Chapter 13 - Fluids
• Pressure variation with
height or depth
• Pascal’s Principle
• Archimedes Principle
• Fluid Flow
• Bernoulli’s Equation
Fluid
• Matter that cannot
maintain its own shape
and therefore flows
readily under the influence
of forces
– Gases – Do not maintain
their size (volume)
– Liquids – Do maintain their
size – “incompressible”
• Solids maintain both their
size and shape under the
influence of forces
Density
• Which is heavier, wood or iron?
• Amount of mass per unit volume
m

V
• Compressible - Density easily altered
• Incompressible - Density varies only slightly or
not at all.
• Specific Gravity - ratio of the density of a
material to that of water
g
H 2 O  1
cm3
 1000
kg
m3
Pressure
• The normal force per unit
area that a fluid exerts on
the walls of its container,
adjacent fluids or other
boundaries.
• Units:
N/m2 = 1 Pascal
–
–
–
–
1 Bar = 105 Pa
1 atm = 1.013 x 105 Pa
1 atm = 14.7 lb/in2
1 atm = 760 Torr (mm Hg)
F
P
A
Variation of pressure with height (depth)
dFG   dm  g  gdV  gAdy
PA   P  dP  A  gAdy  0
dP
 g
dy
Variation of pressure with height (depth)
dP  gdy
P2
y2
P1
y1
 dP    gdy
P2  P1  g  y2  y1 
P  P0  gh
Problem 1 – What is the pressure at the faucet?
What do you do if you want more pressure at the faucet?
Absolute vs. Gauge Pressure
• Gauge Pressure
That read on a gauge
which compares it to
atmospheric
pressure
• Absolute Pressure
Sum of the gauge
pressure and
atmospheric
pressure
Problem 2
• What is the pressure at
a depth of 1300 feet
(approximately 400 m)
• w = 1000 kg/m3
Problem 3
• What is the height of a
mercury column if the
pressure at the bottom is
101.325 kPa and the
pressure at the top is zero?
• Hg = 13.595 x 103 kg/m3
h
Pascal’s Principle
• An increase in the pressure at any point in a
confined fluid is transmitted undiminished
throughout the fluid volume and to the walls
of the container.
A out
Fout 
Fin
A in
Problem 4
• In the system below, a 1.0 N force is applied to the
piston at the left. The piston is moved 5.0 cm
• What is the force on the large mass on the right.
• How far can the large block move?
A = 0.10 m2
A = 1.0 m2
Archimedes Principle
• The buoyancy force on
an object is equal to the
weight of the fluid it
displaces.
• Pressure at the top of an
object is less than at the
bottom
FB  F2  F1
FB  gh 2 A  gh1A  gV
Problem 5
• What volume of water
must be displaced for
a 6900 Ton submarine
to hover?
Fluid dynamics - equation of continuity
• Laminar flow
• Mass flow rate is
constant
m V A


 Av
t
t
t
1A1v1  2 A2 v2
Problem 4
• Water leaves the nozzle of a firehose at 50 m/s.
What is the velocity of water in the hose.
• Hose inner diameter = 10 cm
• Nozzle inner diameter = 3 cm
• Using the rocket equation, how much thrust does a
fireman feel from this exiting fluid?
Bernoulli’s principal
• Where the velocity of a fluid is high, the pressure
of a fluid is low, and where the velocity is low, the
pressure is high.
Bernoulli’s equation
W1  F1
1
 P1A1
W2  P2 A2 
1
2
Wg  mg  y2  y1 
1
1
2
W  mv 2  mv12  P1A1 1  P2 A 2 
2
2
2
 mg  y 2  y1 
Bernoulli’s equation
1
1
2
2
P2 A 2  2  mv 2  mgy 2  P1A1 1  mv1  mgy1
2
2
1 2
1 2
P2  v 2  gy 2  P1  v1  gy1
2
2
Problem 5
• Find the pressure in the fire hose with exhaust
velocity = 50 m/s
Problem 6
• What is the velocity of the fluid leaving the pipe at point 2.
• A small pipe directs the water upward. What is the height
of the plume?
1
h
2
Problem 7 (#47)
• What gauge pressure
is necessary in a fire
main if a firehose is to
spray water to a height
of 15 m?
Problem 8 (#50)
• If the wind blows at
25 m/s over your
house, what is the net
force on the roof if its
area is 240 m2?