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10%20-%20Fluid%20Mechanics - 10 FLUID MECHANICS Page 1...

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10 - FLUID MECHANICS Page 1 Introduction Fluid is a matter in a state which can flow. Liquids, gases, molten metal and tar are examples of fluids. Fluid mechanics is studied in two parts: ( i ) Fluid statics - Study of the forces and pressures acting on stationary fluid. Pascal’s law and Archimedes’ principle and surface tension are discussed in fluid statics. ( ii ) Fluid dynamics - Study of motion of fluid and properties related to it as a result of forces acting on fluid. Bernoulli’s theorem and its applications and viscosity of fluid are discussed here. Fluid dynamics is studied in two sections: Hydrodynamics and Aerodynamics. 10.1 Pressure Pressure is the force acting on a surface per unit area in a direction perpendicular to it. It is a scalar quantity and its S I unit is N / m 2 named pascal ( Pa ) in honour of the French scientist Blasé Pascal. Its dimensional formula is M 1 L - 1 T - 2 . Thus, Pressure, P ( Pa ) = ) m ( A Area, ) N ( F , Force 2 . A bigger unit of pressure is ‘bar’. 1 bar = 10 5 Pa. 1 atmosphere pressure ( atm ) = 1.013 × 10 5 Pa or N / m 2 = 760 mm ( 76 cm ) of Hg column. Density: Density is the ratio of mass to volume of an object. It is a scalar quantity and its S I unit is kg / m 3 . Liquids are almost incompressible. Hence, the density of a liquid remains almost constant at a given temperature for small change in the value of pressure. Gases are compressible. Hence, the volume of gas decreases and density increases with increase of pressure. Relative density / Specific density / Specific gravity: “Relative density also known as specific density or specific gravity of a given substance is the ratio of its density to the density of water at 277 K ( i.e., 4 ° C ). It is a dimensionless quantity and hence does not have a unit. Also, Relative ( specific ) density of an object = K 277 at water of volume same the of Mass object an of Mass 10.2 Pascal’s Law “A change in pressure applied to an enclosed ( incompressible ) fluid is transmitted undiminished to every point of the fluid and the walls of the containing vessel. This statement is known as Pascal’s law.
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10 - FLUID MECHANICS Page 2 Pascal’s law is also given as “If the effect of gravitation is neglected, the pressure at every point in an incompressible liquid, in equilibrium, is the same.” Applications of Pascal’s Law: The figure shows the principle of a hydraulic lift used to raise heavy loads. This device has two vertical cylinders of different diameters connected by a horizontal tube. A liquid is filled in this vessel. Air- tight pistons having cross-sectional areas A 1 and A 2 ( A 1 < A 2 ) are fitted touching the liquid surface in both the cylinders. According to Pascal’s law, in equilibrium, the pressure on liquid in both the arms is the same. Hence, 1 1 A F = P 1 = P 2 = 2 2 A F F 2 = F 1 1 2 A A Thus, a large force, F 2 , is generated using a small force, F 1 , as the magnitude of F 2 is 1 2 A A times the magnitude of F 1 . Using Pascal’s law, devices like hydraulic lift, hydraulic jack, hydraulic brake and hydraulic
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10%20-%20Fluid%20Mechanics - 10 FLUID MECHANICS Page 1...

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