Title Mechanical Properties of Fluids 4.0.pdf ✅

Mechanical Properties of Fluids 1 3 Mechanical Properties of Fluids 1. Pressure The normal force exerted by liquid at rest on a given surface in contact with it is called thrust of liquid on that surface. The normal force (or thrust) exerted by liquid at rest per unit area of the surface in contact with it is called pressure of liquid or hydrostatic pressure. If F be the normal force acting on a surface of area A in contact with liquid, then pressure exerted by liquid on this surface is P = F/A (1) Units : N/m2 or Pascal (S.I.) and Dyne/cm2 (C.G.S.) (2) Dimensional Formula : ML–1T–2 (3) At a point pressure acts in all directions and a definite direction is not associated with it. So pressure is a scalar quantity. (4) Atmospheric pressure : The gaseous envelope surrounding the earth is called the earth's atmosphere and the pressure exerted by the atmosphere is called atmospheric pressure. Its value on the surface of the earth at sea level is nearly 1.013 × 105 N/m2 or Pascal in S.I. other practical units of pressure are atmosphere, bar and torr (mm of Hg) 1 atm = 1.01 × 105 Pa = 1.01 bar = 760 torr The atmospheric pressure is maximum at the surface of earth and goes on decreasing as we move up into the earth's atmosphere. (5) If P0 is the atmospheric pressure then for a point at depth h below the surface of a liquid of density ρ, hydrostatic pressure P is given by P = P0 + hρg P0 h ρ P (6) Hydrostatic pressure depends on the depth of the point below the surface (h), nature of liquid (ρ) and acceleration due to gravity (g) while it is independent of the amount of liquid, shape of the container or cross-sectional area considered. So if a given liquid is filled in vessels of different shapes to same height, the pressure at the base in each vessel will be the same, though the volume or weight of the liquid in different vessels will be different (A) (B) (C) PA = PB = PC but WA < WB < WC


4 Mechanical Properties of Fluids (7) If V1 volume of liquid of density ρ1 and V2 volume of liquid of density ρ2 are mixed, then as: m = ρ1 V1 + ρ2V2 and V = V1 + V2 [As ρ = m/V] If V1 = V2 = V ρ = (ρ1 + ρ2)/2 = Arithmetic Mean Example 3: Two substances of densities ρ1 and ρ2 are mixed in equal volume and the relative density of mixture is 4. When they are mixed in equal masses, the relative density of the mixture is 3. The values of ρ1 and ρ2 are (1) ρ1 = 6 and ρ2 = 2 (2) ρ1 = 3 and ρ2 = 5 (3) ρ1 = 12 and ρ2 = 4 (4) None of these Solution: (1) When substances are mixed in equal volume then density = 1 2 4 2 ρ +ρ = ⇒ ρ1 + ρ2 = 8 ......(i) When substances are mixed in equal masses then density = 1 2 1 2 2 3 ρ ρ = ρ +ρ ⇒ 2ρ1 ρ2 = 3(ρ1 + ρ2) ......(ii) By solving (i) and (ii) we get ρ1 = 6 and ρ2 = 2. Q.1 Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is 36 g and its density is 9 g/cm3 . If the mass of the other is 48 g, its density in g/cm3 is (1) 4 3 (2) 3 2 (3) 3 (4) 5 Q.2 Equal masses of water and a liquid of relative density 2 are mixed together. Then the mixture has a density of (in gcm–3) (1) 2/3 (2) 4/3 (3) 3/2 (4) 3 3. Pascal's Law It states that if gravity effect is neglected, the pressure at every point of liquid in equilibrium of rest is same. or The increase in pressure at one point of the enclosed liquid in equilibrium of rest is transmitted equally to all other points of the liquid and also to the walls of the container, provided the effect of gravity is neglected. Example : Hydraulic lift, hydraulic press and hydraulic brakes Concept Builder-1