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OPEN CHANNEL FLOW: In a channel if the flow is steady (no changes in time)

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OPEN CHANNEL FLOW: In a channel if the flow is steady (no changes in time) and uniform (no changes down stream) we have normal flow Through a balance of the gravity ... – PowerPoint PPT presentation

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Title: OPEN CHANNEL FLOW: In a channel if the flow is steady (no changes in time)


1
OPEN CHANNEL FLOW In a channel if the flow is
steady (no changes in time) and uniform (no
changes down stream) we have normal flow
Through a balance of the gravity (weight) to
friction shear forces-for wide channels
or
where
Manning's Formula mks system
cf is dimensionless BUT n is not
L
If there is no change in friction or slope as we
move down stream Then the depth of the flow
remains constant the normal depth
This value can be calculated for any stream as a
stream characteristicthe value, however will
only coincide with the stream surface under the
Normal flow condition
using the definition of discharge Q (B x h)u
(the volume flow per time)
2
Derivation--once more As a force balance
consider fluid element with unit area base and
height of depth h moving down slope
Shear force acting on fluid element Up along
slope is
Gravity force down stream


L
3
Energy in a fluid In stream settings We have
seen how useful balances of Mass (Volume) and
Momentum (Manning) can be in understanding basic
behavior-. In addition to these conservations we
can also consider the balance of Energy
Engineers (Civil) like to measure energy as a
vertical height above a datum
A
Consider a large fluid filled tank with a hole
near the bottom. If the level h (height) of the
tank is maintained, the flow near A Is essential
still, and the fluid speed at the exit is u. The
potential energy per unit volume at A (relative
to the datum) is
h
This is converted into the Kinetic Energy
Per unit volume at B
B
These energy forms can be expressed in terms of
height (length) dimensions, by dividing by
Then an Energy balance between A and B can be
expressed as
friction head loss
4
Derive Normal flow with Energy balance
consider fluid element with unit area base and
height of depth h moving down slope
a

friction head loss
friction force per unit mass X length /r g
b
L
5
Applying this idea to a stream channel
under-normal flow conditions
Average Velocity
Bed elevation
a
Specific Energy
b
So In uniform flow energy Balance becomes
But by definition of slope S same as
So under normal flow Energy balance will recover
our previous result
6
Specific Energy
Energy Line
h
The specific energy Energy (head) relative to
channel bed
Changes Non-linearly with stream depth, h
See Excell worksheet
(make sure to download open.xls along with this
power point
7
Critical Depth The specific energy
Is non-linear
Can show that, for a given discharge and stream
width E will reach a minimum when
E
The critical depth
At critical depth
Sub-critical Flow
Sp Energy increases with increase in depth
Q 0.5
B 3
And
hcr 0.14147
Super-critical Flow
Sp Energy increases with decreases in depth
8
Why we want to know about this
Normal flow is all well and good.
???
???
Or slope?
What about changes in depth?
The Question How does a disturbance in the flow
propagate up and down stream How far is the
effect felt
9
The form of the flow response to changes such as
this depends on a number called the Froude Number
Flow speed
Max wave speed
10
Flow Over an Object What happens as a
sub-critical normal flow Goes over a low object?
Recognize that this an important SRES question
? ? ?
h 0.3 B3 Q.5
11
We can construct an Energy Balance between A and
Bneglecting slope changes and bed friction
(small distance)
A
B
h 0.3 B3 Q.5
Implies that
12
We can construct an Energy Balance between A and
Bneglecting slope changes and bed friction
(small distance)
A
B
h 0.3 B3 Q.5
implies that
See Excell worksheet
13
What happens when we increase the bump
height The level of the flow over the bump will
continue to decrease--- until the critical
height hcr is reached.
A
B
h 0.3 B3 Q.5
See Excell worksheet
If the bump height increases more The level over
the bump is caught between A rock and a hard
place going both up or down will only increase
the energy --so with an increasing bump the the
level over the bump is fixed at hcr
14
--so with an increasing bump the the level over
the bump is fixed at hcr
The only way to establish an energy balance is
for the height at A to Increase
Back water
A
B
This will mean that down-stream of the bump the
flow Will not be normal
As we move further back friction will
reestablish Normal flowthe distance to
reestablish normal flow is the
Back Water Distancewill be calculated
15
What about down stream of our high bump ?
Since fluid has lost the pot. energy The energy
is more easily recovered By the level dropping
below critical
A
B
Further down stream The bottom friction Will
drive it back up to the normal Depth
16
If normal depth is sub-critical hn gt hcr
something interesting happens
A
B
The flow level can not Pass smoothly Thorough
the critical depth And you get a hydraulic jump
17
How Far down stream in an other wise normal flow
is an obstacle felt ?
This elevation change is important
?
The Stress slope
See derivation on Board
18
Now consider head balance behind an obstacle-not
in uniform flow
Average Velocity
Bed elevation
a
b
19
Now consider head balance behind an obstacle-not
in uniform flow
Average Velocity
a
b
For a small distance deltax
Result follows on subbing for u and noting that
20
Behavior of water surface near an object depends
on normal flow level in relation to critical flow
level
The Stress slope
Assumed to be Slope at normal flow
critical
Fr lt 1, SfltS, A gt 0
normal
SSf
normal
Fr lt 1, SfgtS, A lt 0
Fr lt 1, SfltS, A gt 0
critical
Fr gt1, SfltS, A lt 0
Fr1
Fr gt 1, SfgtS, A gt 0
Fr gt 1, SfgtS, A gt 0
Fr1
SSf
Mild slope, normal flow depth gt critical flow
depth
Steep slope, normal flow depth lt critical flow
depth
Homework find a web page that shows examples of
water level change for obstacles In
streams/channelssend web-address to Voller
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