Classical Mechanics Notes, Study notes of Physics

Download Classical Mechanics Notes and more Study notes Physics in PDF only on Docsity!

QOOSSOSTSSSSSSSSSSCOSCOS Physics (11) COCCOCCOSSooScocCcoceoo: 2. The velocity of light in free space ia constant and ts ts independent of the relative motion of the source and the s observer. Lorentz transformation 7 we vey Poisenille Equation a el In non-ideal Mleid dynamics, the Hagen-Poiseuille equation, giso known as the Hagen-Poiscuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure tewele drop in an incompressible and Newtonian fluid in laminar flow f- TF flowing through a long cytindrical pipe of constant cross section. i can be successfully applied to air flow in hung alveoli, or the In matrix form flow through a drinking straw or through a hypodermic needle. It was experimentally derived independently by Jean Leonard 160 Oo 0") Marie Poiseuille im 1838 and Gotthilf Heinrich Ludwig Hagen @ AO. vo and published by Poiscuille in 1840-41 and 1846. t-|0 0 y éy The assumptions of the equation are that the fluid is 0 0 -ipy incompressible and Newtonian; the flow is laminar through a Y pipe of constant circular cross-section that is substantially longer than its diameter, and there is no acceleration of fluid in the pipe. For velocities and pipe diameters above a threshold, actual fluid flow is not laminar but turbulent, leading to larger pressure drops than calculated by the Hagen-Poiscuille equation. Stokes’ Law velocities of small spherical particles in a fluid medium. The law, fast set forth by the British scientist Sir George G Stokes in 1851, is derived by consideration of the forces acting on a particular Particle as it sinks through a liquid column under the influence of gravity. The force acting in resistance to the fall is equal to 6 1p, in which r is the radius of the sphere, mis the viscosity of the liquid, and v is the velocity of fall. The force acting downward 35 equal to 4/327 (d, — d,)g, in which d, is the density of the sphere, d, is the density of the liquid, and g is the gravitational Constant. At a constant velocity of fall, the upward and downward forces are in balance, Equating the two expressions yea above and solving for v therefore yields the required velocity, pressed by Stokes’ law as v = 2/9 (d - dy) gr?/n, Special Theory of Relativity The theory of relativity consists of two parts - 1. Special theory of relativity. 2. General theory of relativity, General theory deals wi "erence cach nme? having Special theory oS relativity and several of its Predicitions * based upon the following two postulates . 1. The laws of physics are the same in all inertial frames of th the problems involving two accelerated motion with respect to + Lorentz transformations are equivalent to rotation of axes in four dimensional space through an imaginary angle of tan-! (@). * Two successive Lorentz transformations corresponds to a single Lorentz transformation with relative speed. , B+B’ a 1+ BB’ + X, — be the difference vector defined as X= XX fi and 2 shows events] + Note : For values of v << ¢ and ~+0 — =] 1-5 x=x vay v=z-vt r=t * Length contraction