1. Chapter 11
Fluids

2. DEFINITION OF MASS DENSITY
The mass density of a substance is the mass of a
substance divided by its volume:
SI Unit of Mass Density: kg/m3
Relative Density (Specific Gravity) is the ratio of the density of a substance/material to the density of water.
Relative Density = ρ(material) / ρ (water)

3. 11.1 Mass Density

4. Example 1 Blood as a Fraction of Body Weight
11.1 Mass Density
Example 1 Blood as a Fraction of Body Weight
The body of a man whose weight is 690 N contains about
5.2x10-3 m3 of blood.
(a) Find the blood’s weight and (b) express it as a
percentage of the body weight.

5. 11.1 Mass Density
(a)
(b)

6. Student Practice Problems
11.1 Mass Density
Problems
Problem 1: Find the mass density of a chunk of rock of mass 215 g that displaces a volume of 75 cm3 of water.
Problem 2: A piece of aluminum of mass 6.24 kg displaces water that fills a container 12 cm x 12 cm x 16 cm. Find it’s mass density.
Problem 3: What is the mass of gasoline in a 1250 liter gas tank. (Density of gasoline is 680 kg/m3 ; 1 liter = 1000 cm3)
Student Practice Problems
Page 308 of Textbook, Question 1 (Answer: 8.3 x 103 lb)
Page 308 of textbook, Question 2 (Answer: 824 kg/m3)
Page 308 of Textbook, Question 8 (Answer: 2.3 x 10-5 m3)

7. SI Unit of Pressure: 1 N/m2 = 1Pa
Pascal

8. Example 2 The Force on a Swimmer
11.2 Pressure
Example 2 The Force on a Swimmer
Suppose the pressure acting on the back
of a swimmer’s hand is 1.2x105 Pa. The
surface area of the back of the hand is
8.4x10-3m2.
Determine the magnitude of the force
that acts on it.
(b) Discuss the direction of the force.

9. Since the water pushes perpendicularly
11.2 Pressure
Since the water pushes perpendicularly
against the back of the hand, the force
is directed downward in the drawing.

10. Atmospheric Pressure at Sea Level: 1.013x105 Pa = 1 atmosphere

11. Page 309 of Textbook, Question 12 Page 309 of Textbook, Question 16
11.2 Pressure
Problems:
Page 309 of Textbook, Question 12
Page 309 of Textbook, Question 16
Student Practice Problem
Page 309 of Textbook, Question 18 (Answer: a m; b. 4.7 J)

12. 11.3 Pressure and Depth in a Static Fluid

13. 11.3 Pressure and Depth in a Static Fluid

14. 11.3 Pressure and Depth in a Static Fluid
Conceptual Example 3 The Hoover Dam
Lake Mead is the largest wholly artificial
reservoir in the United States. The water
in the reservoir backs up behind the dam
for a considerable distance (120 miles).
Suppose that all the water in Lake Mead
were removed except a relatively narrow
vertical column.
Would the Hoover Same still be needed
to contain the water, or could a much less
massive structure do the job?

15. 11.3 Pressure and Depth in a Static Fluid
Example 4 The Swimming Hole
Points A and B are located a distance of 5.50 m beneath the surface
of the water. Find the pressure at each of these two locations.

16. 11.3 Pressure and Depth in a Static Fluid

17. 11.4 Pressure Gauges

18. 11.4 Pressure Gauges
absolute pressure

19. 11.4 Pressure Gauges

20. Problems
Problem 4
Find the gauge water pressure (in kPa) at 25 m level of a water tower containing water 50 m deep. Find the absolute pressure at the same level.
Problem 5
What is the height of a column of water if the gauge pressure at the bottom of the column is 95 kPa?
Problem 6
What is the mass density of a liquid that exerts a gauge pressure of 180 kPa at a depth of 30 m?

21. Force Exerted By Liquids
The force exerted by a liquid on the horizontal surface of a container depends on the area of the surface, the depth of the liquid and the density of the liquid.
It is given by:
F = ρghA
F is the force exerted by the liquid on the horizontal surface in N
ρ is the density of the liquid in kg/m3
g is acceleration due to gravity in m/s2
h is the depth of the liquid in m
A is the cross-sectional are of the horizontal surface in m2

22. Force Exerted By Liquids
The force exerted by a liquid on a vertical surface of a container (such as the side of a tank) is found by
F = ½ρghA
F is the force exerted by the liquid on vertical surface in N
ρ is the density of the liquid in kg/m3
g is acceleration due to gravity in m/s2
h is the depth of the liquid in m
A is the cross-sectional are of the horizontal surface in m2

23. Problems
Problem 7:
Find the total force on the side of a water-filled cylindrical tank 3 m high with radius 5 m.
Problem 8: (On board with rectangular shaped wall)

24. Any change in the pressure applied
11.5 Pascal’s Principle
PASCAL’S PRINCIPLE
Any change in the pressure applied
to a completely enclosed fluid is transmitted
undiminished to all parts of the fluid and
enclosing walls.

25. 11.5 Pascal’s Principle

26. The input piston has a radius of 0.0120 m
11.5 Pascal’s Principle
Example 7 A Car Lift
The input piston has a radius of m
and the output plunger has a radius of
0.150 m.
The combined weight of the car and the
plunger is N. Suppose that the input
piston has a negligible weight and the bottom
surfaces of the piston and plunger are at
the same level. What is the required input
force?

27. 11.5 Pascal’s Principle

28. 11.6 Archimedes’ Principle

29. Problems
Problem 9:
The small piston of a hydraulic press has an area of 8 cm2. If the applied force is 25 N, find the area of the large piston to exert a pressing force of 3600N
Problem 10:
The large piston of a hydraulic lift has radius 40 cm. The small piston has radius 5 cm to which a force of 75 N is applied.
Find the force exerted by the large piston.
Find the pressure on the large piston.
Find the pressure on the small piston.

30. 11.6 Archimedes’ Principle
Any fluid applies a buoyant force to an object that is partially
or completely immersed in it; the magnitude of the buoyant
force equals the weight of the fluid that the object displaces:

31. 11.6 Archimedes’ Principle
If the object is floating then the
magnitude of the buoyant force
is equal to the magnitude of its
weight.

32. 11.6 Archimedes’ Principle
Example 9 A Swimming Raft
The raft is made of solid square
pinewood. Determine whether
the raft floats in water and if
so, how much of the raft is beneath
the surface.

33. 11.6 Archimedes’ Principle

34. 11.6 Archimedes’ Principle
The raft floats!

35. 11.6 Archimedes’ Principle
If the raft is floating:

36. 11.6 Archimedes’ Principle
Conceptual Example 10 How Much Water is Needed
to Float a Ship?
A ship floating in the ocean is a familiar sight. But is all
that water really necessary? Can an ocean vessel float
in the amount of water than a swimming pool contains?

37. 11.6 Archimedes’ Principle

38. Unsteady flow exists whenever the velocity of the fluid particles at a
11.7 Fluids in Motion
In steady flow the velocity of the fluid particles at any point is constant
as time passes.
Unsteady flow exists whenever the velocity of the fluid particles at a
point changes as time passes.
Turbulent flow is an extreme kind of unsteady flow in which the velocity
of the fluid particles at a point change erratically in both magnitude and
direction.

39. Fluid flow can be compressible or incompressible. Most liquids are
11.7 Fluids in Motion
Fluid flow can be compressible or incompressible. Most liquids are
nearly incompressible.
Fluid flow can be viscous or nonviscous.
An incompressible, nonviscous fluid is called an ideal fluid.

40. When the flow is steady, streamlines are often used to represent
11.7 Fluids in Motion
When the flow is steady, streamlines are often used to represent
the trajectories of the fluid particles.

41. Making streamlines with dye and smoke.
11.7 Fluids in Motion
Making streamlines with dye
and smoke.

42. 11.8 The Equation of Continuity
The mass of fluid per second that flows through a tube is called
the mass flow rate.

43. 11.8 The Equation of Continuity

44. 11.8 The Equation of Continuity
The mass flow rate has the same value at every position along a
tube that has a single entry and a single exit for fluid flow.
SI Unit of Mass Flow Rate: kg/s

45. 11.8 The Equation of Continuity
Incompressible fluid:
Volume flow rate Q:

46. 11.8 The Equation of Continuity
Example 12 A Garden Hose
A garden hose has an unobstructed opening
with a cross sectional area of 2.85x10-4m2.
It fills a bucket with a volume of 8.00x10-3m3
in 30 seconds.
Find the speed of the water that leaves the hose
through (a) the unobstructed opening and (b) an obstructed
opening with half as much area.

47. 11.8 The Equation of Continuity
(b)

48. The fluid accelerates toward the lower pressure regions.
11.9 Bernoulli’s Equation
The fluid accelerates toward the
lower pressure regions.
According to the pressure-depth
relationship, the pressure is lower
at higher levels, provided the area
of the pipe does not change.

49. 11.9 Bernoulli’s Equation

50. fluid speed, and the elevation at two points are related by:
11.9 Bernoulli’s Equation
BERNOULLI’S EQUATION
In steady flow of a nonviscous, incompressible fluid, the pressure, the
fluid speed, and the elevation at two points are related by:

51. 11.10 Applications of Bernoulli’s Equation
Conceptual Example 14 Tarpaulins and Bernoulli’s Equation
When the truck is stationary, the
tarpaulin lies flat, but it bulges outward
when the truck is speeding down
the highway.
Account for this behavior.

52. 11.10 Applications of Bernoulli’s Equation

53. 11.10 Applications of Bernoulli’s Equation

54. 11.10 Applications of Bernoulli’s Equation

55. 11.10 Applications of Bernoulli’s Equation
Example 16 Efflux Speed
The tank is open to the atmosphere at
the top. Find an expression for the speed
of the liquid leaving the pipe at
the bottom.

56. 11.10 Applications of Bernoulli’s Equation

57. 11.11 Viscous Flow
Flow of an ideal fluid.
Flow of a viscous fluid.

58. FORCE NEEDED TO MOVE A LAYER OF VISCOUS FLUID WITH CONSTANT VELOCITY
11.11 Viscous Flow
FORCE NEEDED TO MOVE A LAYER OF VISCOUS FLUID WITH
CONSTANT VELOCITY
The magnitude of the tangential force required to move a fluid
layer at a constant speed is given by:
coefficient
of viscosity
SI Unit of Viscosity: Pa·s
Common Unit of Viscosity: poise (P)
1 poise (P) = 0.1 Pa·s

59. The volume flow rate is given by:
11.11 Viscous Flow
POISEUILLE’S LAW
The volume flow rate is given by:

60. Example 17 Giving and Injection
11.11 Viscous Flow
Example 17 Giving and Injection
A syringe is filled with a solution whose
viscosity is 1.5x10-3 Pa·s. The internal
radius of the needle is 4.0x10-4m.
The gauge pressure in the vein is 1900 Pa.
What force must be applied to the plunger,
so that 1.0x10-6m3 of fluid can be injected
in 3.0 s?

61. 11.11 Viscous Flow

62. 11.11 Viscous Flow