FundamentalsofEngineering
FundamentalsofEngineering
Fundamentals
of
Engineering
Fundamentals
of
Engineering
(
FE
)
Exam
(
FE
)
Exam
()
()
General Section
General Section
Fluid Mechanics Revie
w
Fluid Mechanics Revie
w
StevenBurian
StevenBurian
Steven
Burian
Steven
Burian
Civil & Environmental Engineering
Civil & Environmental Engineering
October26,2010
October26,2010
October
26,
2010
October
26,
2010
X
X
FluidMechanics
FluidMechanics
Fluids and FE
Fluids and FE
X
.
X
.
Fluid
Mechanics
Fluid
Mechanics
A. Flow measurement
A. Flow measurement
B. Fluid properties
B. Fluid properties
C.Fluidstatics
C.Fluidstatics
7% of FE Morning
7% of FE Morning
Session
Session
C.
Fluid
statics
C.
Fluid
statics
D. Energy, impulse, and momentum equations
D. Energy, impulse, and momentum equations
E. Pipe and other internal flow
E. Pipe and other internal flow
IVFluidDynamics
IVFluidDynamics
IV
.
Fluid
Dynamics
IV
.
Fluid
Dynamics
A. Bernoulli equation and mechanical energy balance
A. Bernoulli equation and mechanical energy balance
B. Hydrostatic pressure
B. Hydrostatic pressure
C.Dimensionlessnumbers(e.g.,ReynoldsNumber)
C.Dimensionlessnumbers(e.g.,ReynoldsNumber)
C.
Dimensionless
numbers
(e.g.,
Reynolds
Number)
C.
Dimensionless
numbers
(e.g.,
Reynolds
Number)
D. Laminar and turbulent flow
D. Laminar and turbulent flow
E. Velocity head
E. Velocity head
F. Friction losses
(
e.
g
.
,
p
i
p
es
,
valves
,
fittin
g
s
)
F. Friction losses
(
e.
g
.
,
p
i
p
es
,
valves
,
fittin
g
s
)
(g,pp,,g)
(g,pp,,g)
G. Pipe networks
G. Pipe networks
H. Compressible and incompressible flow
H. Compressible and incompressible flow
I. Flow measurement (e.g., orifices, Venturi meters)
I. Flow measurement (e.g., orifices, Venturi meters)
10% of FE Afternoon
10% of FE Afternoon
Session
Session
J. Pumps, turbines, and compressors
J. Pumps, turbines, and compressors
K. Non
K. Non
Newtonian flow
Newtonian flow
L. Flow through packed beds
L. Flow through packed beds
Fluids
Fluids
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
!
!
Fluids are substances in either the liquid
Fluids are substances in either the liquid
or gas phase
or gas phase
Fluid
Fluid
Properties
Properties
!
!
Fluids cannot support shear, and they
Fluids cannot support shear, and they
deformcontinuouslytominimizeapplied
deformcontinuouslytominimizeapplied
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
deform
continuously
to
minimize
applied
deform
continuously
to
minimize
applied
shear forces
shear forces
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Viscosity
Viscosity
Sht(
Sht(
)
)
f
f
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
!
!
Sh
ear s
t
ress
(
Sh
ear s
t
ress
(
!
!
)
:
)
:
f
orce
f
orce
required to slide one unit
required to slide one unit
area layer of a substance
area layer of a substance
overanother
overanother
Fluid
Fluid
Properties
Properties
over
another
over
another
!
!
Viscosity (
Viscosity (
"
"
):
):
measure of a
measure of a
fluid’s resistance to flow
fluid’s resistance to flow
whenacteduponbyan
whenacteduponbyan
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
when
acted
upon
by
an
when
acted
upon
by
an
external force (i.e., ease with
external force (i.e., ease with
which a fluid pours)
which a fluid pours)
!
!
Asafluidmovesashear
Asafluidmovesashear
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
!
!
As
a
fluid
moves
a
shear
As
a
fluid
moves
a
shear
stress is developed in it;
stress is developed in it;
magnitude is dependent on
magnitude is dependent on
viscosityoffluid
viscosityoffluid
Momentum
Momentum
and Drag
and Drag
viscosity
of
fluid
viscosity
of
fluid
F/A
F/A
is the fluid shear stress (
is the fluid shear stress (
!
!
)
)and the constant
and the constant
of
p
ro
p
ortionalit
y
is the absolute viscosit
y
(
of
p
ro
p
ortionalit
y
is the absolute viscosit
y
(
"
"
)
)
:
:
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
ppyy(
ppyy(
"
"
)
)
du
"
!
#
Fluid
Fluid
Properties
Properties
dy
"
!
Newtonianfluids:
Newtonianfluids:
strainsareproportionaltothe
strainsareproportionaltothe
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Newtonian
fluids:
Newtonian
fluids:
strains
are
proportional
to
the
strains
are
proportional
to
the
applied shear stress
applied shear stress
Non
Non


Newtonianfluids:
Newtonianfluids:
fluidshearstresscanbe
fluidshearstresscanbe
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Non
Non


Newtonian
fluids:
Newtonian
fluids:
fluid
shear
stress
can
be
fluid
shear
stress
can
be
computed using the power law
computed using the power law
Momentum
Momentum
and Drag
and Drag
"
The kinematic viscosity is the ratio of
The kinematic viscosity is the ratio of
the absolute viscosity to mass density:
the absolute viscosity to mass density:
$
"
%
#
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Surface Tension
Surface Tension
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
!
!
The “skin” that seems to form on the free surface
The “skin” that seems to form on the free surface
of a fluid is caused by intermolecular cohesive
of a fluid is caused by intermolecular cohesive
forces and is known as surface tension,
forces and is known as surface tension,
&
&
Fluid
Fluid
Properties
Properties
!
!
Surface tension can be interpreted as the tensile
Surface tension can be interpreted as the tensile
force between two points a unit distance apart on
force between two points a unit distance apart on
thesurface
thesurface
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
the
surface
the
surface
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Capillarity
Capillarity
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
!
!
Capillary action
Capillary action
is caused by surface tension
is caused by surface tension
between the liquid and a vertical solid surface
between the liquid and a vertical solid surface
!
!
In water
,
adhesive forces between li
q
uid
In water
,
adhesive forces between li
q
uid
Fluid
Fluid
Properties
Properties
,q
,q
molecules and surface are greater than cohesive
molecules and surface are greater than cohesive
forces between water molecules; adhesive forces
forces between water molecules; adhesive forces
cause water to attach itself to and climb solid
cause water to attach itself to and climb solid
verticalsurface
verticalsurface
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
vertical
surface
vertical
surface
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Pressure
Pressure
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
!
!
Hydrostatic pressure is the pressure a
Hydrostatic pressure is the pressure a
fluid exerts on an immersed ob
j
ect or
fluid exerts on an immersed ob
j
ect or
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
j
j
on container walls
on container walls
!
!
Pressure is equal to the force per unit
Pressure is equal to the force per unit
Momentum
Momentum
and Drag
and Drag
area of the surface:
area of the surface:
F
A
F
P
#
Pressure
Pressure
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
!
!
Gage pressure:
Gage pressure:
measured relative to a reference
measured relative to a reference
pressure
pressure 
typically local atmospheric pressure
typically local atmospheric pressure
!
!
Absolutepressure:
Absolutepressure:
measuredrelativetoa
measuredrelativetoa
Fluid
Fluid
Properties
Properties
!
!
Absolute
pressure:
Absolute
pressure:
measured
relative
to
a
measured
relative
to
a
perfect vacuum
perfect vacuum
!
!
Absolute, gage, and atmospheric pressure are
Absolute, gage, and atmospheric pressure are
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
related as follows:
related as follows:
P
P
abs
abs
=
= P
P
g
a
g
e
g
a
g
e
+
+ P
P
atm
atm
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Pressure
Pressure
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
P
P
1 gage
1 gage
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
P
P
P
P
2 gage
2 gage
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
P
P
1 abs
1 abs
P
P
2 abs
2 abs
Momentum
Momentum
and Drag
and Drag
Munson et al. (2002)
Hydrostatic Pressure
Hydrostatic Pressure
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
'
'
P = change in pressure
P = change in pressure
(
(
= s
p
ecific wei
g
ht of fluid
= s
p
ecific wei
g
ht of fluid
'
'
P =
P =
('
('
h
h
(
(
pg
pg
'
'
h = change in depth in fluid
h = change in depth in fluid
***Incompressible fluid at rest
***Incompressible fluid at rest
Manometry
Manometry
Mt
Mt
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
!
!
M
anome
t
ers measure pressure or
M
anome
t
ers measure pressure or
pressure differences
pressure differences
!
!
Differentialmanometers:
Differentialmanometers:
bothends
bothends
Fluid
Fluid
Properties
Properties
Differential
manometers:
Differential
manometers:
both
ends
both
ends
connected to pressure sources
connected to pressure sources
!
!
Open manometers:
Open manometers:
one end open
one end open
hh
hh
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
to t
h
e atmosp
h
ere
to t
h
e atmosp
h
ere
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Solving Manometer Problems
Solving Manometer Problems
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
1.
1.Select a convenient starting point (usually at
Select a convenient starting point (usually at
one of the endpoints)
one of the endpoints)
Fluid
Fluid
Properties
Properties
2. Using
2. Using
'
'
P =
P =
(
(
h, write expressions for changes in
h, write expressions for changes in
p
ressure from startin
g
p
oint to
p
oint at
p
ressure from startin
g
p
oint to
p
oint at
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
pgpp
pgpp
opposite end of manometer system. Watch
opposite end of manometer system. Watch
algebraic signs!
algebraic signs!
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
3. Equate expression from step 2 to pressure at
3. Equate expression from step 2 to pressure at
final point
final point
Momentum
Momentum
and Drag
and Drag
4. Substitute known values and solve for desired
4. Substitute known values and solve for desired
q
uantit
y
q
uantit
y
qy
qy
Barometers
Barometers
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Buoyancy
Buoyancy
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
!
!
The buoyant force exerted by a fluid is equal to
The buoyant force exerted by a fluid is equal to
theweightofthefluiddisplacedandisdirected
theweightofthefluiddisplacedandisdirected
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
the
weight
of
the
fluid
displaced
and
is
directed
the
weight
of
the
fluid
displaced
and
is
directed
vertically upward (Archimedes’ Principle):
vertically upward (Archimedes’ Principle):
F
F
V
V
Momentum
Momentum
and Drag
and Drag
F
F
b
b
=
=
(
(
V
V
d
d
where
where
F
F
b
b
= the buo
y
ant force
= the buo
y
ant force
b
b
y
y
(
(
= specific weight of the fluid
= specific weight of the fluid
V
V
d
d
= displaced volume of the fluid
= displaced volume of the fluid
Displaced Volume
Displaced Volume
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Displaced volume
Solving Buoyancy Problems
Solving Buoyancy Problems
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
!
!
If the object is at rest in the fluid, use the
If the object is at rest in the fluid, use the
equation of static equilibrium in the
equation of static equilibrium in the
Fluid
Fluid
Properties
Properties
vertical direction,
vertical direction,
)
)
F
F
y
y
= 0
= 0
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
!
!
The buoyant force passes vertically
The buoyant force passes vertically
through the
through the centroid
centroidof the displaced
of the displaced
lfflidThiitilldth
lfflidThiitilldth
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
vo
l
ume o
f
fl
u
id
.
Thi
s po
i
n
t
i
s ca
ll
e
d
th
e
vo
l
ume o
f
fl
u
id
.
Thi
s po
i
n
t
i
s ca
ll
e
d
th
e
center of buoyancy.
center of buoyancy.
Momentum
Momentum
and Drag
and Drag
Fluid Forces on Surfaces
Fluid Forces on Surfaces
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
!
!
Pressure on a horizontal plane surface is uniform
Pressure on a horizontal plane surface is uniform
over the surface
over the surface
Rlttffditibtit
Rlttffditibtit
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
!
!
R
esu
lt
an
t
f
orce o
f
pressure
di
s
t
r
ib
u
ti
on ac
t
s
R
esu
lt
an
t
f
orce o
f
pressure
di
s
t
r
ib
u
ti
on ac
t
s
through center of pressure of surface and is:
through center of pressure of surface and is:
PA
R
Momentum
Momentum
and Drag
and Drag
PA
R
#
R = resultant vertical force
R = resultant vertical force
P = pressure on the horizontal surface
P = pressure on the horizontal surface
A = area of submerged horizontal surface
A = area of submerged horizontal surface
Fluid Forces on Surfaces
Fluid Forces on Surfaces
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
FreeSurface
Fluid Forces on Surfaces
Fluid Forces on Surfaces
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
*
O
Free
Surface
Fluid
Fluid
Properties
Properties
h
h
C
x
y
y
c
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
dF
R
y
R
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
A
dA
Momentum
Momentum
and Drag
and Drag
I
I
y
"
Centroid, c
"
Center of Pressure, CP
A
h
A
P
R
c
avg
(
#
#
c
c
xc
R
y
Ay
I
y
+
#
c
c
xyc
R
x
Ay
I
x
+
#
Laminar and Turbulent Flow
Laminar and Turbulent Flow
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Laminar Flow:
Laminar Flow:
!
!
Relatively low velocities
Relatively low velocities
Fluid
Fluid
Properties
Properties
!
!
No mixing or a very small degree
No mixing or a very small degree
of mixing
of mixing
Flidtfli
Flidtfli
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
!
!
Fl
u
id
appears
t
o
fl
ow
i
n
Fl
u
id
appears
t
o
fl
ow
i
n
continuous layers with no
continuous layers with no
interaction between the layers
interaction between the layers
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Turbulent Flow:
Turbulent Flow:
Momentum
Momentum
and Drag
and Drag
!
!
Relatively high velocities
Relatively high velocities
!
!
High degree of mixing
High degree of mixing
!
!
Fluid motion appears chaotic
Fluid motion appears chaotic
Flow Distribution
Flow Distribution
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Reynolds Number
Reynolds Number
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Reynolds Number
Reynolds Number
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Re < 2000 laminar flow
Re < 2000 laminar flow
Circular Pipe Flow
Circular Pipe Flow
Fluid
Fluid
Properties
Properties
2000 < Re < 4000 transition region
2000 < Re < 4000 transition region
Re > 4000 turbulent flow
Re > 4000 turbulent flow
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Open Channel
Open Channel
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Re < 500 laminar flow
Re < 500 laminar flow
500 < Re < 2000 transition region
500 < Re < 2000 transition region
Re>2000turbulentflow
Re>2000turbulentflow
Momentum
Momentum
and Drag
and Drag
Re
>
2000
turbulent
flow
Re
>
2000
turbulent
flow
One
One
Dimensional Flows
Dimensional Flows
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Compressible Flows
Compressible Flows
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Continuity:
Continuity:
m
m
!
!
#
Fluid
Fluid
Properties
Properties
A
A
2
1
m
m
#
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
2
2
2
1
1
1
v
A
v
A
$
$
#
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
RT
P
$
Ideal Gas Law:
Ideal Gas Law:
Momentum
Momentum
and Drag
and Drag
RT
P
$
#
[
P is
p
ressure
]
[
P is
p
ressure
]
[p]
[p]
[R is the gas constant]
[R is the gas constant]
[T is temperature]
[T is temperature]
Incompressible Fluids
Incompressible Fluids
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Continuity Equation:
Continuity Equation:
Fluid
Fluid
Properties
Properties
2
2
1
1
v
A
v
A
#
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Bernoulli Equation
Bernoulli Equation
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Mechanical Energy Equation
Mechanical Energy Equation
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Friction Loss
Friction Loss
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Valid for laminar and turbulent flow
Valid for laminar and turbulent flow
Momentum
Momentum
and Drag
and Drag
Moody Chart
Moody Chart
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Friction Loss
Friction Loss
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Hazen
Hazen
Williams Equation:
Williams Equation:
54
.
0
63
.
0
849
0
S
CR
#
v
Fluid
Fluid
Properties
Properties
849
.
0
S
CR
#
v
v = velocit
y
[
m/s
]
v = velocit
y
[
m/s
]
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
y[]
y[]
C = roughness coefficient [varies from 140 to 100]
C = roughness coefficient [varies from 140 to 100]
R = hydraulic radius = A/WP [m]
R = hydraulic radius = A/WP [m]
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Vlidftbltflft
Vlidftbltflft
S = slope of HGL = h
S = slope of HGL = h
L
L
/L [dimensionless]
/L [dimensionless]
Momentum
Momentum
and Drag
and Drag
V
a
lid
f
or
t
ur
b
u
l
en
t
fl
ow o
f
wa
t
e
r
V
a
lid
f
or
t
ur
b
u
l
en
t
fl
ow o
f
wa
t
e
r
Minor Loss
Minor Loss
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
fitting
,
f
f
L
h
h
h
+
#
Fluid
Fluid
Properties
Properties
g
2
v
C
h
2
fitting
,
f
#
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
g
2
[C = loss coefficient (or resistance coefficient)]
[C = loss coefficient (or resistance coefficient)]
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
HGL and EGL
HGL and EGL
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
HGL and EGL
HGL and EGL
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Total Head
or Energy
Grade Line
Velocity Head
Fluid
Fluid
Properties
Properties
(EGL)
(v
2
/
2g)
Hdli
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Pressure Head
H
y
d
rau
li
c
Grade Line
HGL
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
(P/
(
)
Momentum
Momentum
and Drag
and Drag
Elevation
Z = 0
Head (z)
Pump
Pump
Turbines
Turbines
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Net head added to system
Net head added to system
bymechanicaldevice
bymechanicaldevice
Fluid
Fluid
Properties
Properties
P
P
2
2
by
mechanical
device
by
mechanical
device
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
g
2
v
z
P
h
h
g
2
v
z
P
2
2
2
2
L
s
2
1
1
1
+
+
#
,
+
+
+
(
(
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Open Channel & Pipe Flow
Open Channel & Pipe Flow
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Impulse
Impulse
Momentum
Momentum
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Impulse
Impulse
Momentum
Momentum
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
x
1
1
1
x
2
2
2
x
v
Q
v
Q
F
$
$
)
,
#
Fluid
Fluid
Properties
Properties
1
1
1
2
2
2
v
Q
v
Q
F
$
$
)
,
#
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
y
1
1
1
y
2
2
2
y
v
Q
v
Q
F
$
$
)
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
z
1
1
1
z
2
2
2
z
v
Q
v
Q
F
$
$
)
,
#
Momentum
Momentum
and Drag
and Drag
Sumofthe
Sumofthe
Net rate of
Net rate of
tti
tti
Sum
of
the
Sum
of
the
external forces
external forces
momen
t
um en
t
er
i
ng
momen
t
um en
t
er
i
ng
control volume
control volume
Drag Force
Drag Force
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Drag Coefficient
Drag Coefficient
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Pipe Networks
Pipe Networks
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
Fluid
Fluid
Properties
Properties
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
Momentum
Momentum
and Drag
and Drag
Good Luck!!!
Good Luck!!!
Steve Burian
Steve Burian
Department of Civil & Environmental Engineering
Department of Civil & Environmental Engineering
@
@
burian
@
eng.utah.edu
burian
@
eng.utah.edu
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