition, formation, historical context, and practical applications of Pascal.

Pascal Definition

The pascal (Pa) is the SI derived unit of pressure used to quantify internal pressure, stress, Young's modulus, and ultimate tensile strength. It is defined as one newton per square meter.

$$1 \ Pa = 1 \frac{N}{m^2}$$

It can also be described using SI base units:

$$1 \ Pa = 1 \frac{kg}{m \cdot s^2}$$

Formation of Pascal

Pascal as a unit is derived from the fundamental units of mass (kilogram), length (meter), and time (second). Pressure, in general, is defined as force per unit area.

• Force: Measured in Newtons (N), which itself is defined as $kg \cdot m/s^2$ (from Newton's second law, $F=ma$).
• Area: Measured in square meters ($m^2$).

Thus, Pascal combines these: $N/m^2$ which translates to $(kg \cdot m/s^2) / m^2 = kg/(m \cdot s^2)$.

Blaise Pascal and Pascal's Law

The unit is named after Blaise Pascal (1623-1662), a French mathematician, physicist, inventor, writer, and Catholic theologian. He made significant contributions to the fields of mathematics, physics, and early computing.

Pascal's Law (or Pascal's Principle) states that a pressure change occurring anywhere in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere.

Mathematically, this is often represented as:

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

Where:

• $\Delta P$ is the hydrostatic pressure difference
• $\rho$ is the fluid density
• $g$ is the acceleration due to gravity
• $\Delta h$ is the height difference of the fluid

For further reading about Pascal's Law, you can refer to Pascal's Law and Hydraulics.

Real-World Examples

Here are some examples of pressure measured in Pascals or related units (like kilopascals, kPa):

• Atmospheric Pressure: Standard atmospheric pressure at sea level is approximately 101,325 Pa, or 101.325 kPa.
• Tire Pressure: Car tire pressure is often measured in PSI (pounds per square inch), but can be converted to Pascals. For example, 35 PSI is roughly 241 kPa.
• Hydraulic Systems: The pressure in hydraulic systems, like those used in car brakes or heavy machinery, can be several megapascals (MPa).
• Water Pressure: The water pressure at the bottom of a 1-meter deep pool is approximately 9.8 kPa (ignoring atmospheric pressure). The Hydrostatic pressure can be determined with formula $\Delta P = \rho g \Delta h$. Given that the density of water is approximately 1000 $kg/m^3$ and the acceleration due to gravity is 9.8 $m/s^2$
• Weather Forecasts: Atmospheric pressure changes are often reported in hectopascals (hPa), where 1 hPa = 100 Pa.

What is the centimeter of water?

The centimeter of water (cmH2O) is a unit of pressure equal to the pressure exerted by a one-centimeter-high column of water under standard conditions. It is used heavily in medicine and respiratory therapy, where small pressures are common.

Definition

The conventional centimeter of water is defined as the pressure of a 1 cm column of water with a density of 1000 kg/m³ under standard gravity (9.80665 m/s²):

$$1\ \text{cmH2O} = 98.0665\ \text{Pa}$$

This is the conventional value. Because water density varies with temperature, more precise variants exist (for example, cmH2O at 4 °C uses water's maximum density of about 999.972 kg/m³, giving roughly 98.064 Pa).

Origin and History

The unit comes directly from the water manometer, an instrument in which pressure is read as the height difference of a water column. Water was chosen for low pressures because it produces a taller, more readable column than mercury (water is about 13.6 times less dense). The convention fixes water density and gravity so the unit has a single agreed value independent of local conditions.

Law and Notable Facts

The centimeter of water is not an SI unit but is permitted in medical contexts, where it remains standard for measuring airway, ventilator, and cerebrospinal-fluid pressures. Roughly 1 cmH2O equals 0.7356 mmHg, so about 1.36 cmH2O make up 1 mmHg.

Real-World Examples and Conversions

• Mechanical ventilators typically deliver positive end-expiratory pressure (PEEP) of 5 to 10 cmH2O.
• Normal cerebrospinal-fluid opening pressure in a lumbar puncture is roughly 10 to 18 cmH2O.
• 1 cmH2O ≈ 98.0665 Pa ≈ 0.098 kPa.
• A standard atmosphere equals about 1033.2 cmH2O.