Introduction to Fluid Mechanics. Chapter 1.

1. Introduction to Fluid Mechanics.Chapter 1. Phys 404 Dr Nazir Mustapha

2. Al Imam University College of SciencesDr Nazir Mustapha – 323-223-C-1 10 hours

3. Exams - Midterm 1:week: 2 - Midterm 2: week: 4 - Final: week: 6 – or - 7 Grading: - Midterm1: 20 - Midterm 2: 20 • Home works, participation & quizzes: 20 • Final Exam: 40 • Please note that a quiz will be given at the end of each chapter.

4. PHYISCS 404 - Chapter 1-2 Physics 404 –Fluid Mechanics Dr. Nazir Mustapha Office: SR 104, Third Floor Phone: 2582167 e-mail: 94@imamm.org nazirmustapha63@gmail.com OFFICE HOURS Sun:10:00 – 11:20am, LECTURE HOURS Sun & Wed: 1,2,3 &4 and Thurs: 1, 2 SCHEDULE Lectures are on: Sunday, Wednesday and Thursday.

5. Textbooks: 1. Yunus A. Çengel and John M. Cimbala. Fluid Mechanics: Fundamentals and Applications.Second Edition, McGraw Hill, 2010. 2.Fox, McDonald & Pritchard. Introduction to Fluid Mechanics. 5th Edition, Wiley, 2004

6. Mechanical properties of Matter and fluids. Contents: • Definition of a fluid • Density, • Pressure, • Fluid flow, • Pascal Law • Boyle’s Law • Bernoulli's equation and its application, 6

7. Introduction • Fluid mechanics is a study of the behavior of fluids, either at rest (fluid statics) or in motion (fluid dynamics). • The analysis is based on the fundamental laws of mechanics, which relate continuity of mass and energy with force and momentum. • An understanding of the properties and behavior of fluids at rest and in motion is of great importance in Physics. 7

8. Fluid Flow Shear stress – Yes Fluid Rest Shear stress – No 1.1 Definition of Fluid • A fluid is a substance, which deforms continuously, or flows, when subjected to shearing force. • In fact if a shear stress is acting on a fluid it will flow and if a fluid is at rest there is no shear stress acting on it.

9. 9 Definition of a Fluid A fluid is a substance that flows under the action of shearing forcesقوى القص . If a fluid is at rest, we know that the forces on it are in balance. A gas is a fluid that is easily compressed. It fills any vessel in which it is contained. A liquid is a fluid which is hard to compress. A given mass of liquid will occupy a fixed volume, irrespective of the size of the container. A free surfaceis formed as a boundary between a liquid and a gas above it.

10. Definition of a Fluid • “a fluid, such as water or air, deforms continuously when acted on by shearing stresses of any magnitude.” - Munson, Young, Okiishi Water Oil Air Why isn’t steel a fluid?

11. F U b Fluid Deformation between Parallel Plates Side view Force F causes the top plate to have velocity U. What other parameters control how much force is required to get a desired velocity? Distance between plates (b) Area of plates (A) Viscosity!

12. Moving plate Shear force Fluid particles New particle position Fixed surface Shear stress in moving fluid • If fluid is in motion, shear stress are developed if the particles of the fluid move relative to each other. Adjacent particles have different velocities, causing the shape of the fluid to become distorted • On the other hand, the velocity of the fluid is the same at every point, no shear stress will be produced, the fluid particles are at rest relative to each other.

13. Shearing Forces

14. Fluid Mechanics • Liquids and gases have the ability to flow. • They are called fluids. • There are a variety of “LAWS” that fluids obey. • Need some definitions.

15. Differences between liquid and gases.

16. Pressure in a Fluid • The pressure is just the weight of all the fluid above you. • Atmospheric pressure is just the weight of all the air above an area on the surface of the earth. • In a swimming pool the pressure on your body surface is just the weight of the water above you (plus the air pressure above the water).

17. Pressure in a Fluid • So, the only thing that counts in fluid pressure is the gravitational force acting on the mass ABOVE you. • The deeper you go, the more weight above you and the more pressure. • Go to a mountaintop and the air pressure is lower.

18. Pressure in a Fluid Pressure acts perpendicular to the surface and increases at greater depth.

19. Pressure in a Fluid

20. Buoyancy Net upward force is called the buoyant force!!! Easier to lift a rock in water!!

21. Displacement of Water The amount of water displaced is equal to the volume of the rock.

22. Archimedes’ Principle • An immersed body is buoyed up by a force equal to the weight of the fluid it displaces. • If the buoyant force on an object is greater than the force of gravity acting on the object, the object will float. • The apparent weight of an object in a liquid is gravitational force (weight) minus the buoyant force.

23. Flotation • A floating object displaces a weight of fluid equal to its own weight.

24. Flotation

25. Gases • The primary differencebetween a liquid and a gas is the distance between the molecules. • In a gas, the molecules are so widely separated, that there is little interaction between the individual molecules. • IDEAL GAS. • Independent of what the molecules are.

26. Boyle’s Law 26

27. Boyle’s Law • Pressure depends on density of the gas. • Pressure is just the force per unit area exerted by the molecules as they collide with the walls of the container. • Double the density, double the number of collisions with the wall and this doubles the pressure.

28. Boyle’s Law Density is mass divided by volume. Halve the volume and you double the density and thus the pressure.

29. Boyle’s Law • At a given temperature for a given quantity of gas, the product of the pressure and the volume is a constant

30. Elements that exist as gases at 250C and 1 atmosphere

31. The Gas Laws Figure 1.7: The Pressure-Volume Relationship:Boyle’s Law

32. The Gas Laws The Pressure-Volume Relationship: Boyle’s Law • Mathematically: • A sample of gas contained in a flask with a volume of 1.53 L and kept at a pressure of 5.6×103 Pa. If the pressure is changed to 1.5×104 Pa at constant temperature, what will be the new volume? (in-class example).

33. Constant temperature Constant amount of gas Boyle’s Law Pa 1/V P x V = constant P1 x V1 = P2 x V2

34. 726 mmHg x 946 mL P1 x V1 = 154 mL V2 A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL? P1 x V1 = P2 x V2 P1 = 726 mmHg P2 = ? V1 = 946 mL V2 = 154 mL P2 = = 4460 mmHg

35. Atmospheric Pressure • Just the weight of the air above you. • Unlike water, the density of the air decreases with altitude since air is compressible and liquids are only very slightly compressible. • Air pressure at sea level is about 105 newtons/meter2.

36. Barometers

37. Buoyancy in a Gas • An object surrounded by air is buoyed up by a force equal to the weight of the air displace. • Exactly the same concept as buoyancy in water. Just substitute air for water in the statement. • If the buoyant force is greater than the weight of the object, it will rise in the air.

38. Buoyancy in a Gas Since air gets less dense with altitude, the buoyant force decreases with altitude. So helium balloons don’t rise forever!!!

39. Bernoulli’s Principle

40. Bernoulli’s Principle. • Flow is faster when the pipe is narrower. • Put your thumb over the end of a garden hose. • Energy conservation requires that the pressure be lower in a gas that is moving faster. • Has to do with the work necessary to compress a gas (PV is energy, more later).

41. Bernoulli’s Principle • When the speed of a fluid increases, internal pressure in the fluid decreases.

42. Bernoulli’s Principle

43. Bernoulli’s Principle Why the streamlines are compressed is quite complicated and relates to the air boundary layer, friction and turbulence.

44. Bernoulli’s Principle

45. Bernoulli’s Equation

46. Bernoulli’s Equation The speed of water spraying from the end of a hose increases as the size of the opening is decreased with thumb. A fluid flowing through a constricted pipe with streamline flow. The fluid in the section of length Δx1 moves to the section of length Δx2 . The volumes of fluid in the two sections are equal. 46

47. Bernoulli’s Equation • The sum of the pressure, kinetic energy per unit volume, and gravitational potential energy per unit volume has the same value at all points along a streamline. • This result is summarized in Bernoulli’s equation: • P +1/2ρv2 + ρgy = constant 47

48. The Venturi tube The horizontal constricted pipe illustrated in figure known as a Venturi tube, can be used to measure the flow speed of an incompressible fluid. Let us determine the flow speed at point 2 if the pressure difference P1 ̶ P2 is known. Solution:Because the pipe is horizontal, y1 = y2, and applying Bernoulli’s equation: • Pressure P1 is greater Than the pressure P2 since v1 < v2. This device can be used to measure the speed of fluid flow. Figure 15: Venturi Tube 48

49. Bernoulli’s Equation For steady flow, the speed, pressure, and elevation of an incompressibleandnonviscous fluid are related by an equation discovered by Daniel Bernoulli (1700–1782). 49 Figure 16

50. Bernoulli’s Equation In the steady flow of a nonviscous, incompressible fluid of density ρ, the pressure P, the fluid speed v, and the elevation y at any two points (1 and 2) are related by: Figure 17: 50