Pressure

What is Pressure?

Pressure represents the force exerted on a surface per unit area. It quantifies how concentrated a force is when applied to a specific area. The mathematical expression for pressure ( $P$ ) is given as $P=\frac{F}{A}$ , where $F$ is the force applied perpendicular to the surface, and $A$ is the area over which this force is spread.

For example, when you press down on a small area with a given force, the pressure is high because the force is concentrated over a small area. Conversely, the same force spread over a larger area results in lower pressure. This concept of pressure is essential in understanding various phenomena in fluids (liquids and gases), solid mechanics, and even in atmospheric and geological sciences.

Units of Pressure

Pressure in the International System of Units (SI) is measured in pascals (Pa), with one pascal defined as one newton per square meter (N/m²). This unit reflects the force of one newton being applied to an area of one square meter. The pascal, while the standard SI unit for pressure, is relatively small, so pressure is often expressed in kilopascals (kPa) or megapascals (MPa) for practical purposes.

Beyond the Pascal, several other units are commonly used to measure pressure:

Atmospheres (atm): One atmosphere is the pressure equivalent to that exerted by the weight of the Earth’s atmosphere at sea level, approximately 101,325 Pa.
Millimeters of mercury (mmHg): Historically used in meteorology and medicine, this unit is based on the pressure exerted by a column of mercury one millimeter high, with 760 mmHg equating to one atmosphere.
Pounds per square inch (psi): Commonly used in the United States, psi measures the pressure resulting from a force of one pound-force applied to an area of one square inch.
Bars (bar): One bar is defined as 100,000 Pa and is close to the average atmospheric pressure on Earth at sea level.

Types of Pressure

Atmospheric Pressure

Atmospheric pressure is the force per unit area exerted by the Earth’s atmosphere on surfaces and objects within it. This pressure results from the weight of the air above the point where the measurement is taken. At sea level, atmospheric pressure is highest because there is more air above that point pressing down compared to higher elevations.

Atmospheric pressure decreases as one ascends altitude, such as climbing a mountain or flying in an airplane. This reduction occurs because the density of air molecules decreases with altitude—there is less air above a given point to exert pressure. This change in pressure with height is a critical factor in various fields, including meteorology, which affects weather patterns and climate. In aviation, it influences aircraft performance and altimeter settings.

Fluid Pressure

Fluid pressure refers to the force exerted by a fluid (either a liquid or a gas) per unit area on the walls of its container or any object submerged in it. Unlike atmospheric pressure, which is exerted in all directions, fluid pressure acts perpendicular to the object’s surface in contact with the fluid. This pressure increases with the fluid’s depth because the fluid’s weight above the point of measurement adds to the pressure exerted at that point.

The key factors that determine fluid pressure are the depth of the fluid, its density, and the acceleration due to gravity. The deeper you go into a fluid, like water in an ocean or lake, the greater the pressure because more fluid is above exerting weight. Similarly, denser fluids exert more pressure than less dense fluids at the same depth because they have more mass in the same volume.

Pressure in Fluids

Hydrostatic Pressure

Hydrostatic pressure is the pressure exerted by a fluid at rest, primarily due to the fluid’s weight and the depth at which the pressure is measured. It is a fundamental concept in fluid mechanics, affecting everything from the functioning of natural bodies of water to engineered fluid systems.

The key factors influencing hydrostatic pressure are the density of the fluid ( $\rho$ ), the acceleration due to gravity ( $g$ ), and the depth ( $h$ ) within the fluid where the pressure is being measured. The equation $P=\rho \cdot g \cdot h$ succinctly captures this relationship:

$P$ represents the hydrostatic pressure,
$\rho$ (rho) is the fluid’s density, indicating how much mass of the fluid is contained in a given volume,
$g$ is the acceleration due to gravity, which on Earth averages about $9.81 m/s^2$
$h$ is the depth below the surface of the fluid at which the pressure is being calculated.

Pascal's Principle

Pascal’s Principle, named after the French mathematician and physicist Blaise Pascal, is a fundamental concept in fluid mechanics. It posits that when pressure is applied to any part of an enclosed fluid, this change in pressure is transmitted equally and undiminished throughout the entire fluid and to the walls of its container. This means that if you increase the pressure at one point in a confined fluid, that increase is felt equally at every other point, assuming the fluid is incompressible and the system is closed.

This principle forms the operational foundation of hydraulic systems, which use fluids to transmit force. In such systems, a small force applied to a small area can be transformed into a larger force over a larger area, providing a mechanical advantage. Hydraulic systems are widely used in car brakes, jacks, and heavy machinery. When a driver presses the brake pedal in a car, for example, Pascal’s Principle allows this relatively small force to be amplified and transmitted through the brake fluid, pressing the brake pads against the wheels with enough force to stop the car.

Pressure and Force

Pressure and force are interconnected concepts in physics, describing how objects interact with their environment. Force refers to the push or pull exerted on an object, a vector quantity with both magnitude and direction. On the other hand, pressure is a scalar quantity that measures the intensity of force distributed over a specific area.

The equation captures the relationship between pressure and force $P=\frac{F}{A}$ , where $P$ is pressure, $F$ is force, and is the area over which the force is applied. This equation shows that pressure increases with an increase in force or a decrease in the area over which the force is spread. Conversely, pressure decreases if the force diminishes or the area expands.

For example, when you press down on a thumbtack with your finger, you exert a force on a very small area, which creates high pressure at the point of the tack, allowing it to pierce through a surface. In contrast, when the same force is applied over a larger area, such as pressing your hand against a wall, the pressure is much lower because it is spread over a wider area, and thus it doesn’t have the same penetrating effect.