Mechanics of solids and fluids

  1. Inter-atomic forces: the forces acting between the atoms due to electrostatic interaction between the charges of the atoms are called intern-atomic forces. Thus inter-atomic forces are electrical in nature.
  2. In case of non-uniform charge distribution, the center of mass of positive charge may not coincide with the center of mass of negative charge. Such a molecule constitutes an electric dipole, having a dipole moment and is called polar molecule e.g. water, alcohol, ammonia, hydro-chloric acid etc. In general, liquids have polar molecules.
  3. The molecules, in which the center of mass of positive and negative charges coincide so that they do not give rise to any electric dipole are called non-polar molecules e.g. CO2, N2, O2 etc.
  4. Crystalline solids. Those solids which have a definite external geometrical form are called crystalline solids.  They are considered true and stable solids. example; quatrz, calcite, rocksalt, etc.
  5. Amorphous or Glassy solids. Those solids which have no definite external geometrical form are called amorphous solids.
  6. Putty and Paraffin wax are the example of almost nearly perfectly elastic bodies.
  7. Hooke’s law states that the extension produced in the wire is directly proportional to the load applied within elastic limit i.e. within elastic limit. Stress is directly proportion to the Strain.
  8. Stress= E * Strain
  9. Young’s modulus of elasticity (Y)= normal stress/longitudinal strain. For perfectly rigid body Y= infinite.
  10. Bulk modulus of elasticity (K)= normal stress/volumetric strain. For an incompressible liquid K= infinite
  11. Modulus of rigidity (n)= Tangential stress/shearing strain. For a liquid n= 0.
  12. elastic fatigue is the property of an elastic body by virtue of which its behavior become less elastic under the action of repeated alternating deforming forces.
  13. The temporary delay in regaining the orginal configuration by an elastic body after the removal of a deforming force is called elastic after effect.
  14. The torque required to produce a given twist in a hollow cylinder is greater than that required to twist a solid cylinder of the same length and material through the same angle. Hence the hollow shaft is stronger than the solid shaft. It is due to this reason that the electric poles are made hollow.
  15. The three states of matter differ from each other due to the following two factors:
    1. The different magnitudes of the inter-atomic and inter-molecular forces.
    2. The degree of random thermal motion of the atoms and the molecules of a substance depending upon temperature.
  16. Water is more elastic that air, because bulk modulus of elasticity is reciprocal of compressibility and air is more compressible than water.
  17.  Only bulk modulus of elasticity (K) is possible in all the three states of matter.
  18. Poisson ratio is unit less. Theoretical value of Poisson ration lie between -1 to 0.5. Practical value lies between 0-0.5.

Fluid is the name given to a substance which begins to flow when external force is applied on it. Liquid and gases are fluids. Fluids exert thrust.

  1. A liquid in equilibrium of rest always exerts a force normal to the surface of contact.
  2. Pascal law states that if gravity effect is neglected, the pressure at every point of liquid in equilibrium of rest is same. Hydraulic lift, Hydraulic Press (or Brahma Press), and hydraulic brakes are based on Pascal law.
  3. The pressure exerted by a liquid depends only on the height of liquid column and is independent of the shape of the containing vessel. This is known as Hydrostatic paradox.
  4. Torricelli’s experiment: he was the first to device an experiment for measuring atmospheric pressure.
  5. Various units for atmospheric pressure. SI Units: N/m^2 or Pascal; cgs unit is dyne/cm^2; mm or cm of mercury column; 1 torr= one mm of mercury column; unit used for meteorological purposes is called bar. 1 bar – 10^5 pascal.
  6. The law of flotation states that a body will float in a liquid, if weight of the liquid displaced by the immersed part of the body is atleast equal to or greater than the wright of the body.
  7. A body can be in equilibrium if the center of gravity of the body and center of buoyancy must be along the same vertical line.
  8. The cohesive and adhesive forces are Vander Wall Forces. These forces are different from ordinary gravitational forces and do not obey inverse square law.
  9. Tension in the free surface of liquid at rest is called the surface tension. S= F/l
  10. Surface tension of liquid depends on length but not on the area, like the elastic property. S.T of liquid is a molecular phenomenon as it is due to force of cohesion between molecules of liquid.
  11. When a wire of loop is dipped into soap solution and taken out, a soap film is formed on the loop due to surface tension. The molecules of liquid lying in the surface film have greater potential energy in comparison to the inner molecules.
  12. Angle of contact between a liquid and a solid is defined as the angle enclosed between the tangents to the liquid surface and the solid surface inside the liquid surface and the solid surface inside the liquid, both the tangents being drawn at the point of contact of the liquid with the solid.
  13. The value of angle of contact for pure water and glass (without grease) is zero.
  14. Angle of contact increases with increase in temperature of liquid. Angle of contact decreases on adding soluble impurity to a liquid.
  15. Angle of contact does not depend upon the inclination of the solid surface to the liquid surface. .
  16. If the angle of contact of a liquid and a solid surface is less than 90 degree, then the liquid spreads on the surface. At greater than 90 degree, the liquid does not spread on the surface of solid.
  17. Surface tension of liquid is zero at its boiling point and it vanishes at critical temperature.
  18. Since surface tension of soap solution is low, it can spread over large area.Hence, it can wash clothes more effectively. Hot soap solution proves still better as surface tension decreases further on heating. For the same reason, surface tension of all lubricating oils and paints is kept low. Antiseptics like detol have low surface tension, so they spread faster.
  19. When wax is rubbed on cloth, the cloth becomes water proof because capillaries formed in threads disappear when wax is rubbed on cloth.
  20. An ideal liquid has zero viscosity and zero compressibility. Viscosity is due to transport of momentum.
  21. With increase in temperature, the viscosity of liquid decreases but viscosity of gases increases.
  22. Stokes found that the backward dragging force F acting on a small spherical body of radius r, moving through a medium of coefficient of viscosity n (nita), with velocity v. F = 6*pie* n*v*r (stokes law of viscosity). Important of stoke’s law:
    1. This law is used in the determination of electronic charge with the help of Millikan’s experiment.
    2. This law accounts the formation of clouds.
    3. This law accounts, why the speed of rain drops is less than that of a body falling freely with a constant velocity from the height of clouds.
    4. This law helps a man coming down with the help of a parachute.
  23. Terminal velocity is maximum constant velocity acquired by the body while falling freely in a viscous medium.
  24. With increase in pressure, the viscosity of liquids increases but the viscosity of water decreases, whereas the viscosity of gases remains unchanged.
  25. In a streamline flow, no two streamlines can cross each other. The greater is the crowding of stream lines at a place, the greater is the velocity of liquid particles at that place and vice versa.
  26. A flow in which the liquid moves in layers is called a laminar flow. In this flow, one layer slides over the other layer of liquid.
  27. Critical velocity is that velocity of liquid flow, up to which its flow is streamlined and above which its flow becomes turbulent.
  28. Reynolds number is a pure number which determines the nature of flow of liquid through a pipe. If the value of Reynold number lies between 0 to 2000, the flow of liquid is stream line or laminar. Over 3000 the flow will be turbulent. between 2000 to 3000, the flow of liquid is unstable changing from streamline to turbulent flow.
  29. The equation of continuity represents the conservation of mass in case of moving fluids. The falling stream of water becomes narrower, as the velocity of falling stream of water increases so its area of cross-section decreases, according to equation of continuity.
  30. Bernoulli’s theorem: also states that in the streamline flow of an ideal liquid through a horizontal tube, the velocity increases where pressure decreases and vice-versa. This is also called Bernoulli’s principle. application
    1. Atomizer or spray.
    2. Lift on an aeroplane wing
    3. Blowing of the roof during the storm.
    4. Curved motion of spinning ball (magnus effect)
    5. Motion of two parallel boats
  31. Venturimeter is a device, used for measuring the rate of flow of liquid through pipes. It’s working is based on Bernoulli’s theorem.

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