# Chapter 8 Fluid Mechanics

Mechanics

Oct 24, 2013 (4 years and 8 months ago)

185 views

Physics

Chapter 8

Fluid Mechanics

Density

ρ

=
M

V

Therefore:

ρ
V = M

Chapter

8

Density

Fig. T9.3, p. 262

Slide 13

Archimedes’s Principle

Any object completely or partially submerged
in a fluid is buoyed up by a force whose
magnitude is equal to the weight of the fluid
displaced by the object.

Buoyant Force

The upward force is
called the
buoyant force

The physical cause of
the buoyant force is the
pressure difference
between the top and
the bottom of the
object

Buoyant Force, cont.

The magnitude of the buoyant force always equals
the weight of the displaced fluid

The buoyant force is dependent on the volume of the
object and the density of the fluid it is submerged in.

For a floating object, the buoyancy force must equal
the weight of the object.

B=W

Some objects may float high or low

Example: A balloon having a volume of 1.5 cubic meters is filled with
ethyl alcohol and is tethered to the bottom of a swimming pool.
Calculate the tension in the cord tethering it to the bottom of the
swimming pool.

Fy = B

T

W = 0

Therefore, T = B

W

T =

water
Vg

alcohol
Vg

T = (

water

alcohol
)Vg

T = (1000kg/m
3

806kg/m
3
) (1.5m
3
)(9.8m/s
2
)

T = 2851.8 N

B

T

W

FBD

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.

11.6
Archimedes’ Principle

11.6
Archimedes’ Principle

The raft floats!

11.6
Archimedes’ Principle

If the raft is floating:

Pressure

P =
F

N

A m
2

Pascal’s Principal

Pressure applied to a fluid in a closed
container is transmitted equally to every point
of the fluid and to the walls of the container.

Hydraulic Lift

F
2
, A
2

F
1
, A
1

P
1

=P
2

Therefore:

F
1

= F
2

A
1

A
2

Pressure at a Depth

P =
F

=
mg

=
ρ
Vg

=
ρ
Ahg

=
ρ
hg

A A A A

330 m

Find the pressure on the bottom

of the submarine due to the water

above it.

Find the pressure on the bottom

of the submarine due to the water

And air above it.

Equation of Continuity

A
1
v
1

= A
2
v
2

The product of the cross
-
sectional area of a pipe
and the fluid speed is a
constant

Speed is high where the
pipe is narrow and speed
is low where the pipe has
a large diameter

Av is called the
flow rate

How Airplanes Wings Work