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Properties of Solids and Liquids
Elasticity is that property of the material of a body by virtue of which the body opposes any change in its shape or size when deforming forces are applied to it, and recovers its original state as soon as the deforming forces are removed.
On the basis of definition bodies may be classified in two types:
Nearest Approach P.P.: quartz-fibre
Limit of Elasticity: The maximum deforming force up to which a body retains its property of elasticity is called the limit of elasticity of the material of the body.
When a deforming force is applied to a body, it reacts to the applied force by developing a reaction (or restoring force which, from Newton's third law, is equal in magnitude and opposite in direction to the applied force. Thereaction force per unit area of the body which is called into play due to the action of the applied force is called stress. Stress is measured in units of force per unit area, i.e. Nm–2.Thus.
Where F is the applied force and A is the area over which it acts.
Unit of Stress: N/m2
Dimension of the stress: M1L-1T-2
Types of stress:
Three Types of Stress:
(A) Tensile Stress: Pulling force per unit area.
It is applied parallel to the length. It causes increase in length or volume.
B) Compressive Stress: Pushing force per unit area. It is applied parallel to the length it causes decrease in length or volume
(B) Tangential Stress: Tangential force per unit area. It causes shearing of bodies.
Difference between Pressure v/s Stress:
Pressure is always normal to the area
Stress can be normal or tangential
Always compressive in nature
may be compressive or tensile in nature
When a deforming force is applied to a body, it may suffer a change is size or shape. Strain is defined as the ratio of the change in size or shape to the original size or shape of the body. Strain is a number; it has no units or dimensions. The ratio of the change in length to the original length is called longitudinal strain. The ratio of the change in volume to the original volume is called volume strain. The strain resulting from a change in shape is called shearing strain.
Types of strain:
Three Types of Strain:
(A) Linear Strain: Change in length per unit length is called linear strain
(B) Volume Strain: Change in volume per unit volume is called volume strain.
(C) Shear Strain: Angle through which a line originally normal to fixed surface is turned.
Fluid mechanics deals with the behavior of fluids at rest and in motion. A fluid is a substance that deforms continuously under the application of a shear (tangential) stress no matter how small the shear stress may be.
Thus, fluids comprise the liquid and gas (or vapor) phase of the physical forms in which matter exists
Density ρ : Mass of unit volume, Called density
Density at a point of liquid described by
Density is a positive scalar quantity.
SI Unit =kg/m3
CGS Unit= gm/cm3
Relatively Density: It is the ratio of density of given liquid to the density of pure water at 40C
Relatively density or specific gravity is unit less, dimensionless. It is a positive scalar physical Quantity
Value of R.D. is same in SI and CGS system due to dimensionless/unitless
Specific Gravity: It is the ratio of weight of given liquid to the weight of pure water at 40 C
i.e. than specific gravity of a liquid is approximately equal to the relative density. For calculation they can be interchange
PRESSURE IN A FLUID
When a fluid (either liquid or gas) is at rest, it exerts a force perpendicular to any surface in contact with it, such as a container wall or a body immersed in the fluid. While the fluid as a whole is at rest, the molecules that makes up the fluid are in motion, the force exerted by the fluid is due to molecules colliding with their surroundings. If we think of an imaginary surface within the fluid, the fluid on the two sides of the surface exerts equal and opposite forces on the surface, otherwise the surface would accelerate and the fluid would not remain at rest.
2.1 Atmospheric Pressure (p0)
It is pressure of the earth’s atmosphere. This changes with weather and elevation. Normal atmospheric pressure at sea level (an average value) is 1.013 × 105 Pa.
Thus 1 atm = 1.013 × 105 Pa
Variation in Pressure with depth
If the weight of the fluid can be neglected, the pressure in a fluid is the same throughout its volume. But often the fluid's weight is not negligible and under such condition pressure increases with increasing depth below the surface. Let us now derive a general relation between the pressure ρ at any point in a fluid at rest and the elevation y of that point. We will assume that the density and the acceleration due to gravity g are the same throughout the fluid. If the fluid is in equilibrium, every volume element is in equilibrium.
It is a device used to measure atmospheric pressure. In principle, any liquid can be used to fill the barometer, but mercury is the substance of choice because its great density makes possible an instrument of reasonable size.
Here, P1 = atompsheric pressure (P0)
And P2 = 0 + ρgh = ρ gh
Here, ρ = density of mercury
P0 = ρgh
Force on Side Wall of Vessel
Force on the side wall of the vessel cannot be directly determined as at different depths pressures are different. To find this we consider a strip of width dx at a depth x from the surface of the liquid as shown in figure, and on this strip the force due to the liquid is given as:
dF = Xρg × bdx
Surface Tension& Viscosity
The force of attraction between the molecules of the same substance is called cohesive force In case of solids, the force of cohesin is very large and due to this solids have definite shape and size. On the other hand, the force of cohesion in case of liquids is weaker than that of solids. Hence liquids do not have definite shape but have definite volume. The force of cohesion is negligible in case of gases. Because of this fact, gases have neither fixed shape nor volume.
The force at attraction between molecules of different substances is called adhesive force
The property of a liquid at rest due to which its free surface tries to have minimum surface area and behaves as if it were under tension somewhat like a stretched elastic membrane is called surface tension. The molecules of the liquid exert attractive forces on each other. There is zero net force on a molecule inside the volume of the liquid. But a surface molecules is drawn into the volume. Thus, the liquid tends to minimize its surface area, just as a stretched membrane does. Surface tension of a liquid is measured by the force acting per unit length on either side of an imaginary line drawn on the free surface of liquid, the direction of this force being pependicular to the line and tangential to the free surface of liquid. So if F is the force acting on one side of imaginary line of length
T = (F/L)
When the surface area of a liquid is increased, the molecules from the interior rise to the surface. This requires work against force of attraction of the molecules just below the surface. This work is stored in the form of potential energy. Thus, the molecules in the surface have some additional energy due to their position. This additional energy per unit area of the surface is called ‘surface energy’.
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