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PHYSICS-IC Ratio of _density of a given substance to the density of water is known as specific gravity Regarding density it is worth noting that (i) In case of a homogeneous and isotropic substance density is same in all directions. (ii) The demensions of density are MIL-3T0. The SI unit is kg/m3 while the CGS unit is g/cm3 or g/cc; 1 g/cc = 103kg/m3 (iii) When immiscible liquids of different densities are poured in a container, the liquid of highest density will reach the bottom while that of the lowest density will reach the top, at stable equilibrium. The interfaces will be planes. (iv) With rise in temperature, due to thermal expansion, volume of a given mass changes and so the density of the substance changes inversely proportional to volume. 1 p.(l 'ft) (mass is constant) P (v) Bulk modulus of a substance is defined as. poAP AV 1+AP = po Ap Ap (vi) Specific Gravity or Relative Density : The most common fluid in our usage is 'water'. Hence it is customary to compare all the other fluids/solids with water. Similarly to get an easier and a qualitative comparison with water as to how denser or how rarer a given substance is, specific gravity is used. It is defined as the ratio of the density of a given substance to that of water at 40C. At 40C, the density of water is 1000 kg/m Psubstan ce Since S is a ratio, its value does not depend on system of units used and it is a demensionless quantity. More over, S = p (in CGS units) 2.5 PRESSURE TO A FLUD If we fill a vessel with a fluid and a hole is made on the vertical walls of the vessel, the fluid effluxes out of the vessel. Now, if we cover this hole with a plate, which exactly fits the hole, the plate will remain at rest only if we apply some external force on the plate. This shows that the fluid exerts force on the plate to push it outwards. What causes the fluid to exert this force on the plate? At room temperature, molecules in a fluid are continuously moving, oscillating, vibrating rotating and they posses certain amount of kinetic energy. When a small surface area A, such as a small card is submerged in the fluid, the molecules exert a colliding force Fn, normal to each side of the card. This normal component of fluid contact force is known as the pressure force Pressure is defined as the ratio of magnitude of normal force to the area of the card. P = Lt L, The units of P is N/m2 or Pa in SI system FLUID MECHANICS