Title 10.Mechanical Properties of Fluids-F.pdf ✅

1 | P a g e NEET-2022 Ultimate Crash Course PHYSICS Mechanical Properties of Fluids
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3 | P a g e POINTS TO REMEMBER 1. In the absence of gravity, g = 0 or P P 0 2 1 − = or P P 2 1 = , which is the statement of the Pascal’s law. 2. The pressure difference between two points is directly proportional to the height of the liquid column and to the liquid density. 3. The result applies to any depth h. 4. If the point X is taken to be on the surface of the liquid, P 0 1 = and if P P 2 = (say), P h g =  Here, P is the hydrostatic pressure at any point distant h from the liquid surface. 5. The above discussion is also true in case the body, instead of being fully immersed, is partly immersed in the liquid. 6. In case the body is homogeneous (as in the present case), the centre of buoyancy (2) coincides with the centre of gravity (3) of the body. Since the true weight (W)of the body acts vertically downwards, apparent weight of the body | = − = − W F W W b Thus, the body appears lighter when immersed in a liquid and the loss in weight is equal to the weight of the liquid displaced. 7. In a nutshell, wherever a body is immersed in a liquid (either fully or partly), (i) upthrust acting on the body, | F W b = (weight of the liquid displaced by the body) = apparent loss in weight of the body (ii) apparent weight of the body in the liquid | = − = − W F W W b 8. The pressure measured by different pressure measuring devices is in fact the difference between the true pressure and the atmospheric pressure. This difference between the two pressures is called the gauge pressure, while the true pressure is called the absolute pressure. Thus, absolute pressure (P) = gauge pressure (P0) + atmospheric pressure (P0), i.e., P P P = +g 0 For example a tyre inflated to a gauge pressure of 24 lb/in2 contains air at an absolute pressure of 38.7 lb/in2 , since sea-level atmospheric pressure is 14.7 lb/in2 . 9. The gauge pressure may be either above or below atmospheric pressure. An instrument or gauge that reads pressure below atmospheric pressure is usually called a vacuum gauge. 10. Distinction must be made between potential energy and surface energy. Potential energy (W) = surface tension (T)  surface area (  A) Surface energy (E) ( ) potential energy(W) area A =  = surface tension (T) Obviously, surface tension ( ) W T A = =  surface energy (E) ------(1) 11. We have assumed above that the temperature of the film remains constant when it is stretched. But, in fact, on stretching, it gets cooled on account of the work done in extracting the molecules from inside the liquid to its surface against the cohesive forces. Heat has to be supplied from outside to keep the temperature of the film constant. Thus, surface energy (E) of the film is the sum of potential energy per unit area and the heat supplied per unit area (i.e., Q) to keep the temperature of the film constant. If W is the amount of work done in stretching the film through an area  A, E A W Q A  = +  ---------(2) From eqns. (1) and (2), E A T A Q A  =  +  or E=T+Q or T=E—Q Obviously, it is incorrect to say that surface tension is equal to surface energy. (E —Q) is the mechanical part (i.e., potential energy) of the surface energy and is called the free surface energy. Thus, surface tension is equal to the free surface energy. In case, the surface area of the film changes according to the adiabatic conditions, then Q = 0 and in that case T = E, i.e., the surface tension is equal to the surface energy. But now surface the tension changes on account of a change in temperature at always takes place in an adiabatic change. 12. Excess pressure is also called the pressure differential.
4 | P a g e 13. The general expression for excess pressure is: 1 2 1 1 p T R R   = +     where R1 and R2 are the principal radii of curvature of any curved surface. In case of a spherical bubble, R R R 1 2 = = or 2T p R = 14. In case of liquids which do not wet the container,  is obtuse (i.e., 0  90 ) and cos is negative. h is negative, i.e., the level of the liquid in the tube is below the liquid level outside the tube. 15. 2T cos h r g  =  can be obtained in a much simpler way as given below. Let us neglect the volume of the liquid below the meniscus. Weight of the liquid in the cylinder ABCD, i.e., W = volume of cylinder ABCD  density of the liquid  g or W r h g 2 =   ---------(7) As we have already derived in equation, F 2 rTcos =  -------(8) In equilibrium from eqns. (7) and (8), 2   =   r h g 2 rTcos or 2T cos h r g  =  16. 'Specific gravity' is not a proper term for the ratio of the density of a body to that of water as it has nothing to do wits gravity. 'Relative density', which describes the concept more precisely, is to be preferred. 17. The density of a body is not always the same as the density of its material. For example, a copper sphere and s copper shell of the same Sin have the same material density. But the density of copper sphere (as a body) is more than dog of the Copper shell (as a body), i.e., their body densities arc not the same. This concept is very important in floatation as a body floats in a fluid if its body density is less than the density of the fluid. 18. The lack of rigidity exhibited by fluids has three important consequences (1) The forces that a fluid exerts on the walls of the container and vice-versa always act perpendicular to the walls. (2) An external pressure exerted on a fluid is transmitted uniformly throughout the volume of the fluid. If this were not so, the fluid would flow from a region of high pressure to a region of low pressure, thereby equalising the pressure. (3) At any depth in a fluid, the pressure is the same in all directions. If this were not so, the fluid would flaw in such a way as to equalise the pressure. 19. The equilibrium of a liquid is not disturbed if some element of its volume is assumed to be solidified, i.e., if it is replaced by an imaginary solid of the same volume and shape and having the same density as the fluid under consideration. This is called solidification principle. 20. The heights (h1 and h2) of columns of different liquids in communicating vessels are inversely proportional to the densities ( 1 ,2 ) of these liquids, i.e., 1 2 2 1 h / h / =   . This is called the law of communicating vessels. 21. Pascal's law and Archimedes' principle are necessary consequences of laws of mechanics and fluid statics. 22. Free surfaces of the liquids in different vessels are on the same horizontal plane. This fact is usually expressed by saying that a liquid finds its own level. 23. The pressure due to force of gravity of a liquid and depending on the depth under the liquid's surface is called hydrostatic pressure. 24. The hydrostatic pressure is taken into consideration when determining the forces of action of a liquid on the bottom and the walls of a vessel, on solids in the liquid and deriving the conditions of equilibrium of liquids in communicating vessels, etc. The stress within a solid can also be a hydrostatic pressure