While studying conditions of static equilibrium under Mechanics, we conveniently assumed that the bodies under investigation remained perfectly rigid under a set of forces and torques. In reality, no solid body is perfectly rigid. So, when a system of balanced forces or couples acts on a solid body at rest, the body gets deformed. In other words, though the body does not exhibit any translational or rotational motion as a whole, different parts within it change their relative positions with respect to each other. A light wire, attached to the ceiling and holding a load at its free end, stretches in length. A book lying on a table, subjected to a tangential force on the top cover, changes in shape. A metal sphere taken to the depths of the sea shrinks in volume, albeit by a tiny fraction. The common word for any such change is deformation. The property by virtue of which a body resists any change in its size, shape or both and tends to regain its configuration on withdrawal of the deforming forces is known at the elasticity of the body. To impart in-depth knowledge on the theory of elasticity and to develop skill in solving problems based on this topic, we offer a series of video lectures titled Internal Forces and Stress, Strain, Hooke's Law and Young's Modulus, Shear Modulus, Bulk Modulus, Stress Versus Strain Graph, Elastic Potential Energy of a Deformed Body, and so on.
Matter can be classified into three types: solids, liquids and gases. A solid can withstand shear stress; it has definite volume and shape. Liquids and gases cannot withstand static shear stress and begin to flow under it; hence they are collectively referred to as fluids. None of the fluids has any definite shape of its own and eventually takes the shape of the vessel in which it is kept. While a liquid occupies a definite volume almost unaffected even by very high pressure, a gas can be compressed easily. Because of these distinctive features, we can tell a solid from a fluid in most cases. But there are exceptions such as asphalt. It looks so much like a solid but, in reality, it is a fluid that flows very, very slowly. A single substance may remain in any one of the three states under varying physical conditions. As you all know, if the substance is H2O, the states are named ice (solid), water (liquid) and water vapour (gas). The mechanics of fluids is governed by a number of physical principles which are based on Newton's laws of motion and other force laws. Fluid statics is that part of Fluid Mechanics which discusses fluids at rest. We shall impart a comprehensive knowledge on this topic through a series of video lectures titled Pressure at a Point, Variation of Pressure in a Static Fluid, Measurement of Pressure, Pascal's Principle, Buoyancy and Archimedes' Principle, Equilibrium of a Floating Body, and many more.
A piece of camphor dances on the surface of water without any obvious provocation. A water spider can skate on a pond without wetting its legs. A container with a small hole at the bottom can manage to hold mercury. Great effort is required to separate two flat glass plates if there is a thin layer of water between them. When a narrow glass tube open at both ends is dipped into water, water rises in the tube. All these events can be explained by the fluid property called surface tension. Surface tension is a molecular phenomenon which occurs at the surface of separation between two phases such as a liquid and a solid, a liquid and a gas, or a solid and a gas. We shall teach you the basics of surface tension first, and then follow up with a large number of problems at both simple and challenging levels. Our video lectures on this topic are titled Theory of Surface Tension, Angle of Contact and Shape of Meniscus, Excess Pressure within Liquid Drop and Soap Bubble, Force between Two Plates Separated by a Liquid Film, Rise or Fall of a Liquid in a Capillary Tube, and much more.
While the motion of rigid bodies is rather uninteresting, the motion of fluids observed in nature can indeed be pleasing to the eye. The flow of a gurgling stream, the eruption of molten lava, the swirl of hot gases from a burning tinder, ocean waves – all these and more are the subject of fluid dynamics. While each particle of the fluid follows Newton's laws of motion, we find it convenient to describe the properties of the fluid at each point on its path as a function of time. The motion of a real fluid is complex and not yet fully understood. Therefore, we often make matters simple by assuming an ideal fluid which is non-viscous and incompressible. Further, the flow of the ideal fluid is assumed to be steady and irrotational. However, in the latter part of the topic, we discuss viscosity and steady flow of a viscous fluid. The students will acquire a commanding grip on the topic and will learn to solve a variety of problems – simple to moderate to difficult – through a series of video lectures titled Equation of Continuity, Bernoulli's Equation, Some Applications of Bernoulli's Equation, Viscosity, Poiseuille's Law, Critical Speed and Reynolds Number, Motion of a Solid Body in a Viscous Fluid, et cetera.
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