9.2. PRESSURE

A sharp needle when pressed against our skin pierces it. Our skin, however, remains intact when a blunt object with a wider contact area (say the back of a spoon) is pressed against it with the same force. If an elephant were to step on a man’s chest, his ribs would crack. A circus performer across whose chest a large, light but strong wooden plank is placed first, is saved from this accident. Such everyday experiences convince us that both the force and its coverage area are important. Smaller the area on which the force acts, greater is the impact. This impact is known as pressure.

Pressure is a concept that represents how much force is applied over a specific area. When a sharp object like a needle is applied to the skin, it has a small area, leading to a high pressure that can pierce the skin. On the other hand, a blunt object like a spoon has a larger area, distributing the same force over a much larger space, which results in lower pressure, so the skin remains intact. This demonstrates the principle that pressure increases when a force is applied to a smaller area.

Imagine trying to push a nail into a wall with a hammer. If you use the point of the nail, it goes through easily. But if you try to push with the flat part of the hammer, nothing happens because the pressure is too low. Hence, this principle applies not only to body impacts but to all situations involving force and area.

When an object is submerged in a fluid at rest, the fluid exerts a force on its surface. This force is always normal to the object’s surface, because if there were a component of force parallel to the surface, the object would exert a force on the fluid parallel to it, causing the fluid to flow. Since the fluid is at rest, this cannot happen. Hence, the force exerted by the fluid at rest has to be perpendicular to the surface in contact with it.

When something is placed in a stationary fluid, the fluid pushes up against it. This push is directed straight out and does not vary with the direction of the surface. If it did have a sideways component, it would disturb the fluid, causing it to flow and making it no longer at rest. Therefore, the force from the fluid is always perpendicular to the surface of the object that is submerged.

Think of a balloon underwater. If you look closely, the water pushes up against all sides of the balloon. This upward force is what keeps it afloat while it remains at rest.

The normal force exerted by the fluid at a point may be measured. An idealized form of one such pressure-measuring device is shown in Fig. 9.1(b). It consists of an evacuated chamber with a spring that is calibrated to measure the force acting on the piston. This device is placed at a point inside the fluid. The inward force exerted by the fluid on the piston is balanced by the outward spring force and is thereby measured.

Pressure measuring devices often use a piston setup where the force exerted by the fluid pushes down on the piston, which then compresses a spring. The amount that the spring compresses tells us how much pressure is being applied by the fluid, since there's a direct relationship between the force applied and how much the spring compresses, enabling precise measurements of pressure.

Consider a bathroom scale that uses springs to measure weight. Just like how the scale shows your weight based on how much you push down on it, a pressure gauge uses a similar principle where the fluid pushes down on a piston, and the resulting force is used to calculate the pressure.

If F is the magnitude of this normal force on the piston of area A then the average pressure Pav is defined as the normal force acting per unit area. Pav = F/A. In principle, the piston area can be made arbitrarily small, and pressure is then defined in a limiting sense as P = lim ∆A → 0 ΔF/ΔA.

Pressure can be mathematically defined as the force acting over a specific area. This means for a given force, as the area diminishes, the pressure increases. Essentially, if you were to keep reducing the area to a point, you could calculate pressure as the limit of the change in force divided by the change in area as that area approaches zero. This concept helps in understanding how pressure can be extremely high when applied over a very small area.

Think of a sharp knife cutting through a piece of fruit. The same amount of force applied to the wide edge of the knife might not cut, but when applied to the thin blade, it exert a higher pressure, easily slicing through the fruit.

Pressure is a scalar quantity. It is important to note that it is the component of the force normal to the area under consideration and not the vector force. Its dimensions are [ML–1T–2]. The SI unit of pressure is N m–2, known as pascal (Pa). Common unit of pressure is atmosphere (atm), which is the pressure exerted by the atmosphere at sea level (1 atm = 1.013 × 105 Pa).

Unlike many physical quantities, pressure does not have a direction—it only has a magnitude. This means pressure is considered a scalar quantity, similar to temperature, and is most often measured in pascals. Moreover, it can also be expressed in atmospheres, particularly when discussing weather or environmental pressures.

When you're at the beach, the pressure felt at sea level (1 atmosphere) feels different than when you scuba dive deeper into the ocean. These variations in pressure can be important for things like managing how submarines are built or understanding why our ears pop when we climb mountains!

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