1. Fluid Dynamics Yohanes Edi Gunanto Gen. Physics I Biology and Math. Edu. Program TC - UPH

2. Fluids essential to life – Human body 65% water – Earth’s surface is 2/3 water – Atmosphere extends 17km above the earth’s surface

3. 57:020 Fluid Mechanics 3 History Faces of Fluid Mechanics Archimedes (C. 287-212 BC) Newton (1642-1727) Leibniz (1646-1716) Euler (1707-1783) Navier (1785-1836) Stokes (1819-1903) Reynolds (1842-1912) Prandtl (1875-1953) Bernoulli (1667-1748) Taylor (1886-1975) Kolmogorov (1903-1987)

4. 57:020 Fluid Mechanics 4 Significance Fluids omnipresent – Weather & climate – Vehicles: automobiles, trains, ships, and planes, etc. – Environment – Physiology and medicine – Sports & recreation – Many other examples!

5. 57:020 Fluid Mechanics 5 Weather & Climate Tornadoes HurricanesGlobal Climate Thunderstorm

6. 57:020 Fluid Mechanics 6 Vehicles Aircraft Submarines High-speed rail Surface ships

7. 57:020 Fluid Mechanics 7 Environment Air pollution River hydraulics

8. 57:020 Fluid Mechanics 8 Physiology and Medicine Blood pumpVentricular assist device

9. 57:020 Fluid Mechanics 9 Sports & Recreation Water sports Auto racing Offshore racingCycling Surfing

10. 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

11. Density Regardless of form (solid, liquid, gas) we can define how much mass is squeezed into a particular space

12. Pressure A measure of the amount of force exerted on a surface area

13. 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 on 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)

14. 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

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

16. Pressure in a Fluid

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

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

19. 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

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

21. Flotation

22. Gases The primary difference between 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 moledules IDEAL GAS Independent of what the molecules are

23. Boyle’s Law

24. 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

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

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

27. 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 10 5 newtons/meter 2

28. Barometers

29. 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

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

31. Bernoulli’s Principle

32. 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)

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

34. Bernoulli’s Principle

35. Why the streamlines are compressed is quite complicated and relates to the air boundary layer, friction and turbulence.

36. Bernoulli’s Principle

37. Heart Attacks & Bernoulli artery plaque Arteries can become constricted with plaque (atherosclerosis), especially if one eats a poor diet and doesn’t exercise. The red streamlines show the path of blood as it veers around the plaque. The situation is similar to air flowing around a curved airplane wing. The pressure is lower where the fluid (blood) is flowing faster. The pressure difference can dislodge the plaque. The plaque can then lodge in and block a smaller artery. If it blocks an artery supplying blood to the heart, a heart attack can ensue. high pressure low pressure close up view

40. Bernoulli’s Equation: derivation Consider a volume  V of mass  M of incompressible fluid,

41. Example 1. A very large pipe carries water with a very slow velocity and empties into a small pipe with a high velocity. If P 2 is 7000 Pa lower than P 1, what is the velocity of the water in the small pipe? 3.74 m/s Venturi Meter

42. Applications of Bernoulli’s Equation Venturi meter Curve balls Airplanes Beach Ball & Straws Demos

43. Example 2. Consider an ideal incompressible fluid, choose >, < or =  1 ____  2 a) = b) < c) >

44. Example 3. Consider an ideal incompressible fluid, choose >, < or = Mass that passes “1” in one second _____ mass that passes “2” in one second a) = b) < c) >

45. Example 4. Consider an ideal incompressible fluid, choose >, < or = v 1 ____ v 2 a) = b) < c) >

49. THANKS