# Fundamentals of Engineering (FE) Exam

Mechanics

Jul 18, 2012 (4 years and 10 months ago)

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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
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
,
q
uid
In water
,
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
or Energy
Fluid
Fluid
Properties
Properties
(EGL)
(v
2
/
2g)
Hdli
Fluid Statics
Fluid Statics
Fluid
Fluid
Dynamics
Dynamics
H
y
d
rau
li
c
HGL
Energy,
Energy,
Friction Loss,
Friction Loss,
and Pipe Flow
and Pipe Flow
(P/
(
)
Momentum
Momentum
and Drag
and Drag
Elevation
Z = 0
Pump
Pump-
-Turbines
Turbines
FE Fluid
FE Fluid
Mechanics
Mechanics
Review
Review
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