Tiêu đề P - IX - FLUID MECHANICS (SYN).pdf ✅

CLASS IX PHYSICS FLUID: A Substance which has no definite shape and has the ability to flow is called Fluid. Example: Liquids and gases 1 The difference between liquids and gases is that liquid cannot be compressed but gas can be compressed and liquids have free surface but gases cannot have any free surface. 2 Fluid mechanics is a branch of physics that deals with the behaviour of fluids at rest and motion. 3 Liquid Statics deals with the behaviour of fluids in rest. 4 Fluid dynamics deals with the behaviour of fluids in motion. DENSITY (p): Density of a substance is defined as the mass per unit volume. i) Density (ρ) = mass volume = m v ii) Its SI unit is kgm−3 iii) Its CGS unit is gcm−3 iv) Its Dimensional formula is [M1 L −3 T 0 ] v) It is a Scalar vi) 1 g cm−3 = 1000 kg m−3 Relative density (RD): It is defined as the ratio of density of the substance to the density of water at 4 0C. Relative Density = Density of Substance Density of water at 4 0C It is unit less and dimensionless Physical quantity. Density of a mixture of two or more 1iquids' Case 1: Suppose two liquids of densities ρ1 and ρ2 having masses m1 and m2 are mixed together then the den- sity of mixture will be ρ = Total mass Total Volume = m1 + m2 V1 + V2 ρ = m1 + m2 m1 ρ1 + m2 ρ2 If m1 = m2 ρ = 2ρ1ρ2 ρ1 + ρ2 Case 2: If the liquids of densities ρ1 and ρ2 having volumes V1 and V2 are mixed, then the density of the mix- ture is ρ = m1 + m2 v1 + v2 ρ = ρ1v1 + ρ2v2 v1 + v2 If v1 = v2 ρ = ρ1 + ρ2 2 Factors effecting Density: FLUID MECHANICS SYNOPSIS - 1
CLASS IX PHYSICS As the temperature of a liquid is increased, the mass remains the same while the volume increases and hence, the density of liquids decreases ρα 1 V (vαT) ρ 1 ρ = V V1 = V V + dV = 1 1 + γVT (Δv = v(1 + γΔT)) Where γ is Thermal coefficient of volume expansion = ΔV VΔT ρ 1 = ρ 1 + γVT As the pressure is increased, volume decreases and hence density will increase, in the case of compressible liq- uids. ρα 1 V ρ 1 ρ = V V1 = V V + dV = 1 V − ( dP B ) V [dV = −VdP B ] ρ 1 ρ = 1 1 − dP B where dp = change in pressure B = Bulk modulus of elasticity of the liquid = −VdP dV THRUST: A force acting normally on a surface is called thrust. i) It's unit in CGS system is dyne. ii) It's unit in SI System is newton (N). iii) The gravitational unit of thrust is Kilogram force (kgf). iv) Its Dimensional formula is [M1 L 1 T −2 ]. v) It is a vector quantity. PRESSURE: The force (thrust) acting normally on unit surface area is called pressure. If a thrust F acts on an area A such that P is the pressure. Pressure = Thrust Area P = F A i) Pressure unit in CGS system is Dyne /cm2 . ii) Its unit in SI system is newton /m2 .(or) pascal (Pa) iii) Its Dimensional formula [M1 L −1 T −2 ] iv) It is a Scalar quantity Nm−2 is also called Pascal (Pa) in the honour of physicist Pascal who discovered law for the transmission of pressure in the fluids. Pascal: When a force of 1 N (thrust) acts normally on an area of 1 m2 , then pressure acting on the surface is called 1 Pascal. i) 1kgfm−2 = 10 Pa( approx) ii) 1bar = 105 Pa iii) 1 torr = 1 mm of Hg

CLASS IX PHYSICS ∴ Volume of liquid column = area of cross section × length = a × h ∴ Mass of liquid column = volume × density = V × ρ = a × h × ρ ∴ Weight of liquid column = mass × acceleration due to gravity = m × g = a × h × ρ × g ∴ Weight of liquid column = mass × acceleration due to gravity = m × g = a × h × ρ × g ∴ Thrust exerted by liquid column on the base of the beaker = a × h × ρ × g ∴ Pressure due to liquid column P = Force Area = F a = ahρg a ∴ P = ρgh Factors on which the pressure at a point in fluids depends a) Pressure in a fluid is directly proportional to its height or depth. b) Pressure in a fluid is directly proportional to its density. c) Pressure in a fluid is directly proportional to acceleration due to gravity. d) Pressure in a fluid is independent of the area of cross-section. e) If PA is pressure due to atmosphere then total pressure at point B is PB = PA + hρg. This pressure is called absolute pressure. Absolute presure & Gauge pressure: The excess pressure above the atmospheric pressure is usually called gaų pressure and the total pressure is called absolute pressure. Thus Absolute pressure = Atmospheric pressure + Gauge pressure Pabsolute = Patm + ρgh Gauge pressure = Pabsolute − Patm = ρgh Barometer is used to measure atmospheric pressure. Manometer is used to measure gauge pressure. Law of liquid pressure: a) Pressure at a point inside the liquid increases with the depth from the free surface of the liquid. b) Pressure at a point inside liquid at a given depth increases with increase in the density of the liquid. c) Pressure is same in all directions, about a given point within the liquid. d) Pressure is same at all points in a horizontal plane at a given depth in stationar liquid.