Title 9. MECHANICAL PROPERTIES OF FLUIDS.pdf ✅

MECHANICAL PROPERTIES OF FLUIDS Pressure due to a fluid column, Pascal’s law and its applications (hydraulic lift and hydraulic brakes). effect of gravity on fluid pressure. Viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow, critical velocity, Bernoulli’s theorem and its applications. Surface energy and surface tension, angle of contact, excess pressure across a curved surface, application of surface tension ideas to drops, bubbles and capillary rise. Topic-1 Fluids at Rest Revision Notes  Pressure : (i) Pressure is defined as the thrust acting per unit area of the surface in contact with liquid, i.e., P = Thrust( ) Area( ) F A = F A = hρg (ii) Liquid pressure is independent of shape of the liquid surface as well as area of the liquid surface, but depends upon height of liquid column. (iii) Total pressure at a depth h below liquid surface is P = hρg + P0 , where P0 is the atmospheric pressure. (iv) S.I. unit of pressure is Nm–2 or pascal (denoted by Pa) and its dimensional formula is [ML–1T–2]. (v) Pressure is a scalar quantity because a liquid at rest exerts equal pressure in all directions at all points in the same horizontal plane.  Pascal’s Law : It states that if gravity effect is neglected, the pressure at every point of liquid in equilibrium of rest is same. Pascal’s law also states that the increase in pressure at one point of the enclosed liquid in equilibrium of rest is transmitted equally to all other points of liquid provided the gravity effect is neglected.  Atmospheric pressure : (i) It is defined as the pressure exerted by atmosphere. (ii) At S.T.P., the value of atmospheric pressure is 1.01 × 105 Nm–2 or 1.01 × 106 dyne/cm2 .  Archimedes' principle : It states that when a body is immersed partly or wholly in a liquid at rest, it loses some of its weight, which is equal to the weight of the liquid displaced by the immersed part of the body. Observed weight of body = True weight – Weight of liquid displaced. If w is the observed weight of body of density ρ when immersed in a liquid of density σ, then w = Mg – mg = Ahρg – Ahσg Syllabus TOPIC - 1 Fluids at Rest TOPIC - 2 Surface Energy & Surface Tension .... TOPIC - 3 Viscosity & Bernoulli’s Theorem CHAPTER 9
MECHANICAL PROPERTIES OF FLUIDS = Ahg (ρ – σ) = Ahgρ 1 –   σ     ρ = W 1 –   σ     ρ ∴ True weight, W = ( ) apparent weight 1– / σ ρ  Laws of floatation : It states that a body will float in a liquid if weight of the liquid displaced by the immersed part of the body is at least equal to or greater than the weight of the body. (a) When true weight of the body W > w (weight of the liquid displaced), the body will sink to the bottom of the liquid. It will be so when the density of solid body (ρ) is greater than the density of liquid (σ), i.e., ρ > σ. (b) When W < w, the body will rise above the surface of liquid to such an extent that the weight of the liquid displaced by immersed part of the body (i.e., upward thrust) becomes greater than the weight of the body. The body then will float. In this case the density of solid body is less than the density of liquid, i.e., ρ < σ. (c) When W = w, the body is at rest anywhere in the liquid. The body will float with its whole volume just immersed in the liquid. In this case the density of body is equal to density of liquid, i.e., ρ = σ. There will be equilibrium of floating body when (i) Weight of liquid displaced by the immersed part of body is equal to the weight of the body. (ii) The centre of gravity of the body and the centre of buoyancy lie along the same vertical line. (iii) If the centre of gravity of the body lies vertically below the meta centre then body is in stable equilibrium. The body will be in unstable equilibrium if centre of gravity lies vertically above the meta centre. Key Words  Fluid is the name given to a substance which begins to flow when external force is applied on it. It includes liquid and gas.  Thrust : The total normal force exerted by liquid at rest on a given surface in contact with it is known as thrust of liquid on that surface. It is due to collision of molecules of liquid while moving at random, with the walls of the container and rebounding from them.  Buoyancy is the upward force acting on the body immersed in a fluid.  Metacentre is a point where the vertical line passing through the centre of buoyancy intersects the central line. Key Formulae  Pressure = F A = hρg (due to h height of liquid) h = height, ρ = Density of liquid, g = Acceleration due to gravity.  Gauge pressure = Total pressure – Atmospheric pressure  For Hydraulic lift; 1 1 F A = 2 2 F A F1 , F2 = Forces on pistons of area of cross - sections A1 , A2  Density = Mass Volume , Relative density = Density of substance Density of water at 4°C  Archimedes' Principle : Loss of weight of body in liquid = Weight of liquid displaced = Volume × Density of liquid × g  Law of floatation : A body will float if, weight of body = Weight of liquid displaced. Very Short Answer Type Questions (1 mark each) Q. 1. Define Pascal’s law. R Ans. It states that if the effect of gravity is neglected, pressure in a fluid at rest is the same at all points. 1 Commonly Made Error Students forget to mention 'fluid at rest' and 'effect of gravity is neglected' terms in the statement for pascal's law.