Chapter:1 Fluids & Properties Fluid Statics Fluid Dynamics

Fluid Mechanics Statics Fluid Dynamic fluid Kinetic fluid Kinematic fluid

Density or Mass density: It is define as the ration of mass of fluid to its volume Unit: kg/m3 Water= 1000 kg/m3 Specific Weight or Weight density: It is the ration of Weight of fluid to its volume Unit: 9.81 * 1000 N/ m3

Specific Volume: It is the ration of Volume of fluid to its Mass Unit: m3/kg Specific Gravity: Specific gravity is defined as ration of Weight density of fluid to the weight density of standard fluid. Density (ς) = S x 1000 kg/m3

Ex 1 Calculate the Specific weight, density and Specific gravity of One liter of a liquid which weighs 7 N Specific Weight (W) = Weight/Volume Density(ς) = W/g Specific Gravity = Density of Liquid/ Density of water Ans. 7000N/m3, 731.5 kg/m3, 0.7135

Ex 2 Calculate the density, specific weight and weight of one liter of Petrol of specific gravity 0.7

Viscosity: Viscosity is defined as the property of a fluid which offers resistance to movement of one layer of fluid over another adjacent (adjoining) layer of the fluid. u + du dy u du y Velocity Profile u

Kinematic Viscosity: It is define as the ration between the dynamic viscosity and density of fluid 1 stoke = 1 cm2/s = 10-4 m2/s 1 Centistoke = 1/100 stoke

Types of Fluid: Ideal Fluid: A fluid, which is incompressible and is having no viscosity, is known as an ideal fluid Real Fluid: A fluid, which having a viscosity, is known as real fluid Newtonian fluid: A real fluid, in which the shear stress is directly proportional to the rate of shear strain . Non-Newtonian Fluid: A real fluid, in which the shear stress is not proportional to the rate of shear strain. Ideal Plastic Fluid: A fluid, in which shear stress is more than the yield value and shear stress is proportional to the rate of shear strain I P F N N F N F Shear Stress I F Velocity Gradient

Ex 2 A Plate 0.0025 mm distant from a fixed plate, moves at 60 cm/s And requires a force of 2N per unit area i.e. 2 N/m2 to maintain this Speed. Determine the fluid viscosity between the plates. Ans: 8.33 x 10-4 poise

Ex 3 Two horizontal plates are placed 1.25 cm apart, the space Between them being filled with oil of viscosity 14 poises. Calculate The shear stress in oil if upper plate is moved with a velocity of 2.5 m/s. Ans: 280 N/m2

Ex 4 Determine the specific gravity of a fluid having viscosity 0.05 Poise and kinematic viscosity 0.035 stokes. Ans: ς=1428.5 kg/m3, S =1.43

Ex 5 Determine the viscosity of a liquid having kinematic viscosity 6 Stokes and specific gravity 1.9 Ans: μ =1.14 NS/m2

Surface tension and Capillarity: Surface tension is defined as the tensile force acting on the surface of A liquid in contact with a gas or on the surface between two immiscible Liquids such that the contact surface behaves like a membrane Under tension.

Surface Tension on liquid Droplet: Let σ = Surface tension of the liquid p = Pressure intensity inside the droplet d = Dia. Of droplet. Tensile force due to surface tension acting around the Circumference of the cut portion = σ x Circumference = σ x П d (1) ii) Pressure force on the Area = p x П/4 d2 (2) Under the Equilibrium Condition 1 =2 p = 4 σ /d

ii) Surface Tension on a Hollow Bubble: p x П/4 d2 = 2 (σ x Пd) p = 8 σ/ d iii) Surface Tension on a Liquid jet: p = Pressure intensity inside the liquid jet above the outside pressure σ = Surface tension of the lquid. Force due to pressure = p x area of semi jet = p L d Force due to surface tension = σ 2L Equating the firce , we have P L d = σ 2 L

Ex 6 The surface tension of water in contact with air at 20o C is 0.00725 N/m. The pressure inside a droplet of water is to be 0.02 N/cm2 greater than the outside pressure. Calculate the Dia. of the droplet of water. p = 4 σ /d Ans. 1.45 mm

Ex 6 Find the surface tension in a soap bubble of 40 mm Dia. when The inside pressure is 2.5 N/m2 above atmospheric pressure. p x П/4 d2 = 2 (σ x Пd) p = 8 σ/ d Ans. σ = 0.0125 N/m

Capillarity: Capillarity is defined as a phenomenon of rise or fall of a liquid Surface in a small tube relative to the adjacent general level of Liquid when the tube is held vertically in the liquid. Expression for Capillary Rise: Let d = diameter of small tube h = height of the liquid in the tube σ = Surface tension of liquid θ = Angle of contact bet. Liquid & Gass Weight of liquid of height h in tube (1) Vertical Component Sur. Tensile For. (2)

(1) = (2) Value of θ water = 0

Expression for Capillary Fall: If the glass tube is dipped in mercury, the level Of mercury in the tube will be lower than the General level of the outside liquid. 1) Surface tension downward= 2) Hydrostatic force upward = (1) = (2) Value of θ = 128o-130o (Mercury & Glass tube)

Ex Calculate the capillary rise in a glass tube of 2.5 mm dia. When Immersed vertically in Water Mercury Take surface tension σ = 0.0725 N/m for water and σ = 0.52 N/m for mercury in contact with air The specific gravity for mercury is given as 13.6 and angle =130o Ans. A) h = 1.18 cm b) h = - 0.4 cm

Ex The capillary rise in the glass tube is not exceed 0.2 mm of water Determine its minimum size, given that surface tension for water in Contact with air = 0.0725 N/m Ans. D = 14.8 cm

Ex Calculate the capillary effect in millimeter in a glass tube of 4mm Dia., when immersed in 1) water 2) mercury The temperature of the liquid is 20o C and the values of the surface Tension of water and mercury at 20oC in contact with air 0.073 N/m And 0.51 N/m respectively. The angle of contact for water is zero That for mercury 130o. Take density of water at 20oC as equal to 998 kg/m3. Ans. A) h = 7.51mm b) h = - 2.46 mm

Vapour Pressure: Vapor pressure is the pressure at which the liquid is converted into Vapours, at given temperature. Cavitation: The pressure developed by the collapsing bubbles is so high that the Material from the adjoining boundaries gets eroded and cavities are Formed on them. This phenomenon is known as cavitations

Prepared by, Dr Dhruvesh Patel