SARDAR VALLABHBHAI PATEL INSTITUTE OF TECHNOLOGY CIVIL DEPARTMENT

ENROLLMENT NO.NAME BURHANUDDIN ADENWALA PRIYANK AGRAWAL TAMANNA BADAR BHAVIK BRAHMBHATT GROUP MEMBERS

FLUID MECHANICS TOPIC : PROPERTIES OF FLUIDS

CONTENTS NO.TOPICS 1)DEFINITION OF FLUIDS AND FLUID MECHANICS 2)DIFFERENCE BETWEEN SOLID, LIQUID AND GASES 3)APPLICATIONS OF FLUID MECHANICS 4)PROPERTIES OF FLUIDS 5)VISCOSITY 6)NEWTON’S LAW OF VISCOSITY 7)VARIATION OF VISCOSITY WITH TEMPERATURE 8)CLASSIFICATION OF FLUIDS 9)VAPOUR PRESSURE 10)COMPRESSIBILITY 11)EXAMPLES

DEFINITION OF FLUID : When a body or matter flows from one point to another point on application of shear force is known as fluid. DEFINITION OF FLUID MECHANICS : Fluid mechanics is the branch of engineering dealing with the study of behaviour of fluid when it is at rest or motion.

SR. NO. SOLIDLIQUIDGASES 1)It has definite shape.The liquid retains its volume and forms a free surface in the container. The gas has no fixed volume and it will expand continuously unless restrained by a containing vessel. 2)Distance between molecules is less.The space between molecules is relatively small. The space between molecules is relatively large. 3)Intermolecular cohesive forces are more. Intermolecular cohesive forces are comparatively less. Intermolecular cohesive forces are negligible. 4)Resistance to shear force is more.It deforms continuously when subjected to shear stress. It also deforms continuously when subjected to shear stress. 5) Liquids are incompressible for all practical purposes. Gases are readily compressible. 6)e.g. chalk,pencil,crystals,etcE.g. water,oil,diesel,mercury,etce.g. air,CO 2, O 2, H 2, etc DIFFERENCE BETWEEN SOLID, LIQUID AND GASES :

APPLICATIONS OF FLUID MECHANICS Design of hydraulic structures like dams, canals,weirs, etc. Design of machinery like pumps, turbines, etc. Design of aeroplanes and ships. Design and analysis of gas turbines, rocket engines, etc. Fluidic control devices both pneumatic and hydraulic. Methods and devices for the measurement of various parameters, e.g. the pressure and velocity of a fluid at rest remains at rest or in motion. Human blood circulatory system, i.e. flow of blood in veins.

PROPERTIES OF FLUIDS Density/mass density Specific weight/weight density Specific volume Specific gravity Surface tension Cohesion and adhesion Capillarity Viscosity Bulk modulus of elasticity Compressibility Vapour Pressure

VISCOSITY Viscosity is defined as the property of fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of the fluid.

TYPES OF VISCOSITY There are two types of viscosity : i.Dynamic viscosity : When viscosity of fluid is studied w.r.t. force,it is called dynamic viscosity.  It is denoted by “μ”(mu).  Its unit is “N.s/m 2”. ii.Kinematic viscosity : When viscosity of fluid is studied w.r.t. motion of fluid, it is called kinematic viscosity.  It is denoted by “ν”(nu).  Its unit is “stoke”.

NEWTON’S LAW OF VISCOSITY It states, “The shear stress on a layer of a fluid is directly proportional to the rate of shear strain”. Shear stress α velocity gradient ζ α du/dy therefore, ζ = μ.du/dy Where, du/dy = velocity gradient = shear strain

EFFECT OF TEMPERATURE ON VISCOSITY The viscosity of a fluid is due to contributing factors, namely 1.Cohesion between the fluid molecules 2.Transfer of momentum between the molecules  In case of liquids the molecules are very close to each other and accordingly a large cohesion exists. Hence in liquids, the viscosity is mainly due to intermolecular cohesion, while in gases viscosity is mainly due to molecular momentum transfer.  The intermolecular cohesive forces decreases with rise of temperature and hence with the increase in temperature the viscosity of a liquid decreases.  In case of gases, viscosity mainly depends on transfer of molecular momentum in a direction at right angles to the direction of motion.as the temperature increases, the molecular agitation increases i.e. there will be large momentum transfer and hence the viscosity increases.

CLASSIFICATION OF FLUIDS There are five types of fluids : i.Ideal fluid : A fluid which is incompressible, and is having no viscosity, no surface tension, is known as an ideal fluid. ii.Real fluid : A fluid which is compressible, has viscosity and surface tension, is known as Real fluid. iii.Newtonian fluid : A real fluid in which the shear stress is directly proportional to the rate of shear strain, is known as Newtonian fluid. iv.Non-Newtonian fluid : A real fluid, in which the shear stress is not proportional to the rate of shear strain, is known as Non-Newtonian fluid. v.Ideal Plastic fluid : A fluid in which shear stress is more than yield value and shear stress is proportional to the rate of shear strain is known as ideal plastic fluid.

VAPOUR PRESSURE The vapour pressure (P°) is the pressure of the vapour of a compound in equilibrium with its pure condensed phase (solid or liquid). Vapour pressures depend strongly on the temperature and vary widely with different compounds due to differences in molecule – molecule interactions. The normal boiling point of a liquid is defined as the temperature at which the vapour pressure of the liquid is 1 atmosphere (P° = 1 atm ). The vapour pressure of a substance is an intrinsic physical property that plays a crucial role in determining it’s distribution to and from gaseous environmental phases (the atmosphere, marsh bubble gas). Vapour pressure is the pressure at which the liquid is converted to vapours, at given temperature. Vapour pressure of a liquid increases with its temperature due to its molecular activity.

COMPRESSIBILITY Bulk (volume) modulus of elasticity, Ev. K= - dp/(dv/v) Where, dp = change in pressure dv = change in volume v = original volume Ev represents the dp required to produce a unit change in specific volume (dv/v) For a fixed mass of liquid at constant temperature, the bulk modulus does not change much on a moderate range of temperature

EXAMPLES EXAMPLE PROBLEM : A solid circular cylinder slides inside a vertical smooth pipe. The space between the cylinder and the pipe is lubricated with an oil film. Calculate the terminal velocity of the cylinder. GIVEN : Pipe diameter: D = mm Cylinder diameter: d = 100 mm Cylinder length: l = 300 mm Cylinder weight: W = 50 N Oil: 0.8 Oil temperature: 20 o C ASSUMPTIONS : The cylinder is concentric with the pipe as it falls. Once dropped inside the pipe, the cylinder will accelerate for a while. At some point all the forces acting on it will balance out. From that point on the cylinder will descend with a constant velocity (known as terminal velocity). · We will only take into consideration the oil resistance due to viscous forces acting on the sides of the cylinder neglecting any pressure forces acting on its top and bottom surfaces (i.e., we will neglect pressure drag).

SOLUTION : If the cylinder descends with constant velocity, it is in equilibrium under all the forces acting on it. The free body diagram is shown below: ΣFy = 0 W –F viscous = 0 F viscous = W Now F viscous =ζS Where S is the surface area of the cylinder in contact with the oil: S = πdl The viscous shear stress is given by Newton’s law of viscosity: ζ=μdu/dx The no-slip condition requires that the velocity of the oil in contact with the pipe is zero, while the velocity of the oil in contact with the cylinder is U (the same as the velocity of the cylinder itself). Since the gap between the two surfaces is very small, the velocity profile may be assumed to be linear between these two surfaces. In this case, the derivative du/dx can be written as: du/dx=U-0/δ where δ is the gap between the cylinder and the pipe so: δ=D-d/2 Combining eqs. and solving for the velocity U gives: U=W(D-d)/2πdlμ Hence,we calculate the terminal velocity of the cylinder to be U=0.89 m/s.