OPEN CHANNEL FLOW
An
open channel can be defined as the structure through which the upper portion of
liquid flows freely exposed to the atmosphere and under the atmospheric
pressure. The flow of water through the open channel which has certain bed
slope is purely due to the action of gravity and pressure difference plays no
role in the flow of water like of closed channels or as like in pipe flow. Open
channels can be natural like rivers, streams or it can be artificial. While
artificial refers to the man made features like canals, culverts etc. Mostly
rectangular or trapezoidal shape is preferred while designing the open
channels. But due to the high discharge rate of circular shaped channel for
given area is highest, it is also constructed sometimes .While constructing
irrigation canals, open type is preferred with rectangular or trapezoidal in
shape and while constructing sewer, an oval or egg shape is preferred. While
constructing sewer, an open type is preferred due to the need of time to time
cleansing and maintenance. While designing any open channels, it should be kept
in mind that velocity should be designed and considered in such a way that
maximum velocity of flow should not cause any scouring or abrasion effects on
the channel sides and beds and the minimum velocity should not cause any silt
deposition action. Even if the condition cannot be met to its full level but
the maximum attention, certain limits and standards are to be followed to avoid
any kind of unpleasant effects. Lining of the channels can be done if the
project is for the long term purpose.
FIG: RECTANGULAR CHANNEL FLOW
WHAT IS STEADY AND UNSTEADY FLOW?
FOR STEADY FLOW:
Let us
take the example of a perennial river. Consider a particular section of the
river at a certain point, now if the water flow area of the river does not vary
or changes with the change in the time or for more accuracy say let us say at
different times for that particular section then, that flow of water is
considered to be the steady flow. The point that is to be noted while having
the concept of the steady flow is that the flow area of water at different
points or places or regions of that specific river can be different or same, it
does not matter but the flow area or discharge rate of particular point let us
say at point “a “of the same river should be constant at all times or at
different times. In more expanded sense it could be understood as when the flow
characteristics like velocity, density etc of the water at particular point
does not change with the passage of the time, then the flow is said to be
steady.
FOR UNSTEADY FLOW
Let us take the example of the same river, let us consider
that river is flowing from the north direction to the south direction. Let us
consider a point ‘a’ on the river at particular position. Now let us consider
another point ‘b’ 100m downstream in the same river. If the discharge rate at
point ‘a’ at different times is different then the flow is said to be unsteady.
So, thus it has nothing to do with the discharge rate of flow at point ‘b’. the
discharge rate of the two points ‘a’ and ‘b’ may be same or different but the
point to be noted that is, if the
discharge rate of a particular point of the same river has changed currently
than while recorded some hours or time back ,then the flow is unsteady.
WHAT IS UNIFORM AND NON-UNIFORM FLOW?
FOR UNIFORM FLOW
If the depth of flow of water at all sections of the river is
same, then the flow is said to be uniform. Suppose, a river is flowing from
north direction to the south direction. Let
‘a’ be a point on the upstream and in 100 meters gap there is second
point ‘b’, third point ’c’, fourth
point ’d’ etc . So, the distance between
‘a’ and ‘b’ is 100 metres, the distance between the point ‘b’ and ‘c’ is 100
metres and so on. Now, if the depth of flowing water at every point that is at
point ‘a’, ‘b’, ‘c’, ‘d’ etc is same, then the flow of water is said to have
uniform flow.
Similarly if the depth of flow is different at different
sections, then it is considered as non uniform flow. In above example, if the
depth of flow at point ‘a’, ‘b’, ‘c’, ‘d’ etc are different, then the flow is
said to be non uniform.
There can be conditions like:
11)
Steady
uniform flow: well, if the discharge rate of the river at a particular section
of river or channel at different times is constant and if the depth of flow of
water at different sections is same, then the flow is said to be steady uniform
flow.
22)
Steady
non uniform flow: if the discharge rate of the river or channel at a particular
section at different times is constant and if the depth of flow of water at
different sections is different, then the flow is said to be steady non uniform
flow.
33)
Unsteady
uniform flow: if the discharge rate of the river or the channel at a particular
section of the river at different times is different or not constant and if the
depth of flow of water at different sections is same, then the flow is said to
be unsteady uniform flow.
44)
Unsteady
non uniform flow: if the discharge rate of the river or the channel at a
particular sections is not constant and varies, and if the depth of the flow of
river or the channel at different sections is not same or is different, then
the flow is said to be unsteady non uniform flow.
NOTE: 1) the depth of flow and the
depth of river or channel are different. For example, a channel may not run
full to its height constructed, so the depth of flow of channel is less than
the depth of channel itself.
2) In steady flow, it is to be noted
that, even if the discharge rate at different points or sections of the same
river is different but if the discharge rate at a particular point after
different time interval remains same, then it is steady flow. So, it does not
matter whether the discharge rate at two different points of the same river is
same or different at a specific time point, say at 2 p.m. , to be in steady
condition.
3) For a given rate of flow, constant
slope and cross section of the channel, there will be one distinct depth
throughout the channel, thus creating the condition for the uniform flow.
4) Changes in bed slope,
irregularities, sudden obstruction in the path, varied roughness etc are the reasons
that create a non uniform flow.
CHEZY’S FORMULA FOR UNIFORM FLOW
Let us consider that, an open channel
has the bed slope‘s’. Let 1-1 and 2-2 be the two sections of the channel at
certain distance ‘l’. Let ‘A’ be the cross section of channel at any sections
and similarly ‘P’ be the wetted perimeter.
Let us suppose that the mean velocity
of flow of water through the open channel be ‘v’.
Then the total weight of water or
flow in between the two sections 1-1 and 2-2 is ‘wAl’.
Also since the mean velocity is ‘v’
and the bed slope of the channel is ‘s’, so the distance travelled by flow in
one second is v and the vertical depth it falls through is ‘vs’ .
In one second, the loss of potential
energy is ‘wAlvs’.
The flow of the water body goes through
certain resistance against the flow itself, hence the frictional resistance
developed can be determined as f*contact area* velocity^2
Thus the resistance = f*p*l*(v^2)
Similarly work done against the
friction =f*p*L*(v^2)*v
Now,
Equating the loss of potential energy
and the work done against the friction,
wAlvs=fplv(v^2)
or, v^2=(w*A*s)/(f*p)
now , A/p=m and
w/f=c^2
So,
v=c*{(m*s) ^ (1/2)}
Where m is hydraulic mean depth.
Similarly when determining the discharge Q then,
Q= Ac*{(m*i)^(1/2)}
And we can write,
Q=k*i^ (1/2)
Here, k is the conveyance of the channel section.
K=Ac*m^(1/2)
HOW TO DETERMINE THE HRDRAULIC MEAN
DEPTH FOR GIVEN SHAPE CHANNEL?
1) RECATNGULAR SECTION:
Hydraulic
mean depth= m= A/p
=(b*d)/(b+2*d)
Where,
b= width of the section of the channel
d= depth of the flow of the channel
A= area of the section
P= wetted perimeter of the rectangular
channel section
2) TRIANGULAR SECTION:
Hydraulic
mean depth= m= A/p
= (n*d^2)/{2*d*(n^2+1)^(1/2)}
Where,
side slope of the triangular channel = 1vertical to n horizontal
So for 1 vertical distance there is n horizontal
distance and hence for the d vertical distance there is nd horizontal distance.
d=
depth of the flow
area ‘A’=
(1/2)*nd*d+(1/2)*nd*d
=nd*d
For wetted
perimeter, we calculate length of the side slope of the triangular channel section as
Length= (nd)^2+d^2
Hence the
total wetted perimeter becomes
(2* length
of the sides slopes of the triangular channel section)
= 2*d*(n^2+1)^(1/2)
3) FOR THE TRAPEZOIDAL SECTION
Hydraulic
mean depth= m =A/p
=d*(b+n*d)/b+2*d*(n^2+1)^(1/2)
=d*(b+n*d)/b+2*d*(n^2+1)^(1/2)
Where, b= bottom width of the trapezoidal
section
d= depth of the flow of water
in the trapezoidal section
side slopes= 1 vertical to n
horizontal
hence
the top width becomes= b+2*n*d
area=
(1/2)*d*(b+b+2*n*d)
wetted
perimeter= b+2*(n^2*d^2+d^2)^(1/2)
4) FOR SEMI CIRCULAR CHANNEL
Hydraulic
mean depth= m= A/p= d/4
Where,
d= diameter of the channel
Area ‘A’ = (∏*d*d)/8
Wetted
perimeter ‘p’ = (∏*d)/2
5) FOR CIRCULAR SECTION IN WHICH WATER IS RUNNING
FULL
Hydraulic mean
depth= m =A/p
= d/4
Where, d=
diameter of the channel
Area ‘A’ =(∏*d*d)/4
Wetted perimeter
= p = ∏*d
NOTE: Discrimination and choices are two
completely different things. Discrimination may have choices but choices do not
have discrimination. It is never my intention to hurt someone's feeling,
emotions and pride. Above material is solely just for entertainment
purpose only and should be taken light heartedly.
Finally we all are humans. Humans have
different physical forms and mental forms and should be respected no matter
what. Abusing in any form whether it be verbal, emotional or physical surely is
a criminal act that deserves serious attention with punishment. In other hand,
jokes and comedy are completely different things which should exist within the
circle of loved and near ones and can be extended to some extent beyond the
limits but surely we need to be conscious towards the fact that our loved ones
are not hurt by our words and actions. Peace, love and respect should not be
destroyed to the extent that it becomes impossible to repair or rebuild.
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