Mechanical Properties of Fluids

Fluids are substances that can flow and adapt to the shape of their container, including liquids and gases like water and air. Mechanical properties of fluids refer to viscosity, density, and pressure, which describe how fluids respond to external forces and influence their behavior in various situations.

In this article, we will learn about all the mechanical properties of fluids and related formulas in detail.

What are Fluids?

Fluids are substances that can flow and take the shape of their container. They include liquids and gases like water, air, and oil. Unlike solids, fluids do not have a fixed shape or volume. They can easily move and change their form when subjected to external forces, making them essential in various aspects of daily life and industry.

Mechanical Properties of Fluids

The properties of fluids describe their characteristics and behaviour. These properties include:

• Density
• Viscosity
• Pressure
• Buoyancy
• Surface Tension
• Compressibility
• Fluidity
• Thermal Expansion

Density

Density refers to the mass of a substance per unit volume. In the context of fluids, it indicates how much matter is packed into a given volume. Dense fluids have more mass in a given volume, while less dense fluids have less mass. It is measured in kilograms per cubic meter (kg/m³) or grams per cubic centimetre (g/cm³).

Viscosity

Viscosity is a measure of a fluid’s resistance to flow. It’s essentially internal friction within the fluid. High-viscosity fluids resist flowing more than low viscosity fluids. For instance, honey has a high viscosity, while water has low viscosity. Viscosity is influenced by factors like temperature and composition and is commonly measured in units like Pascal-seconds (Pa·s) or centipoise (cP).

For instance, honey has a higher viscosity compared to water, as it flows more slowly due to its greater resistance to deformation.

Pressure

Pressure is the force applied perpendicular to the surface of an object per unit area. In fluids, it’s caused by the collisions of fluid particles with the walls of a container or other objects. Pressure increases with depth in a fluid due to the weight of the fluid above. It is measured in units such as Pascals (Pa) or pounds per square inch (psi).

An example is atmospheric pressure, which is the pressure exerted by the Earth’s atmosphere on the Earth’s surface and is measured at sea level to be approximately 101,325 Pascals (Pa).

Buoyancy

Buoyancy is the upward force exerted on an object immersed in a fluid. It’s caused by the pressure difference between the top and bottom of the object. This force is equal to the weight of the fluid displaced by the object. Buoyancy is crucial for understanding phenomena like why objects float or sink in fluids.

An example is a boat floating on water, where the buoyant force exerted by the water supports the weight of the boat, allowing it to float.

Surface Tension

Surface tension is the cohesive force that causes the surface of a liquid to behave like a stretched elastic membrane. It’s caused by the attraction between molecules at the surface of the liquid. Surface tension is responsible for phenomena like capillary action, where liquids rise or fall in narrow tubes and the formation of droplets.

An example is the formation of droplets on a surface, where the surface tension of the liquid minimizes its surface area, leading to the spherical shape of the droplets.

Compressibility

Compressibility refers to the change in volume of a fluid in response to a change in pressure. Gases are highly compressible because their particles are more spread out and can be easily compressed closer together. Liquids are considered to be nearly incompressible under ordinary conditions.

An example is the compression of air in a bicycle pump when it is pumped, increasing its pressure.

Fluidity

Fluidity describes how easily a fluid flows. It’s influenced by factors like viscosity, temperature, and pressure. High fluidity means the fluid flows easily with little resistance, while low fluidity implies greater resistance to flow.

Water has high fluidity, as it flows easily and readily takes the shape of its container. In contrast, molasses has low fluidity, as it flows very slowly due to its high viscosity.

Thermal Expansion

Thermal expansion is the tendency of a substance to change in volume with a temperature change concerning. As the temperature of a fluid increases, its particles move more rapidly, causing the fluid to expand. The coefficient of thermal expansion quantifies this relationship between volume change and temperature change.

An example is the expansion of mercury in a thermometer as it is exposed to heat, causing the mercury level to rise.

Types of Fluid Flow

Fluid flow can be classified into different types based on various characteristics such as velocity, viscosity, and the nature of the flow. Some of the common types of fluid flow include:

• Steady and Unsteady Flow: In steady flow, the velocity, pressure, and other flow properties at any point in the fluid remain constant over time. Conversely, unsteady flow involves variations in flow properties concerning the time.

• Laminar and Turbulent Flow: concerning the chaotic and irregular motion of fluid particles, resulting in mixing and eddy formation.

• Compressible and Incompressible Flow: Incompressible flow occurs when the density of the fluid remains constant, regardless of changes in pressure and temperature. Compressible flow involves changes in fluid density due to variations in pressure and temperature.

• Internal and External Flow: Internal flow occurs within enclosed boundaries such as pipes, ducts, and channels. External flow occurs over surfaces exposed to the fluid, such as flow over wings, airfoils, and vehicle bodies.

Reynold’s Number

Reynolds Number is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It helps determine whether the flow is laminar, turbulent, or transitional. It’s calculated by dividing the product of the fluid velocity, characteristic length, and fluid density by the fluid viscosity.

For example, in fluid flow through a pipe, a low Reynolds number indicates laminar flow, characterized by smooth, parallel layers of fluid, while a high Reynolds number suggests turbulent flow, characterized by chaotic and irregular motion. Understanding the Reynolds number helps engineers design efficient pipelines and optimize fluid flow in various applications, from water distribution systems to oil pipelines.

Poiseuille’s Equation

Poiseuille’s Equation describes laminar flow in a cylindrical pipe and calculates the volume flow rate of an incompressible fluid. It’s derived from the principles of fluid mechanics and relates flow rate, pressure gradient, fluid viscosity, and pipe geometry.

Poiseuille’s Equation is commonly used in medical settings to understand blood flow through arteries and veins. By applying Poiseuille’s Equation, healthcare professionals can assess factors affecting blood flow, such as vessel diameter and viscosity, and diagnose conditions like atherosclerosis or hypertension.

Stoke’s Law

Stoke’s Law describes the force of viscosity experienced by small spherical particles settling through a viscous fluid. It’s used to calculate the drag force acting on the particles and predicts their terminal velocity based on fluid viscosity, particle size, and density difference.

Torricelli’s Law

Torricelli’s Law states that the velocity of fluid flowing out of an orifice under the influence of gravity is proportional to the square root of the depth of the fluid above the orifice. It’s derived from Bernoulli’s Equation and is commonly applied in hydrodynamics and fluid mechanics.

Torricelli’s Law finds applications in various engineering fields, such as hydraulics and civil engineering. For instance, it’s used to design spillways and weirs in dams to control water flow rates and prevent flooding downstream. By applying Torricelli’s Law, engineers can determine the velocity of water flowing over the spillway and design appropriate structures to manage water discharge.

Pascal’s Law 

Pascal’s Law states that in a confined fluid at rest, the pressure applied at any point is transmitted undiminished throughout the fluid in all directions. It’s the basis for hydraulic systems and is used in various applications such as hydraulic lifts, brakes, and jacks.

Hydraulic brakes in automobiles use Pascal’s Law to transmit force from the brake pedal to the brake pads. When the brake pedal is depressed, a small force is exerted on a small piston, which transmits pressure through the hydraulic fluid to larger pistons at the brake pads, generating a greater force to stop the vehicle.

Bernoulli’s Principle and Equation

Bernoulli’s Principle states that in a fluid flow, an increase in the fluid’s velocity occurs simultaneously with a decrease in pressure or potential energy. Bernoulli’s Equation quantifies this relationship and is used to analyze fluid flow along streamlined aeroplane paths, considering factors such as velocity, pressure, and elevation.

An everyday example of Bernoulli’s Principle in action is the operation of an aeroplane wing. As air flows over the curved upper surface of the wing, its velocity increases, resulting in lower pressure according to Bernoulli’s Principle. This creates a pressure difference between the upper and lower surfaces, generating lift and enabling the aircraft to fly.

Archimedes Principle

Archimedes Principle states that the buoyant force exerted on a submerged or partially submerged object is equal to the weight of the fluid displaced by the object. It’s used to determine the buoyant force acting on objects immersed in a fluid and explains why objects float or sink.

Archimedes Principle, naval architects can design ships that remain afloat and maintain stability even when loaded with cargo.

Hydraulic Machine Lift

Hydraulic machine lift uses Pascal’s Law to lift heavy loads with relatively little force. By applying a small force to a small piston connected to a confined fluid, the pressure is transmitted through the fluid to a larger piston, exerting a greater force to lift the load.

An example of a hydraulic machine lift is a car hydraulic jack. When a small force is applied to the jack’s handle, it creates pressure in the hydraulic fluid, which is transmitted to a larger piston under the car. This amplifies the force, allowing the jack to lift the heavy vehicle with ease.

Variation of Pressure with Height

According to hydrostatics, the pressure in a fluid at rest increases linearly with depth due to the weight of the fluid above. This variation is described by the hydrostatic pressure equation and is fundamental in understanding the fluid behaviour in various natural and engineered systems.

For example, the pressure variation with height is essential in atmospheric science to understand weather phenomena such as atmospheric pressure gradients and the formation of high and low-pressure systems. Meteorologists use this knowledge to forecast weather patterns and predict changes in atmospheric conditions.

Mechanical Properties of Fluid Formula

The various formulas related to mechanical properties of fluids are:

Law	Formula
Pascal’s Law	P = F/A​ (Pressure equals force divided by area)
Archimedes’ Principle	Fb​ = ρ×g×V (Buoyant force equals density times gravitational acceleration times volume)
Bernoulli’s Equation	[Tex]P_1 + \frac{1}{2}\rho v_1^2 + \rho gh_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho gh_2[/Tex] (Total mechanical energy per unit volume is constant in a flowing fluid)
Poiseuille’s Law	[Tex]Q = \frac{\pi r^4 \Delta P}{8 \eta L}[/Tex] (Volume flow rate equals pressure difference times pi times radius to the fourth power divided by eight times viscosity times length)
Stokes’ Law	F = 6πηrv (Force equals six times pi times viscosity times radius times velocity)

Conclusion

Fluids are substances that can flow and take the shape of their container. They exhibit various mechanical properties such as density, viscosity, pressure, buoyancy, surface tension, compressibility, fluidity, and thermal expansion. Understanding these properties helps explain how fluids behave in different situations, from everyday occurrences to industrial processes.

FAQs on Mechanical Properties of Fluids

What are the mechanical properties of fluid?

The mechanical properties of fluids refer to characteristics that describe how fluids behave under mechanical forces. These properties include viscosity, density, surface tension, and compressibility, among others.

What are the eight properties of fluids?

The eight properties of fluids include viscosity, density, surface tension, compressibility, elasticity, bulk modulus, vapor pressure, and capillarity.

What do you mean by mechanical properties?

Mechanical properties refer to the characteristics of a material that describe how it responds to applied mechanical forces, such as stress, strain, or deformation.

What is the unit of viscosity?

The unit of viscosity is typically measured in Pascal-seconds (Pa·s) in the International System of Units (SI). Other common units include poise (P) and centipoise (cP).