FLUID MECHANICS

FLUID MECHANICS AND HYDRAULIC MACHINERIES

1. UNIT - 1 FLUID PROPERTIES AND FLOW CHARACTERISTICS

2. DEFINE FLUID A fluid (or) liquid, which is capable of flowing. It has no own shape, but confirms to the shape of the containing vessels. A fluid is a substance that continually deforms under an applied shear stress Liquids are like water, milk, air, steam. MATTER EXISTS IN TWO STATES: solids and the fluids. fluids state being commonly divided into the liquid and gaseous states.

3. DIFFERENCES BETWEEN SOLIDS AND FLUIDS A solid is generally own shape and change in volume under pure compressive load. It resistance to change in shape without a change in volume under the application of tangential forces. The spacing and latitude of motion of molecules are very small in solids, large in a liquid and extremely large in gas. The intermolecular bonds are very strong in solids, weak in liquids and very weak in gases. Solids are very compact and rigid. Solids materials are steel, wood, plastics etc.

4. FLUID MECHANICS Fluid mechanics is that branch of science which deals with the behavior of fluids (liquids or gases) at rest as well as in motion. This branch of science deals with the static, kinematics and dynamic aspects of fluids. The study of fluids at rest is called fluid statics. The study of fluids in motion, where pressure forces are not considered, is called fluid kinematics. The pressure forces are also considered for the fluids in motion, that branch of science is called fluid dynamics.

5. UNITS AND DIMENSIONS The word dimensions are used to describe basic concepts like mass, length, time, temperature and force. Units are the means of expressing the value of the dimension quantitatively or numerically. All physical quantities are measured by units. There are two types of units: ( i ). Fundamental units. (ii). Derived units. FUNDAMENTAL UNITS. All physical quantities are expressed the following : 1.Length(L) 2.Mass(M) 3.Time(T) DERIVED UNITS. Derived units are expressed in terms of fundamental units, this are area, velocity, pressure etc.

6. SYSTEM OF UNITS CGS Units The fundamental units of length, mass and time are taken as centimeter, gram and second respectively. FPS Units The fundamental units of length, mass and time are taken as feet, pound and second respectively. MKS Units In this system, the fundamental units of length, mass and time are taken as meter, kilogram, and seconds respectively. The MKS units are called as gravitational units or engineers units. SI Units This system has six basic units, two supplementary units and twenty seven derived units.

7. S.I Six Basic Units Quantity SI Unit Dimension Length Metre , m L Mass Kilogram, kg M Time Second, s T Temperature Kelvin, K Current Ampere, A I Luminosity Candela Cd

8. Two Supplementary Units One is for measuring the plane angle called radian( rad ). Another for measuring solid angle called stearadian ( Sr ).

9. Derived Units Quantity SI Unit Volume m 3 Area m 2 velocity m/s Discharge m 3 /s acceleration m/s 2 force N Torque, energy, work Joule J (or) N m power Watt W pressure ( or stress) N/m 2 density kg /m 3 Dynamic viscosity N s/ m 2 surface tension N/m Kinematic viscosity m 2 /s

10. Thermal conductivity W/ mK Specific heat J/ kgK Entropy J/K Momentum Kg-m/s Weight density N/m 3 Frequency Hz Angular velocity Rad /s Angular acceleration Rad / s 2

11. DIFFERENT TYPES OF FLUIDS Basically the fluids are classified into 5 types and these are 1. Ideal fluid 2. Real fluid 3. Newtonian fluid 4. Non-Newtonian fluid, and 5. Ideal plastic fluid

12. Ideal Fluid   A fluid which is incompressed and have no viscosity falls in the category of  ideal fluid. Ideal fluid is not found in actual practice but it is an imaginary fluid because all the fluid that exist in the environment have some viscosity. there in no ideal fluid in reality. Real Fluid A fluid which has at least some viscosity is called real fluid. Actually all the fluids existing or present in the environment are called real fluids.. Newtonian Fluid If a real fluid obeys the Newton's law of viscosity ( i.e the shear stress is directly proportional to the shear strain) then it is known as the Newtonian fluid. Example: water, kerosene Non-Newtonian Fluid If real fluid does not obeys the Newton's law of viscosity then it is called Non-Newtonian fluid. Example: paint, toothpaste Ideal Plastic Fluid A fluid having the value of shear stress more than the yield value and shear stress is proportional to the shear strain (velocity gradient) is known as ideal plastic fluid.

13. PROPERTIES OF FLUIDS Density (or) Mass Density:(ρ) Density or mass density of a fluid is defined as the ratio of the mass of a fluid to its volume. Thus mass per unit volume of a fluid is called density. ρ = Mass of fluid / Volume of fluid Its units ,kg/m 3 Temperature increase with density decrease Pressure increase with density increase To estimate the density from characteristic gas equation of Pv = mRT (R= 287J/ kgK (or) 0.287 KJ/kg) Water = 1000 kg/m 3 , Mercury = 13600 kg/m 3, Air = 1.23 kg/m 3 , Paraffin Oil = 800 kg/m 3 . (at pressure =1.013 N/m 2, and Temperature = 288.15 K.)

14. Specific weight or weight density:(w) Specific weight or weight density of a fluid is the ratio between the weight of a fluid to its volume. The weight per unit volume of a fluid is called Specific weight or weight density It various from place to place because of acceleration due to gravity changing from place to place. Specific weight, w = Weight of fluid / Volume of fluid w = ρg (w=W/V = mg/V = ρg ) Its units, N/m 3 Temperature increase with specific weight decrease Pressure increase with specific weight increase Water =9810 N/m 3 , Mercury = 132943 N/m 3 , Air =12.07 N/m 3 , Paraffin Oil =7851 N/m 3

15. Specific Volume:(v) Specific volume of a fluid is defined as the volume of a fluid occupied by a unit mass or volume per unit mass of a fluid. v = Volume of fluid / Mass of fluid = 1/ ρ Its units, m 3 /kg

16. Specific Gravity (or) Relative Density :(S) Specific gravity is defined as the ratio of the density of a fluid to density of a standard fluid. S = density of a fluid / density of a standard fluid. Specific gravity of mercury is 13.6

17. Viscosity Viscosity is the property of a fluid, due to cohesion and interaction between molecules, which offers resistance to sheer deformation. Different fluids deform at different rates under the same shear stress. Fluid with a high viscosity such as syrup, deforms more slowly than fluid with a low viscosity such as water. Shear stress,

18. Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over adjacent layer of the fluid. When two layers of a fluid, a distance ‘ dy ’ apart, move one over the other at different velocities, say u and u+du . The viscosity together with relative velocity causes a shear stress acting between the fluid layers. The top layer causes a shear stress on the adjacent lower layer while the lower layer causes a shear stress on the adjacent top layer. This shear stress is proportional to the rate of change of velocity with respect to y.

19. Dynamic Viscosity (µ): Its defined as the Shear stress(τ), required causing unit rate of shear deformation(du/ dy ). µ = τ /(du/ dy ). Its units, N-s/m 2 (or) kg/m-s (or) poise Kinematic Viscosity (ν): Its defined as the ratio of dynamic viscosity to mass density. Its units, m 2 /s (or) stoke

20. VAPOUR PRESSURE H 2 O( g ) molecules (water vapor) H 2 O( l ) molecules

21. VAPORIZATION: A change from the liquid state to the gaseous state is known as vaporization. VAPOUR PRESSURE: The liquid is kept in closed vessel. The vaporization take place, the molecules escapes from the free surface of the liquid. This vapour molecules occupies the space b/w free liquid surface and the top of the vessel. These accumulated vapours exert a pressure on the liquid surface. This pressure is called the vapour pressure of the liquid. Water vapour pressure is 2337N/ m 2 at 20 C, but 101325 N/ m 2 at 100 C.

22. SURFACE TENSION 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. Due to molecules attraction, liquids have properties of cohesion and adhesion. Cohesion is due to the force of attraction b/w molecular of same liquid. This force is very small. Adhesion is due to the force of attraction b/w the molecules of two different liquid. The molecules of the liquid and molecules of solid surface

23. BULK MODULUS It define as the ratio of change in pressure to the rate of change of volume is called as bulk modulus of the material. Bulk modulus (K) = (change in pressure) / (volumetric strain) K = -( dp /( dV /V)) Volumetric strain is the change in volume divided by the original volume. ( dV /V) Negative sign for  dV indicates the volume decreases as pressure increases. K =  dp /( dρ /ρ) [ dV /V = - dρ /ρ] Typical values of Bulk Modulus: K = 2.05 x 10 9  N/m 2  for water K = 1.62 x 10 9  N/m 2  for oil.

24. COMPRESSIBILITY The compressibility of a fluid is the reduction of the volume of the fluid due to an external pressure acting on it. A compressible fluid will reduce (or) change in volume in the presence of external pressure. Compressibility is the reciprocal of the bulk modulus of elasticity, K which is defined as the ratio of compressive stress to volumetric strain. Compressibility is given by = 1/K Its unit in N/m 2 In nature all the fluids are compressible. Gases are highly compressible but liquid s are not highly compressible. Relationship b/w bulk modulus (K) and Pressure(P) for a gas The relationship b/w bulk modulus of elasticity(K) and Pressure for a gas for two different processes of compression are as: ( i ). Isothermal process. (ii). Isentropic (or) adiabatic process.

25. CAPILLARITY Capillarity is defined as a phenomenon of rise or fall of a liquid surface relative to the adjacent general level of liquid in a small tube, when the tube is held vertically in the liquid Capillarity occurs because of intermolecular forces b/w the liquid and surrounding solid surface. And due to pressure of cohesion and adhesion which cause the liquid work against gravity It is expressed in terms of cm or mm of liquid. Its value depends upon the specific weight of the liquid, diameter of the tube and surface tension of the liquid.

26. CAPILLARY RISE If the glass tube is inserted vertically in a liquid, say water. The liquid will rise in the tube above the level of the liquid surface is known as capillary rise σ = Surface tension of liquid. θ = Angle of contact b/w liquid and glass tube. The Weight of liquid of height h in the tube = (Area of tube x h) x ρ x g = (π/4 x d 2 x h) x ρ x g ------------------------- ( i ) Vertical component of the surface tensile force = (σ x Circumference) x cos θ = σ x πd x cos θ ------------------------------- (ii) Equating equation ( i ) & (ii) (π/4 x d 2 x h) x ρ x g = σ x πd x cos θ h = σ x πd x cos θ / (π/4 x d 2 ) x ρ x g h = 4 σ cos θ / ρ x g x d

27. CAPILLARY DEPRESSION If the glass tube is dipped vertically in a liquid, say mercury. The level of mercury in the tube will be lower than the general level of the outside liquid. Two forces are acting on the mercury inside the tube. First one is due to surface tension acting in the down ward direction and equal to σ x πd x cos θ --------- ( i ) Second force is due to hydrostatic force acting upward and is equal to intensity of pressure at a depth ‘h’ x Area = p x (π/4 x d 2 ) = ρg x h x (π/4 x d 2 ) -------------- (ii) Equating equation ( i ) & (ii) σ x πd x cos θ = ρ x g x h x (π/4 x d 2 ) h = 4 σ cos θ / ρ x g x d

28. APPLICATION OF BERNOULLI’S EQUATION Venturi meter Orifice meter Pitot tube

29. VENTURIMETER

30. VENTURI METER

31. ORIFICE METER

32. ORIFICE METER

33. PITOT TUBE