Module 111. Pressure, Flotation, Surface Tension, Density, Viscosity

The study of pressure, flotation, surface tension, density, and viscosity is fundamental to understanding the physical behaviour of fluids — both liquids and gases — in various scientific and engineering contexts. These interrelated properties explain phenomena ranging from the rise of air balloons and the floating of ships to the motion of blood through arteries and the formation of droplets.

Pressure

Pressure is defined as the force exerted per unit area on the surface of an object. Mathematically,Pressure (P) = Force (F) / Area (A).
Its SI unit is the pascal (Pa), equivalent to one newton per square metre (N/m²). Pressure can be exerted by solids, liquids, or gases, and its effects are observed in everyday applications such as hydraulic systems, weather forecasting, and respiration.
In fluids, pressure acts equally in all directions at a given depth — a principle known as Pascal’s Law. According to this law, when pressure is applied to a confined fluid, it is transmitted undiminished throughout the fluid. This principle underlies the operation of hydraulic brakes and lifts.
The atmospheric pressure, exerted by the weight of air above the Earth’s surface, decreases with altitude. It is measured using a barometer and is approximately 101,325 Pa at sea level.

Flotation

Flotation is the phenomenon by which an object partially or wholly rests on the surface of a fluid without sinking. This behaviour is governed by Archimedes’ Principle, which states:
“When a body is wholly or partially immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the body.”
If the buoyant force equals the weight of the object, it floats; if less, it sinks.
The principle explains why large ships made of steel float on water despite steel being denser than water. The ship’s hull encloses air, reducing its average density below that of water. Similarly, hot-air balloons rise because the heated air inside them is less dense than the surrounding cooler air.
Key applications of flotation include:

• Designing ships and submarines.
• Hydrometry (measurement of liquid density using hydrometers).
• Hot-air and helium balloon operation.
• Icebergs floating in oceans, where about one-tenth of their volume remains above water.

Surface Tension

Surface tension is the property of a liquid that allows it to resist an external force due to cohesive interactions between its molecules. At the liquid’s surface, molecules experience an inward cohesive pull, forming a “film-like” surface that behaves elastically.
Surface tension (T) is defined as the force acting per unit length along the surface and is measured in N/m.
Phenomena explained by surface tension include:

• The spherical shape of water droplets, minimising surface area.
• The ability of certain insects, such as water striders, to walk on water.
• Capillary action, where liquids rise or fall in narrow tubes (as in plant xylem).
• The formation of soap bubbles and liquid jets.

Surface tension decreases with temperature, as increased molecular motion weakens cohesive forces. Substances known as surface-active agents or surfactants (e.g., soaps and detergents) lower surface tension, enhancing cleaning efficiency.

Density

Density is the mass of a substance per unit volume and is expressed asDensity (ρ) = Mass (m) / Volume (V).
Its SI unit is kilogram per cubic metre (kg/m³). Density determines whether an object will float or sink in a fluid.
Water has a density of approximately 1000 kg/m³ at 4°C. Substances denser than water, such as iron, sink, while less dense substances, such as oil or wood, float.
The relative density (or specific gravity) of a substance is the ratio of its density to that of water. Being dimensionless, it provides a convenient way to compare materials.
Density is also a key factor in atmospheric and oceanic circulation, as temperature and salinity variations cause density-driven convection currents that influence weather and climate.

Viscosity

Viscosity is the internal resistance of a fluid to flow. It arises due to friction between adjacent layers of the fluid moving at different velocities. Liquids with higher viscosity flow more slowly, such as honey or oil, whereas low-viscosity fluids, like water and alcohol, flow easily.
Mathematically, viscosity (η) relates the shearing force (F) acting between layers to their velocity gradient:η = (F × d) / (A × dv)where A is the area, d the distance between layers, and dv the velocity difference.
The SI unit of viscosity is pascal-second (Pa·s).
Viscosity decreases with temperature in liquids (as molecular cohesion weakens) and increases in gases (as molecular collisions intensify).
Applications of viscosity include:

• Lubrication in machinery to reduce wear.
• Blood flow analysis in medical physiology.
• Formulation of paints, syrups, and cosmetics.
• Design of hydraulic systems and fluid pipelines.

The coefficient of viscosity helps engineers and scientists determine the optimal performance of mechanical and biological systems involving fluid motion.

Interrelationship Among Fluid Properties

The concepts of pressure, density, viscosity, and surface tension are deeply interconnected in fluid mechanics. For example, pressure differences drive fluid flow, while viscosity resists it. Density variations influence buoyancy and convection, and surface tension affects fluid interfaces and droplet formation. Together, these properties explain the stability and movement of fluids in natural and technological systems.
In biological systems, these principles are equally vital — the human circulatory system relies on pressure gradients to pump blood, the alveoli in lungs function through surface tension modulation by surfactants, and buoyant forces support aquatic organisms.