CBSE Class 11th Mechanical Properties of Fluids:
A branch of physics known as "mechanical properties of fluids" describes the mechanics of fluids, which includes liquids, gases, and plasmas. Fluids are incompressible, which means that a liquid's density stays constant regardless of changes in pressure. They rank as the least viscous as well. It indicates that there is no tangential force acting on any of the two liquid surfaces that came into contact.
Fluids: Fluids are substances that have the ability to flow in the presence of an external force. Fluids include gases and liquids.The total normal force that a liquid at rest exerts on a particular surface is referred to as the thrust of the liquid. Liquids lack a defined shape; instead, they take on the shape of the containing vessel. The newton is the SI unit of thrust.In fluid mechanics, The following properties of fluids would be considered:
When the fluid is at rest – hydrostatics
When the fluid is in motion – hydrodynamics
Pressure Exerted by the Liquid : Liquid pressure, sometimes known as hydrostatic pressure, is the normal force that a liquid applies to a unit area of the surface it is in contact with.
The liquid column's pressure, p = hρg
where g is the acceleration caused by gravity, ρ is the liquid's density, and h is the height of the liquid column.
The average pressure on a vessel's walls that holds liquid up to a height of h = (hρg / 2).
Pascal’s Law: A location in the confined liquid that is in equilibrium experiences an increase in pressure, which is equally transmitted to the walls of the container and the liquid in all directions.Pascal's law is the foundation for the operation of hydraulic presses, hydraulic lifts, and hydraulic brakes.
Atmospheric pressure: Atmospheric pressure is the force that the earth's atmosphere exerts. It's roughly 100,000 N/m2.
- It is comparable to ten tons of weight on one square meter.
- The atmospheric pressure at sea level is equivalent to 76 centimeters of mercury column. Atmospheric pressure is then equal to hdg, or 76 x 13.6 x 980 dyne/cm2.
- The pressure of the blood passing through our circulatory system balances this air pressure, our body is not crushed. Torr and bar are other units used to measure atmospheric pressure.
- 1 mm of mercury column equals 1 torr.
- An aneroid barometer is used to measure atmospheric pressure.
Buoyancy: A body experiences an upward force known as buoyant force, or simply buoyancy, when it is submerged entirely or partially in a fluid.
The center of buoyancy is the point where the buoyant force acts, which is the center of gravity of the liquid displaced by the body part submerged in it.
Archimedes’ Principle: A body loses weight when submerged entirely or partially in a liquid. and it is equivalent to the weight of the liquid that the body part that is submerged has displaced.
When a body with density σ is completely submerged in a liquid with density p, its observed weight (T) is the body's true weight.
Laws of Floatation: If the body's weight is the same as the weight of the liquid that the body's submerged portion is displacing, the body will float in the liquid.
If w is the buoyant force and W is the body's weight, then
- body will sink to the bottom of the liquid if W > w.
- The body will partially submerge in the liquid if W< w.
- If the body's entire volume is submerged in the liquid, it will float in the liquid if W = w.
- If the meta-centre, also known as the center of buoyancy, is positioned vertically above the body's center of gravity, the floating body will be in stable equilibrium.
- If the body's center of gravity is vertically below the meta-centre, or center of buoyancy, the floating body will be in an unstable equilibrium.
- If the body's center of gravity and meta-centre, or center of buoyancy, align, the floating body will be in neutral balance.
Density and Relative Density:
Density: A substance's density is determined by dividing its mass by its volume.
Liquid density is equal to mass / volume. d = M/V,
Water has a density of 1 g/cm3, or 103 kg/m3.
The dimensional formula for this scalar quantity is [M1L–3]. The ratio of a substance's density to that of water at 4°C is known as its relative density. Density of material / density of water equals relative density. Weight of material in air / weight lost in water equals a. There is no measurement or unit for relative density, sometimes referred to as specific gravity. Density of body equals density of substance for a solid body. In contrast, a hollow body has a lower body density than substance density.
The liquid with the highest density will be at the bottom of a container containing immiscible liquids with varying densities, while the liquid with the lowest density will be at the top, resulting in smooth surfaces. Density of a Substance Mixture When two liquids with respective masses of m1 and m2 and densities of p1 and p2 are combined, the mixture's density is
The density of the mixture is calculated when two liquids with the same mass (m) but different densities (p1 and p2) are combined.
When two liquids of same volume V but of different densities (p1 and p2) are mixed together, the density of mixture is
density of a liquid varies with pressure,where = initial density of the liquid, K = bulk modulus of elasticity of the liquid and Δp = change in pressure
FAQ –
Q. What are the mechanical properties of fluids?
Ans. The mechanical properties of fluids refer to the characteristics that describe how fluids respond to external forces, including viscosity, density, surface tension, and compressibility.
Q. How do viscosity and density affect fluid behavior?
Ans. Viscosity determines a fluid's resistance to flow, while density influences its buoyancy and weight. Both properties play crucial roles in fluid dynamics and can affect various phenomena, such as flow rates and pressure distributions.
Q. What is surface tension, and why is it important in fluid mechanics?
Ans. Surface tension is the force that causes the surface of a liquid to minimize its surface area. It is essential in fluid mechanics as it influences phenomena like capillary action, droplet formation, and the behavior of interfaces between fluids and solids.
Q. What role does shear stress play in fluid mechanics?
Ans. Shear stress is the force per unit area that acts parallel to a surface. In fluid mechanics, it describes the resistance to flow caused by internal friction within the fluid. Shear stress is central to understanding fluid flow behavior, especially in viscous fluids.
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