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.