1. Hydrostatics: Fluids at Rest

2. applying Newtonian principles to fluids hydrostatics—the study of stationary fluids in which all forces are in equilibrium Fluid Mechanics

3. hydrodynamics—the study of fluids in motion Fluid Mechanics

4. abbreviation: ρ mass per unit volume g/cm³ is commonly used SI unit: kg/m³ Density

5. specific gravity: density relative to water dimensionless number numerically equal to the density of the substance in g/cm³ Density

6. Pressure is defined as the force exerted perpendicular to a unit area. When a fluid is at rest, the pressure is uniform throughout the fluid in all directions. Units of Pressure

7. At the boundaries of a fluid, the container exerts a pressure on the fluid identical to the pressure the fluid exerts on the container. Units of Pressure

8. SI unit: Pascal (Pa) Earliest: atmosphere (atm) 1 atm = 1.013 × 10 5 Pa torr bars and millibars (mb) 1 atm = 1.013 bar = 1013 mb Units of Pressure

9. gauge pressure (P g ) often used with piping systems absolute pressure (P) Units of Pressure

10. pressure changes with depth density is usually assumed to be constant throughout depth y = d 2 = d 1 + Δd Σ F = 0 N Incompressible Fluids

11. Σ F y = F d1 + F d2 + F w = 0 N to calculate the pressure at any depth d: Incompressible Fluids P d = P ref + ρgd

12. Incompressible Fluids d is expressed as a negative scalar distance g = -9.81 m/s² P ref is atmospheric pressure if the liquid’s container is open to the atmosphere P d = P ref + ρgd

13. usually referring to gases, since their density is not constant with height/depth Compressible Fluids P = P ref e P ref ρ ref - |g|h

14. must remember that temperature also affects the pressure of a gas Compressible Fluids

15. Pascal’s principle: the external pressure applied to a completely enclosed incompressible fluid is distributed in all directions throughout the fluid Hydraulic Devices

16. machines that transmit forces via enclosed liquids small input forces can generate large output forces Hydraulic Devices

17. note the cross- sectional areas of each F out = nF in Hydraulic Devices

18. note the distance each piston travels Hydraulic Devices

19. manometer barometer first instrument to accurately measure atmospheric pressure used mercury Pressure Indicators

20. famous problem: Archimedes and the crown What happens when an object is placed in a fluid? Buoyancy

21. for object in fluid: F w-o : gravitational force on object in fluid F b : buoyant force on object F b = ρ|g|V Buoyancy

22. F b = ρ|g|V ρ is the density of the displaced fluid Buoyancy

23. Archimedes’ principle: any system that is submerged or floats in a fluid is acted on by an upward buoyant force equal in magnitude to the weight of the fluid it displaces Buoyancy

24. If the buoyant force is equal to the system’s weight, the forces are balanced and no acceleration occurs. requires object and fluid to have equal density Buoyancy

25. If the weight of a system is greater than that of the displaced fluid, its density is greater than the fluid’s. Since weight exceeds the buoyant force, the object will sink. Buoyancy

26. If the weight of a system is less than that of the displaced fluid, its density is less than the fluid’s. Since buoyant force is greater than weight, the object will accelerate up. Buoyancy

27. When the object rises to the surface of the liquid, its volume remaining beneath the surface changes the buoyant force until they are in equilibrium. Buoyancy

28. This is also true with gases. The density of a gas changes with altitude and temperature. The object may respond to a change in pressure. Buoyancy

29. Every object submerged in a fluid has both a center of mass and a center of buoyancy. These are the same for objects of uniform density that are completely submerged. Center of Buoyancy

30. defined: the center of mass of the fluid that would occupy the submerged space that the object occupies Center of Buoyancy

31. If the center of mass and center of buoyancy are not the same, the object will experience a torque and rotate. The center of buoyancy will be directly above the center of gravity. Center of Buoyancy

32. instrument used to measure density has many uses Hydrometer

33. Hydrodynamics: Fluids in Motion

34. assumptions: the fluid flows smoothly the velocity of the fluid does not change with time at a fixed location in the fluid path Ideal Fluids

35. assumptions: the density of the fluid is constant (incompressible) friction has no effect on fluid flow Ideal Fluids

36. Streamlines not a physical reality laminar turbulent flow tube Ideal Fluids

37. The rate of volume and mass flow into a segment of a flow tube equals the rate of volume and mass flow out of the flow tube segment. Ideal Fluids

38. equation of flow continuity: Flow Continuity A 1 v 1 = A 2 v 2 requires tubes with smaller cross-sectional areas to have higher fluid velocities

39. background equations: Bernoulli’s Principle ΔK = ½ρΔVv 2 2 – ½ρΔVv 1 2 ΔU = ρΔV|g|h 2 – ρΔV|g|h 1 Equation 17.12 Equation 17.13

40. background equations: Bernoulli’s Principle W ncf = ΔK + ΔU W ncf = P 1 ΔV – P 2 ΔV Equation 17.14 Equation 17.15

41. Bernoulli’s Equation: Bernoulli’s Principle P 1 + ½ρv 1 2 + ρ|g|h 1 = P 2 + ½ρv 2 2 + ρ|g|h 2

42. if the velocity does not change: v 1 = v 2 Bernoulli’s Principle P 1 + ½ρv 1 2 + ρ|g|h 1 = P 2 + ½ρv 2 2 + ρ|g|h 2 P 1 + ρ|g|h 1 = P 2 + ρ|g|h 2

43. if the elevation of the fluid does not change: h 1 = h 2 Bernoulli’s Principle P 1 + ½ρv 1 2 + ρ|g|h 1 = P 2 + ½ρv 2 2 + ρ|g|h 2 P 1 + ½ρv 1 2 = P 2 + ½ρv 2 2

44. A faster-flowing fluid will have streamlines that are closer together. A lower-pressure fluid will have streamlines that are closer together. Bernoulli’s Principle

45. airfoil: any device that generates lift as air flows along its surface hydrofoil: object that creates lift in liquid Lift

46. Bernoulli principle Conadă effect Theories of Lift

47. viscosity: a measure of the resistance of fluid to a flow caused by cohesive forces between particles of a fluid a type of internal friction coefficient of viscosity (η) Real Fluids

48. lower coefficients of viscosity indicate that the fluids flow more easily viscosity is sometimes referred to as the “thickness” of a fluid Real Fluids

49. particles closest to the walls move more slowly than those farther from the walls Real Fluids