Chapter 9
Fluids
Objectives
for Today
Hydrostatic Pressure; P = rgh
 Buoyancy; Archimedes’ Principle



Pascal’s Equation


P=F/A = f/a
Continuity Equation


Fbuoyancy = rg(Volume displaced)
A1V1=A2V2
Bernoulli’s Equation

P +1/2 rv2 + rgh = constant
Density

The density of a substance of uniform
composition is defined as its mass per unit
volume:
m
r
V
robj
 specific gravity
r fluid
Units are kg/m3 (SI) or g/cm3 (cgs)
 1 g/cm3 = 1000 kg/m3

Pressure

The force exerted by
a fluid on a
submerged object at
any point if
perpendicular to the
surface of the object
F
N
P
in Pa  2
A
m
Variation of Pressure
with Depth
If a fluid is at rest in a container, all
portions of the fluid must be in static
equilibrium
 All points at the same depth must be at
the same pressure


Otherwise, the fluid would not be in
equilibrium (Think weather)
Pressure and
Depth

Examine the darker
region, assumed to
be a fluid



It has a crosssectional area A
Extends to a depth h
below the surface
Three external
forces act on the
region
Pressure and Depth
equation
P  Po  rgh

Po is normal
atmospheric pressure



= 101.3 kPa
= 14.7 lb/in2
The pressure does not
depend upon the shape
of the container
Pressure Units

One atmosphere (1 atm) =
760 mm of mercury
 101.3 kPa
 14.7 lb/in2

Pressure
Calculation
Worksheet #1
Hoover Dam
 Average Head


158.5 meters of
water
Max Pressure;

???

Pressure Calculation
P = Po + rgh
 h=158.4 meters
 r = 1000 kg/m3
 Pressure:


Po + rgh = 101.3KPa + 1000 x 9.8 x 158.5 Pa
= 101.3 KPa + 1,553,300 Pa
 = 1655 KPa

Why Black and
White?
Power turbines
Downstream
Video Clip
Archimedes'
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
Archimedes’ Principle:
Totally Submerged Object
The upward buoyant force is
B=ρfluidVobjg
 The downward gravitational force is
w=mg=ρobjVobjg
 The net force is B-w=(ρfluid-ρobj)gVobj

Totally Submerged
Object
The object is less
dense than the fluid
 The object
experiences a net
upward force

Totally Submerged
Object
The object is more
dense than the fluid
 The net force is
downward
 The object
accelerates
downward

Archimedes’ Principle:
Floating Object
Fbuoyancy = rg(Volume displaced)
 The object is in static equilibrium.
 The upward buoyant force is balanced by the
downward force of gravity.
 Volume of the fluid displaced corresponds to
the volume of the object beneath the fluid
level.

Buoyancy in action
Worksheet #2
Ship displacement
810 million N!
332 meters long
How many cubic
meters are
displaced?
Got milk?

Ship weighs 810 x 106 N = B
B=rfluidgVdisp
Density of water = 1000
Vdisp=Wship/rwaterg
 Volume of water displaced is
 B=(810 x 106 )=Vdisp x (1000 x 9.8)

 Vdisp
kg/m3
= 82600 cubic meters or
 22 million gallons!
Pascal’s Principle

A change in pressure applied to an
enclosed fluid is transmitted undimished
to every point of the fluid and to the
walls of the container.
Pascal’s Principle

The hydraulic press is
an important application
of Pascal’s Principle
F1 F2
P

A1 A 2

Also used in hydraulic
brakes, forklifts, car
lifts, etc.
Application
Worksheet #3a
Fluids in Motion:
Streamline Flow

Streamline flow



every particle that passes a particular point moves
exactly along the smooth path followed by
particles that passed the point earlier
also called laminar flow
Streamline is the path


different streamlines cannot cross each other
the streamline at any point coincides with the
direction of fluid velocity at that point
Characteristics of an
Ideal Fluid

The fluid is nonviscous


The fluid is incompressible


Its density is constant
The fluid is steady


There is no internal friction between adjacent
layers
Its velocity, density and pressure do not change in
time
The fluid moves without turbulence

No eddy currents are present
Equation of
Continuity

A1v1 = A2v2

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 – what are its
units?
Application
Worksheet #3b
Bernoulli’s Equation
1 2
P  r v  r gh  constant
2
Let’s take a minute to show how much you already know
about this equation!
Do a dimensional analysis -
Bernoulli’s Equation
1 2
P  r v  r gh  constant
2
What do the second and third terms look like?
What happens we multiply by Volume?
Conservation of
energy
1 2
P  r v  r gh  constant
2

States that the sum of the pressure,
the kinetic energy per unit volume,
and the potential energy per unit
volume has the same value at all
points along a streamline.
Application
Worksheet #4
Applications of Bernoulli’s
Principle: Venturi Meter




Shows fluid flowing
through a horizontal
constricted pipe
Speed changes as
diameter changes
Can be used to measure
the speed of the fluid
flow
Swiftly moving fluids
exert less pressure than
do slowly moving fluids
Prairie Dogs
Build burrows with
two openings
 One is even with
ground, the other
built up, why?

Prairie Dogs
He wants his family
to have fresh air.
 Apply Bernoulli’s
Eq’n to a breeze
over both holes.

Breeze
1 2
P  r v  r gh  constant
2
Prairie Dogs
How will the
pressures over each
hole compare?
 What will this do the
air in the tunnel?

Breeze
1 2
P  r v  r gh  constant
2
Questions?
Hydrostatic Pressure; P = rgh
 Buoyancy; Archimedes’ Principle


Fbuoyancy = rg(Volume displaced)
Pascal; F/A=f/a
 Continuity Equation



A1V1=A2V2
Bernoulli’s Equation

P + 1/2 rv2 + rgh = constant
Greek or Geek?
Greek or Geek?
Greek or Geek?
Greek or Geek?
Greek or Geek?
Video Clip