1. Chapter 11
Fluids

2. Defining a Fluid Ability to flow Difference between gas and liquid
Gas or liquid
Difference between gas and liquid
Liquid has a definite volume

3. Mass Density Mass per unit volume Symbol => r Units => kg/m3
Specific Gravity
Ratio of density of a substance to the density of water at 4° C
Density of water is 1000 kg/m3 at 4°C

4. Pressure Force per unit area Units => N/m2 = pascal(Pa) psi
1 bar = 105 Pa

5. Atmospheric Pressure Caused by the weight of air above
Extremely large pressure
1 atm = 1.013×105 Pa
Exerted in all directions
Barometers measure pressure

6. Pressure and Depth
Fluid pressure increases with depth

7. Pressure and Depth
Gauge pressure is only pressure relative to the atmospheric pressure
Absolute or Total pressure must include the pressure of the atmosphere

8. Example Problem
How much pressure would a submarine have to withstand at a depth of 5 km in the ocean? ( of sea water=1.025* 103kg/m3)

9. Example Problem

10. Example Problem

11. Pascal’s Principle
Applied pressure to a fluid in a closed container is transmitted equally throughout the fluid
Example: Hydraulic lifts

12. Archimede’s PrincipleFB
A Buoyant Force that acts upward on an object submerged in or floating on a liquid Fg
Apparent weight of the object will be less

13. Archimede’s Principle

14. Archimede’s Principle

15. Archimedes' Principle
A buoyant force is equal to the weight of the fluid displaced FB Fg

16. Floating Object FB
Net force is zero on floating object Fg

17. Archimedes' Principle
Submerged object FB Fg

18. Archimede’s Principle
Objects will float if the density of the object is less than or equal to the density of the liquid

19. Example Problem
A piece of metal weighs N in the air and 68 N in water. What is the density of the metal? (Density of water=1.00*103kg/m3)

20. Example Problem

21. Example Problem

22. Fluids in Motion Steady vs Unsteady Flow Steady flow Unsteady flow
Velocity of particles at any point is constant
Velocity at another point may be different, but still constant for that point
River—Faster in the center and slower on the edges
Unsteady flow
Velocity of particles at a point continually changes
Turbulent flow-an extreme case of unsteady flow
River Rapids

23. Fluid in Motion Compressible vs Incompressible Incompressible
Density of fluid is constant
Liquids
Compressible
Gases are highly compressible

24. Fluid in Motion Viscous vs Nonviscous Viscous Does not flow readily
One layer hinders other layers from flowing freely
Honey-High Viscosity
Water-Low viscosity
No real fluid is nonviscous

25. Ideal Fluid Incompressible Non-viscous
Non-turbulent—would form nice straight constant streamlines

26. Equation of Continuity
Mass flow rate
mass of fluid per second that flows through a tube
Kg/s

27. Equation of Continuity
Mass flow rate is constant for any given section of pipe
What enters at one end of the pipe, must exit the other side of the pipe
Thus, fluids will flow faster if size of tube gets smaller.
Incompressible fluid
Density is constant
Called the volume flow rate

28. Example Problem
Water flows through a 4.1 m diameter tunnel at a speed of 3.0 m/s. It then enters a 2.7m tunnel at the same level where the pressure is 82 kPa.
Find the velocity of the water in the small tunnel.

29. Example Problem

30. Bernoulli’s Equation
Pressure in a fluid is inversely proportional to fluid velocity
Explains unbalanced force in acceleration of fluids
Lift in planes
As a fluid raises its elevation, the pressure decreases because of less fluid above it

31. Principle’s of Fluid Flow
Bernoulli’s Equation
Conservation of energy in fluids
Work-energy theorom
Uses energy per unit volume

32. Example Problem
A large storage tank, open at the top, develops a hole 5 m below the surface of the water. What is the velocity of the water when it leaves the hole?

33. Example Problem

34. Example Problem

35. Example Problem
Water flows through a 4.1 m diameter tunnel at a speed of 3.0 m/s. It then enters a 2.7m tunnel at the same level where the pressure is 82 kPa.
Find the pressure in the wide portion of the tunnel.

36. Viscous Flow Fluid Flow is hindered by viscosity
A fluid is visualized as thin layers
Slowest at a boundary
Fastest at the center
Called Laminar flow
A force is required to keep offset the forces from neighboring layers

37. Viscous Flow Force required to move any layer depends on
Area of contact(A)
Velocity of layer(v)
Distance from immobile surface(y)
Coefficient of viscocity (η)—Units are Pas

38. Viscous Flow
This force is caused by a difference in pressure between two points in a pipe for viscous flow
Flow rate depends on
Pressure difference
Radius of pipe
Length of pipe
Viscosity of fluid