Mechanical Properties of Fluids
How liquids and gases behave under pressure — from hydraulic lifts to airplane wings
Table of Contents
9.1 Introduction
Liquids and gases can flow and are therefore called fluids. This property distinguishes them from solids. Fluids are everywhere around us — Earth has an envelop of air and two-thirds of its surface is covered with water.
Unlike a solid, a fluid has no definite shape of its own. Solids and liquids have a fixed volume, whereas a gas fills the entire volume of its container. The key property of fluids is that they offer very little resistance to shear stress — their shape changes by application of very small shear stress.
The shearing stress of fluids is about a million times smaller than that of solids. This is why fluids flow — they cannot resist shear forces like solids do.
9.2 Pressure
When an object is submerged in a fluid at rest, the fluid exerts a force on its surface. This force is always normal (perpendicular) to the object's surface. The normal force exerted by the fluid at a point per unit area is known as pressure.
Pascal's Law
Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel. This principle is the basis of hydraulic systems.
Hydrostatic Pressure
The pressure at a depth h in a fluid of density ρ is given by:
The pressure at a given depth is the same regardless of the shape or size of the container. A narrow tube and a wide tank produce the same pressure at the same depth — this is known as the hydrostatic paradox.
Applications of Pascal's Law
Hydraulic Lift
A small force on a small piston creates a large force on a large piston: F₂ = F₁ × (A₂/A₁). Used in car lifts and industrial presses.
Hydraulic Brakes
Pressing the brake pedal applies pressure through brake fluid to all four wheels equally, providing balanced braking force.
Hydraulic Press
Used in forging, crushing, and molding operations where enormous forces are needed from relatively small input forces.
Medical Devices
Blood pressure monitors, syringes, and IV drip systems all rely on principles of fluid pressure.
9.3 Streamline Flow
When a fluid flows such that every particle passing through a point has the same velocity, the flow is called steady or laminar. The path traced by a fluid particle in steady flow is called a streamline.
The equation of continuity for an incompressible fluid flowing through a tube of varying cross-section:
At low velocities, flow is smooth and predictable (laminar). At high velocities, flow becomes chaotic and unpredictable (turbulent). The Reynolds number (Re = ρvd/η) determines the transition — Re < 2000 is laminar, Re > 4000 is turbulent.
9.4 Bernoulli's Principle
Bernoulli's principle relates pressure, speed, and height in a flowing fluid. For an incompressible, non-viscous fluid in steady flow:
This means: where fluid speed is high, pressure is low, and vice versa. This principle explains many everyday phenomena.
Applications of Bernoulli's Principle
Airplane Lift
Air moves faster over the curved top of a wing than the flat bottom. Higher speed → lower pressure on top → net upward force (lift).
Chimney Draft
Wind blowing across the top of a chimney creates low pressure, drawing smoke upward through the chimney.
Atomizer/Sprayer
Blowing air across a tube creates low pressure, drawing liquid up and spraying it as fine droplets.
Magnus Effect
A spinning ball curves because air speed differs on each side, creating a pressure difference. This explains curved shots in football and cricket.
At high speed, water builds up between tires and road, reducing contact. The tire essentially hydroplanes on a thin film of water. Bernoulli's principle explains how the water pressure under the tire increases with speed, lifting the tire off the road.
9.5 Viscosity
Viscosity is the property of a fluid that opposes the relative motion of its layers. It is essentially internal friction — the resistance to flow. Honey has high viscosity; water has low viscosity.
Stokes' law gives the viscous force on a spherical body moving through a fluid:
When a body falls through a viscous fluid, it eventually reaches a constant speed called terminal velocity where gravitational force = buoyant force + viscous force. For a raindrop: v_t = 2r²(ρ-σ)g / 9η
Viscosity in Everyday Life
- Oil in engines: Lubricants reduce friction between moving parts by forming a thin viscous layer.
- Blood flow: Blood viscosity affects heart workload. Higher viscosity means the heart must pump harder.
- Paint and honey: Flow slowly due to high viscosity — they need to be spread or poured.
- Shake (thixotropic): Some fluids become less viscous when shaken (ketchup, paint) — they are called thixotropic fluids.
9.6 Surface Tension
The property of the free surface of a liquid that allows it to behave like a stretched elastic membrane is called surface tension. It arises because molecules at the surface experience a net inward force from molecules below.
Surface Energy and Excess Pressure
Surface tension is numerically equal to surface energy per unit area. A soap bubble has excess pressure inside:
The angle at which a liquid surface meets a solid surface is called the contact angle. Water on clean glass: θ ≈ 0° (wetting). Mercury on glass: θ ≈ 140° (non-wetting). This determines capillary action.
Applications of Surface Tension
Needle Floating
A steel needle can float on water if placed gently — surface tension supports its weight against gravity.
Soap Bubbles
Soap reduces surface tension but creates a elastic film that can form bubbles. Adding soap makes bubble-blowing easier.
Capillary Action
Water rises in thin tubes due to surface tension — this is how plants draw water from roots to leaves.
Detergents
Soap reduces surface tension of water, allowing it to penetrate fabric fibers and dissolve grease and dirt.
Water striders and other insects use surface tension to walk on water. Their legs have hydrophobic (water-repelling) coatings that prevent them from breaking the water surface, allowing them to glide across.