Title Mechanical Properties of Fluids 4.0.pdf ✅

2 Mechanical Properties of Fluids (7) In a static liquid, at same level, the pressure will be same at all points. If not, due to pressure difference the liquid cannot be at rest. This is why the height of liquid is the same in vessels of different shapes containing different amounts of the same liquid at rest when they are in communication with each other. (8) Gauge pressure : The pressure difference between hydrostatic pressure P and atmospheric pressure P0 is called gauge pressure. P – P0 = hρg Example 1: If pressure at half the depth of a lake is equal to 2/3 pressure at the bottom of the lake then what is the depth of the lake ? Height of atmosphere = 10 m of water (1) 10 m (2) 20 m (3) 60 m (4) 30 m Solution: (2) Pressure at bottom of the lake = P0 + hρg and pressure at half the depth of a lake 0 h P g 2 = +ρ According to given condition 0 0 1 2 P h g (P h g) 2 3 + ρ= +ρ ⇒ 0 1 1 P hg 3 6 = ρ ⇒ 5 0 3 2P 2 10 h 20 m g 10 10 × = = = ρ × Example 2: A U-tube in which the cross-sectional area of the limb on the left is one quarter the limb on the right contains mercury (density 13.6 g/cm3 ). The level of mercury in the narrow limb is at a distance of 36 cm from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water? Water Mercury (1) 1.2 cm (2) 2.35 cm (3) 0.56 cm (4) 0.8 cm

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