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Note for Mechanics - MECH By Amity Kumar

  • Mechanics - MECH
  • Note
  • Amity University - AMITY
  • Civil Engineering
  • 14 Topics
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Text from page-2

Shear force, F y δl δu δy x Fluid deforms continuously under the action of a shear force τ yx = dFx = f (Deformation Rate) dA y Shear stress in a moving fluid: Although there can be no shear stress in a fluid at rest, shear stresses are developed when the fluid is in motion, if the particles of the fluid move relative to each other so that they have different velocities, causing the original shape of the fluid to become distorted. If, on the other hand, the velocity of the fluid is same at every point, no shear stresses will be produced, since the fluid particles are at rest relative to each other. Differences between solids and fluids: The differences between the behaviour of solids and fluids under an applied force are as follows: i. For a solid, the strain is a function of the applied stress, providing that the elastic limit is not exceeded. For a fluid, the rate of strain is proportional to the applied stress. ii. The strain in a solid is independent of the time over which the force is applied and, if the elastic limit is not exceeded, the deformation disappears when the force is removed. A fluid continues to flow as long as the force is applied and will not recover its original form when the force is removed.

Text from page-3

Differences between liquids and gases: Although liquids and gases both share the common characteristics of fluids, they have many distinctive characteristics of their own. A liquid is difficult to compress and, for many purposes, may be regarded as incompressible. A given mass of liquid occupies a fixed volume, irrespective of the size or shape of its container, and a free surface is formed if the volume of the container is greater than that of the liquid. A gas is comparatively easy to compress (Fig.1). Changes of volume with pressure are large, cannot normally be neglected and are related to changes of temperature. A given mass of gas has no fixed volume and will expand continuously unless restrained by a containing vessel. It will completely fill any vessel in which it is placed and, therefore, does not form a free surface. Free surface k k k k (a) Solid (b) Liquid (c) Gas Fig.1 Comparison of Solid, Liquid and Gas 1.2 Systems of Units: The official international system of units (System International Units). Strong efforts are underway for its universal adoption as the exclusive system for all engineering and science, but older systems, particularly the cgs and fps engineering gravitational systems are still in use and probably will be around for some time. The chemical engineer finds many physiochemical data given in cgs units; that many calculations are most conveniently made in fps units; and that SI units are increasingly encountered in science and engineering. Thus it becomes necessary to be expert in the use of all three systems.

Text from page-4

SI system: Primary quantities: Derived quantities: Quantity Unit Quantity Unit Mass in Kilogram kg Force in Newton (1 N = 1 kg.m/s2) N Length in Meter m Pressure in Pascal (1 Pa = 1 N/m2) N/m2 Time in Second s or as sec Work, energy in Joule ( 1 J = 1 N.m) J Power in Watt (1 W = 1 J/s) W Temperature in Kelvin K Mole mol CGS Units: The older centimeter-gram-second (cgs) system has the following units for derived quantities: Quantity Unit Force in dyne (1 dyn = 1 g.cm/s2) dyn Work, energy in erg ( 1 erg = 1 dyn.cm = 1 x 10-7 J ) erg Heat Energy in calorie ( 1 cal = 4.184 J) cal Dimensions: Dimensions of the primary quantities: Fundamental dimension Symbol Length L Mass M Time t Temperature T

Text from page-5

Dimensions of derived quantities can be expressed in terms of the fundamental dimensions. Quantity Representative symbol Dimensions Angular velocity ω t-1 Area A L2 Density ρ M/L3 Force F ML/t2 Kinematic viscosity ν L2/t Linear velocity v L/t 1.3 Properties of fluids: 1.3.1 Mass density or Specific mass (ρ ρ): Mass density or specific mass is the mass per unit volume of the fluid. ∴ ρ= ρ= Mass Volume M dM or V dV Unit: kg/m3 With the increase in temperature volume of fluid increases and hence mass density decreases in case of fluids as the pressure increases volume decreases and hence mass density increases. 1.3.2 Weight density or Specific weight (γ): Weight density or Specific weight of a fluid is the weight per unit volume. ∴ γ= dW Weight W = or dV Volume V Unit: N/m3 or Nm-3.

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