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CEE 4476b Environmental Hydraulics Design
Instructor: Dr. Andrew Binns Email: abinns2@uwo.ca Office: CMLP 1302 Phone: (519) 661-2111 ext. 88633 Week 2, Lecture 3 Monday, January 14, 2013
Alt-J
CEE 4476b: Environmental hydraulics design
Teaching assistants and office hours:
ã
Phil Spencer: pspence3@uwo.ca
–
Office hours: Friday from 1-2pm (CMLP 1316)
ã
Nadeem Ahmad: nahmad33@uwo.ca ã
Zoheb Nasir: znasir@uwo.ca
My office hours:
ã
Tuesday from 12:30-1:30pm (CMLP 1302)
–
abinns2@uwo.ca
CEE 4476b: Environmental hydraulics design
Today
s lecture
ã
Specific energy
–
Definition
ã
Specific energy diagram ã
Choke ã
Example
Bakhmeteff (1932)
ã
First introduced concept of specific energy E ã
Useful concept for solving open channel flow problems
For a given approach flow (
V
1
,
y
1
given), what is the depth
y
2
after channel rise of
!
z
?
Specific energy
Neglecting losses and applying the energy equation, we have:
z
1
+
y
1
+
V
12
2
g
=
z
2
+
y
2
+
V
22
2
g
y
1
+
V
12
2
g
=
y
2
+
V
22
2
g
+
z
Specific energy
Combining the continuity equation:
y
1
+
V
12
2
g
=
y
2
+
V
22
2
g
+
z
y
1
+
Q
2
2
gA
12
=
y
2
+
Q
2
2
gA
22
+
z
Removes an additional unknown (
V
2
)
Specific energy
Combining the continuity equation:
y
1
+
V
12
2
g
=
y
2
+
V
22
2
g
+
z
y
1
+
Q
2
2
gA
12
=
y
2
+
Q
2
2
gA
22
+
z
Removes an additional unknown (
V
2
)
y
1
,
y
2
=
discharge depths
Q
=
discharge
A
1
,
A
2
=
cross-sectional area of flow
z
=
z
2
#
z
1
=
change in bottom elevation from section 1 to 2
Specific energy
ã
From this equation, we can see that the sum of depth and velocity head must change by
!
z
–
The change must result in an interchange between depth and velocity such that the energy equation is satisfied
y
1
+
Q
2
2
gA
12
=
y
2
+
Q
2
2
gA
22
+
z
Specific energy Definition:
ã
Specific energy (E) = sum of depth and velocity head
–
Possible solutions of problem for depth depend on variation of specific energy with depth
Specific energy Definition:
ã
Specific energy (E) = sum of depth and velocity head
–
There are actually two real solutions for the depth in this problem
Plot of depth (
y
) versus specific energy (
E
) clarifies which will prevail
Specific Energy Diagram
Specific energy
ã
Specific energy can also be represented (defined) as the height of the energy grade line (EGL) as shown below
–
Above the channel bottom –
Parallel to channel bottom in uniform flow –
E
is constant in flow direction (until a change
!
z
)
Specific energy
ã
Note:
Total energy must remain constant or decrease, but specific energy
E
can decrease or increase
Specific energy Definition:
ã
Specific energy (
E
) defined as:
E
=
y
+
V
2
2
g
y
=
flow depth
V
=
mean cross-sectional velocity
=
kinetic energy flux correction
Specific energy Assumptions:
1.
E
defined at cross-sections where flow is gradually varied
–
Free surface = Hydraulic Grade Line
Specific energy Assumptions:
2.
Water surface and Energy Grade Line (EGL) are horizontal across cross-section
–
Therefore, a single value of
V
corrected by
!
suffices for entire cross-section
Specific energy Assumptions:
3.
Slope is small such that
y
!
d
–
If
(longitudinal slope of channel bed) is greater than 6
o
, we have to make adjustments to our equation
p
= pressure
W
= weight
d
= flow depth
y
= channel depth

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