11.6 Gauge Pressure, Absolute Pressure, and Pressure Measurement

Pressure Concepts

Pressure shows up constantly in physics and everyday life, from checking your tire pressure to reading a weather forecast. This section covers the difference between gauge and absolute pressure, the devices used to measure pressure, and how to convert between pressure units.

Gauge vs. Absolute Pressure

There are two ways to report a pressure value, and mixing them up is a common source of errors.

Gauge pressure ($P_g$) measures pressure relative to the atmosphere around you. A tire pressure gauge reading of 32 psi means the air inside the tire pushes 32 psi more than the atmosphere outside. Gauge pressure can be positive (above atmospheric) or negative (below atmospheric, sometimes called vacuum pressure). You'll see gauge pressure used for tire pressure, blood pressure, and hydraulic or pneumatic systems.

Absolute pressure ($P_{abs}$) measures pressure relative to a perfect vacuum, meaning zero pressure. Because it includes atmospheric pressure on top of gauge pressure, absolute pressure is always positive.

The two are related by a simple equation:

$P_{abs} = P_g + P_{atm}$

where $P_{atm}$ is the local atmospheric pressure (about 101,325 Pa at sea level).

Quick example: A tire gauge reads $P_g = 200 \text{ kPa}$. What's the absolute pressure inside the tire?

$P_{abs} = 200 \text{ kPa} + 101.325 \text{ kPa} \approx 301.3 \text{ kPa}$

Pressure Measurement Devices

Manometers measure pressure differences using a U-shaped tube partially filled with a liquid (often mercury or water). The pressure difference between the two sides of the tube is:

$\Delta P = \rho g h$

• $\rho$ = density of the manometer liquid (kg/m³)
• $g$ = acceleration due to gravity (9.81 m/s²)
• $h$ = height difference between the two liquid columns (m)

There are two main types:

• Open-tube manometers have one end open to the atmosphere. The height difference directly gives you the gauge pressure of whatever is connected to the other end.
• Closed-tube (differential) manometers have both ends connected to sealed systems, so they measure the pressure difference between those two systems.

Barometers measure atmospheric pressure. Two common designs:

1. Mercury barometers use a glass tube filled with mercury, inverted into a mercury reservoir. A vacuum forms at the sealed top of the tube, and the mercury column settles at a height proportional to atmospheric pressure. At sea level and 0°C, that height is 760 mmHg.
2. Aneroid barometers use a sealed, flexible metal capsule that compresses or expands as atmospheric pressure changes. That deformation is mechanically amplified and shown on a dial. These are the type you'll find in portable weather stations and aircraft altimeters.

Pressure transducers convert pressure into an electrical signal, which makes them useful for digital readouts and automated monitoring systems.

Pressure Unit Conversions

The SI unit of pressure is the pascal (Pa), defined as one newton per square meter ($1 \text{ Pa} = 1 \text{ N/m}^2$). Because a single pascal is quite small, you'll often see kilopascals (kPa) used instead.

Here are the key conversion relationships to know:

To convert between units, multiply by the appropriate conversion factor so that the old unit cancels out.

Example 1: Convert 1,520 mmHg to atm.

$1{,}520 \text{ mmHg} \times \frac{1 \text{ atm}}{760 \text{ mmHg}} = 2 \text{ atm}$

Example 2: Convert 3 atm to kPa.

$3 \text{ atm} \times \frac{101.325 \text{ kPa}}{1 \text{ atm}} = 303.975 \text{ kPa}$

Fluid Statics and Pressure

A few additional concepts tie into pressure in static fluids:

• Hydrostatic equilibrium is the condition where a fluid is at rest and all pressure forces within it are balanced. This is the assumption behind the equation $\Delta P = \rho g h$.
• Pressure head refers to the height of a fluid column that would produce a given pressure. It's a convenient way to express pressure in terms of a length (e.g., "10 meters of water").
• Compressibility describes how much a fluid's density changes under pressure. For most liquids in introductory problems, compressibility is negligible, so you can treat $\rho$ as constant. Gases, on the other hand, are highly compressible, which is why pressure changes with altitude in the atmosphere are more complex.