Fluid mechanics fluid properties and characteristics

Fluid mechanics fluid properties

1. UNIVERSITY OF TECHNOLOGY AND APPLIED SCIENCES – IBRI EGME2220 Fluid Mechanics

2. Topics Fluid Mechanics – Introduction, Branches, Applications Units & dimensions Properties of fluids Types of fluids Problems solved

3. Fluid Mechanics Introduction Fluid Fluid is defined as a physical substance which deforms continuously or it flows continuously when it is subjected to a tangential shear stress. It includes both liquids and gases. Fluid Mechanics Fluid Mechanics is the science that deals with behavior of fluids at rest (fluid statics) or in motion (fluid dynamics) and the interaction of fluids with solids or other fluids at the boundaries.

4. 4 Hydrodynamics The study of the motion of fluids that can be approximated as incompressible (such as liquids, especially water, and gases at low speeds ). Hydraulics A subcategory of hydrodynamics , which deals with liquid flows in pipes and open channels. Gas dynamics It deals with the flow of fluids that undergo significant density changes , such as the flow of gases through nozzles at high speeds. Aerodynamics: It d eals with the flow of gases (especially air ) over bodies such as aircraft, rockets, and automobiles at high or low speeds. Fluid Mechanics Introduction

5. Application areas of fluid Mechanics Medicine : All artificial hearts, breathing machines. Medicine: Lab-on-a Chip device , glucose monitor, controlled drug delivery, etc . Oil and Gas : The piping systems for cold water. Ducting network of heating and A/c systems. Pipeline, pump, valve, offshore rig, oil spill clean-up, etc . Electronics : Convective cooling of generated heat . Military : Missile, aircraft, ship, underwater vehicle, dispersion of chemical agents etc. Energy : Combustor, burner, boiler, gas, hydro and wind turbine , etc . Almost everything in our world is in contact with a fluid or is itself a fluid.

6. Units and Dimensions

7. Primary and Secondary units Derived Units Primary Units

8. Fluid Properties

9. Fluid Properties Density : It is defined as the ratio of mass of the fluid to its volume Density (  ) = (kg/m3) Density of water = 1000 kg/m3 Density of mercury= 13600 kg/m3 Specific volume: It is the reciprocal of density. i.e Specific volume = ( m3/kg) Weight Density or Specific weight: It is defined as the ratio of weight of the fluid to its volume. Weight Density = ( N/m3) (Note: Weight = mg; Weight density =  g)

10. FLUID PROPERTIES Specific Gravity Specific Gravity is defined as the ratio between density or weight density of the fluid to density or weight density of standard fluid. For liquids the standard fluid considered is water, and for gases the standard fluid considered is air. For liquids: Specific gravity of liquids = or For gases: Specific gravity of gas = or

11. Viscosity It is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of the fluid . When two layers of fluid at a distance ( dy ) apart move with 2 different velocities (u) and ( u+du ), then there will be a shear stress (  ) acting . Newton's law of Viscosity This shear stress is directly proportional to the rate of change of velocity with respect to y. Mathematically,   du/ dy  =  du/ dy Where  - Shear stress in (N/m2) du / dy – Velocity gradient

12. Types of Viscosity Dynamic (or Absolute) Viscosity : The dynamic viscosity (  ) of a fluid is a measure of the resistance it offers to relative shearing motion.  = Ꞇ/(du/ dy ) N-s/m² (SI unit) Shear stress Ꞇ= F/A Another unit of viscosity is Poise 1 Poise = Kinematic Viscosity : It is defined as the ratio of absolute viscosity to the density of fluid. ν=  / ρ m²/s (SI unit) ; ρ= density of fluid The unit of kinematic viscosity = Another unit of kinematic viscosity is stoke 1 stoke = 10 -4 m²/s

13. Surface tension Surface tension ( ) is defined as : the tensile force acting on the surface of the liquid contact with a gas or on the surface between two immiscible liquids such that the contact surface behaves like a membrane under tension For liquid droplet: , where ( ) is the pressure For hollow bubble: The unit of surface tension is:  

14. CAPILLARITY Capillarity ( ) is defined as : the phenomenon of fall or rise of liquid surface in a small tube relative to the adjacent general level of liquid when the tube is held vertically in the liquid . The rise of liquid is called capillarity rise: The fall of liquid is called capillarity rise: The unit of capillarity is  

15. Relationship between Linear velocity and Angular velocity Linear velocity , du = Where D = Diameter of rotating shaft in m, N = Speed of rotating shaft in rpm, Torque transmitted by the shaft: Torque transmitted, T = F x D/2 ; Power lost in the bearing: Power lost, P = F X u

16. Types of fluids IDEAL FLUID: A fluid which is incompressible and having no viscosity.it is an imaginary fluid as all the fluids REAL FLUID: A fluid which possesses 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 is known as Newtonian Fluid NON-NEWTONIAN FLUID: A real fluid in which the shear stress is not directly proportional to the rate of shear strain is known as Non Newtonian fluid 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 is known as Ideal Plastic fluid.

17. Problem 1 One litre of liquid weighs 6N. Calculate the Specific weight, density and Specific gravity of that liquid. Assume density of water as 1000 kg/m 3

18. Problem 2 Determine the specific weight, density and weight of one litre of petrol of specific gravity = 0.9

19. Problem 3 The liquid is having a dynamic viscosity of 0.045 poise and kinematic viscosity of 0.035 stokes. Find the specific gravity of that liquid .

20. Problem 4 A flat plate of area 1.5 X 10 6 mm 2 is pulled with a speed of 0.4 m/s relative to another plate located at a distance of 0.15 mm from it. Find the force and power required to maintain this speed, if the fluid separating them is having the viscosity 1 poise.

21. Problem 5 Calculate the dynamic viscosity of an oil, which is used for lubrication between a square plate of size and an inclined plane with angle of inclination as shown in the figure. The weight of the square plate is and it slides down the inclined plane with a uniform velocity of . The thickness of the oil film is .  

22. Problem 6 The velocity distribution for flow over a flat plate is given by in which u is the velocity in m/s at a distance of ‘y’ meter above the plate . Determine the shear stress at y=0.15 m. Assume dynamic viscosity of oil as 8.5 poise.

23. Problem 7 An oil of dynamic viscosity is 6 poise is used for lubricate the space between the shaft and sleeve. The diameter of the shaft is 0.4 m and rotates at 190 rpm. Determine the ( i ) Torque transmitted and (ii) power lost in the bearing for a sleeve length of 90mm. The thickness of oil film is 1.5mm.

24. Problem 8 The surface tension of water in contact with air at is . The pressure inside a droplet water is to greater than the outside pressure. Calculate the diameter of droplet of water.  

25. Problem 9 Find the surface tension in a soap bubble of diameter when the inside pressure is above the atmospheric pressure.  

26. Problem 10 Find out the minimum size of a glass tube that can be used to measure water level if the capillary rise in the tube is to be restricted to . Consider the surface tension of water in contact with air as .  

27. Problem 11 Calculate the capillarity effect in millimeters in a glass tube of diameter when immersed in ( i ) water, (ii) mercury. The temperature of the liquid is and the values of the surface tension of water and mercury at in contact with air are and respectively. The angle of contact of water is zero, and that for mercury is . Take the density of water at as equal to .  

28. Exercise problems 1. One litre of crude oil weighs 9.6N. Calculate its specific weight, density and specific gravity. ( Ans : 9600 N/m3, 978.6 kg/m3, 0.978) 2. A plate, 0.025 mm distant from a fixed plate, moves at 50 cm/s and requires a force of 1.471 N/m2 to maintain this speed. Determine the fluid viscosity between the plates in the poise. ( Ans : 7.357 x 10-4) 3. Determine the intensity of shear of an oil having viscosity = 1.2 poise and is used for lubrication in the clearance between a 10 cm diameter shaft and its journal bearing. The clearance is 1.0 mm and shaft rotates at 200 rpm. ( Ans : 125.6 N/m 2 ) 4. Two plates are placed at a distance of 0.15 mm apart. The lower plate is fixed while the upper plate having surface area 1.0 m2 is pulled at 0.3 m/s. Find the force and power required to maintain this speed, if the fluid separating them is having viscosity 1.5 poise. ( Ans : 300N, 89.8 W)

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