Lesson #7: Branching Pipe Systems
3-Reservoir Problem
Assuming that minor losses are negligible and that the friction factors in all the pipes are
constant (f = 0.024), compute the flow (Q) in each pipe segment for the following
conditions:
Reservoir
Leve
Lesson 19: Flow Profiles and Natural Channels
Example Problem
The compound channel shown below has a channel slope (S0) of 0.004 m/m. The water
depth (y), as measured from the main channels bed, is 3 m.
a) Determine the conveyance (K) for all three channe
Lesson #4: Frictional Resistance
Head Loss Example Problem
A 50 mm diameter commercial steel pipe (ks = 0.046 mm) has a length of 100 m. Find
the head loss (in m) for water for the two discharge rates below. Assume that the water
has a kinematic viscosity
Lesson #5: Minor Losses and Grade Lines
Energy Losses in a Pipe System
Water flows from reservoir 1 to reservoir 2 in an 8-in diameter, 600-ft long pipeline.
Determine the velocity (in ft/s) assuming the pipe friction factor f is 0.020, and including
the
Lesson #7: Branching Pipe Systems
3-Reservoir Problem
Assuming that minor losses are negligible and that the friction factors in all the pipes are
constant (f = 0.024), compute the flow (Q) in each pipe segment for the following
conditions:
Reservoir
Leve
Lesson 12: Hydraulic Transients
Water Hammer Example
The velocity of flow in the pipe segment is 2 m/s when a valve is closed suddenly. The
temperature of the water is 20C.
Reservoir
Valve
Pipe Segment
100 m
The water properties:
= 998.2 kg/m3
E = 2.18 1
Lesson 14: Open Channel Flow Equations
Mannings Equation Example
A rectangular open channel has bottom width (b) of 4 ft and a slope (S0) of 0.001 ft/ft.
The channel is constructed out of concrete.
a) Determine the flow velocity (ft/s) for steady uniform
Lesson 15: Specific Energy & Critical Depth
Critical Depth for a Rectangular Channel
The rectangular channel shown below has a discharge rate of 2 m3/s.
Find the critical depth yc (the depth where the specific energy is minimized) and the
specific energy
Lesson 18: Classification of Water-Surface Profiles
Example Problem
A rectangular channel with a 10 m bottom width has a slope of 0.01 and a Mannings
coefficient of 0.025. For a flow rate of 50 m3/s, the normal depth yn is 1.25 m.
a) Determine the critica
Lesson 19: Flow Profiles and Natural Channels
Example Problem
The compound channel shown below has a channel slope (S0) of 0.004 m/m. The water
depth (y), as measured from the main channels bed, is 3 m.
a) Determine the conveyance (K) for all three channe
Lesson 20: Computation of Water-Surface Profiles
Direct-Step Method Example
A rectangular channel with a 5 m bottom width has a slope of 0.005 and a Mannings
coefficient of 0.030. For a flow rate of 50 m3/s, the normal depth yn is 3.34 m and the
critical
Lesson 26: Frequency Analysis
Flood Probabilities
On Fourmile Creek, the 1993 flood produced the 6th largest peak discharge in the 21-year
streamgage record. What is the estimated return period T (in years) for the 1993 flood
(by the non-parametric method
Lesson 28: Rational Method
10-Year Design Flow Using the Rational Method
Compute 10-year design discharge on an Iowa City creek for culvert design:
A = 100 acres
C = 0.35 (Single family residential for Hydrologic Soil Group B)
tc = 15 min
P 1.20 in
i = 4.
53:071 Principles of Hydraulics & Hydrology
Exam 1 (Closed Conduit Flow)
Spring 2010
Name: _
Equations and constants you may (or may not) find useful:
du
/
dy
VD
Q VA
Re
E
p h
4 0 L
D
64
f
Re
hL f
hL f
L V2
f
D 2g
cP
p vcV
vc
K
V2
hLm K
2g
Q
cQ
nD
53:071 Principles of Hydraulics & Hydrology
Exam 1 (Closed Conduit Flow)
Spring 2010
Name: _
Equations and constants you may (or may not) find useful:
du
/
dy
VD
Q VA
Re
E
p h
4 0 L
D
64
f
Re
hL f
hL f
L V2
f
D 2g
cP
p vcV
vc
K
V2
hLm K
2g
Q
cQ
nD
53:071 Principles of Hydraulics & Hydrology
Exam 1 (Closed Conduit Flow)
Practice Exam
Name: _
Equations and constants you may (or may not) find useful:
du
=
= /
dy
VD
Q = VA
Re =
2
4 L
pV
h= z+ +
hf = 0
2g
D
p
/
E=
p= h
hf = f
1.85
L V
h f = 6.82 1
53:071 Principles of Hydraulics & Hydrology
Exam 1 (Closed Conduit Flow)
Practice Exam
Name: _
Equations and constants you may (or may not) find useful:
du
=
= /
dy
VD
Q = VA
Re =
2
4 L
pV
h= z+ +
hf = 0
2g
D
p
/
E=
p= h
hf = f
1.85
L V
h f = 6.82 1
53:071 Principles of Hydraulics & Hydrology
Exam 2 (Open Channel Flow)
Spring 2010
Name: _
Equations and constants you may (or may not) find useful:
V C RS f
R A/ P
0 RS f
Q VA
V
V
Q
1
AR 2 / 3 S 1 / 2
f
n
Q 2 Ac3
g
Tc
1 2 / 3 1/ 2
R Sf
n
1.49
Q
AR 2 / 3
53:071 Principles of Hydraulics & Hydrology
Exam 2 (Open Channel Flow)
Practice Exam
Name: _
Equations and constants you may (or may not) find useful:
Q = VA
Re =
0 = RS f
R = A/ P
V (4 R)
8g
RS f
f
V=
1
V = R 2 / 3 S 1/ 2
f
n
Q 2 Ac3
=
g
Tc
q2
yc =
g
53:071 Principles of Hydraulics & Hydrology
Exam 2 (Open Channel Flow)
Practice Exam
Name: _
Equations and constants you may (or may not) find useful:
Q = VA
Re =
0 = RS f
R = A/ P
V (4 R)
8g
RS f
f
V=
1
V = R 2 / 3 S 1/ 2
f
n
Q 2 Ac3
=
g
Tc
q2
yc =
g
53:071 Principles of Hydraulics & Hydrology
Exam 3 (Engineering Hydrology)
Practice Exam
Name: _
Equations and constants you may (or may not) find useful:
x
F ( x) exp exp
6
0.5772
y ln( ln(1 p)
1
R 1 1
T
KT
T
1
p
T
6
0.5772 ln ln
T 1
xT
Lesson 3: Flow in a Pipe
Definitions
Closed Conduit: Fluid _ volume
Steady-State:
Flow properties (e.g., velocity, pressure, discharge, energy) do not
_
Uniform Flow:
Flow properties do not _
Figures
Figure 2.1: Flow through closed conduit
Figure 2.2: For
Lesson 4: Energy (Head) Losses Due to Pipe Friction
Darcy-Weisbach: Problems and Solution Procedures for Turbulent Flow
Find head loss (hf) given pipe size (D), type and discharge (Q):
k
1. Compute s
D
2. Compute Re
3. Read f (Moody Diagram)
4. Compute hf
Lesson 5: Minor Losses and Grade Lines
Energy Grade Line (EGL) and Hydraulic Grade Line (HGL)
p
V2
1. A plot of the total (energy) head, z
, versus location in the pipe
2g
system is known as the energy grade line (EGL).
p
2. A plot of the hydraulic (piez
Lesson #5: Minor Losses and Grade Lines
Sudden Expansion
Entrance
Exit
1 of 4
Lesson #5: Minor Losses and Grade Lines
Fittings, Valves, Entrance/Exit Losses
2 of 4
Lesson #5: Minor Losses and Grade Lines
Transitions and Fittings
3 of 4
Lesson #5: Minor Lo