# Open ChannelFlow Open-Channel Flow

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```					     CE 473
Open-Channel
Open Channel Flow

Chapter 3
Channel Controls
3.1      Introduction
t              h       feature, which fi
A controll iis any channell f t                      l ti hi between d th
hi h fixes a relationship b t  depth
and discharge in its neighborhood. It may be natural or human-made.
Also we may have:
•Overflow structures -→spillways, weirs, free falls
•Underflow structures-→sluice gates, gates

Why use need control structures?
computation provides
1.Flow profile computation-provides the boundary condition.
2.To measure discharge;
As an engineer we are concerned with the functioning of the control
itself, such as the ability of a spillway to discharge floodwaters at the
required rate.
(sections).Since
We have rapid flow in the vicinity of control structures (sections) Since the
streamlines are highly curved near the control sections we can not solve
the equations analytically, Therefore we go to empirical relations based
experiments.
on experiments
Vena Contracta
• Vena contracta is the section where the flow becomes parallel or it is
the section where area of the jet becomes constant and minimum.
j

Coefficient of velocity,

Coefficient of contraction
3.2 Flow through orifices and short tubes
Typical examples of orifices and short tubes are shown. As the flow issues
occur.
out vena contracta will occur

Orifices

A knowledge of the laws of the flow through them is necessary in
determining the discharge through sluiceways and the entrances to
conduits.
• If the entrance is not properly shaped, a contraction of the jet occurs as
shown in sketch of vena contracta.
• The area of the jet is not as great as the area of the orifice or tube. For
l      d d           h t ifi           d the     t t di       t h t
properly rounded approaches to orifices, and th constant diameter short
tubes, the diameter of the jet is equal to the area of the orifice or tube.
entrances,
• In case of short tubes without rounded entrances the contraction does
occur; but the jet expands again, with certain exceptions, a partial
vacuum occurring just inside the entrance.
Let
• H = the head of water on the center line of a freely flowing orifice or
tube, or the difference in water level for a submerged orifice or tube
A= the area of the orifice and tube
V= the theoretical velocity corresponding to head H;
g                          g
g= the acceleration of gravity  y
R
Energy equation between points R and N:
HR=HN
H
PR + U R =        PN + U N ,
2                   2

zR +              zN +
γ     2g         γ         2g
datum   N     P R                U R    , a n d    z R
= P N = P at m     =0                = H

T h e r e f o r e

U
2
H                                   U
=              N
⇒           N   = 2gH
2g
Q= the discharge
A jet
Cc=the coefficient of contraction    =
Aorif
Cf= the coefficient of friction, the reduction in total head due to friction
Cv= the coefficient of velocity
Cd= the coefficient of discharge
The general equation for the velocity of the spouting water is
V = 2 gH
Considering the friction, the actual velocity due to the head H is

Vactual = C v 2gH or               Vactual = C f 2gH
The discharge is equal to the product of the actual velocity and the area
of the jet; and the area of the jet is
A j = Cc A
Therefore
Q = Vact C c A = C v C c A 2gH

•In experiments conducted to determine the discharge through orifices
tubes
and tubes, the coefficient of friction and the contraction coefficient are
combined and the general equation is given as:

H h
Q = C d A 2gH , where C d = C v C c
Cd= discharge coefficient → it depends on the shape of the orifice
and tube, it is not greatly affected by the submergence. If we do not
have submergence and enough friction contracted jet does not expend
in tube. It shoots out as contracted without touching the walls.
Orifices and Their Nominal Coefficients

Cd
Dimensional Analysis
•Let’s consider the following figure;

V0       H

W              L

According to values of L, W and roundness, it can be a weir or sharp
crested weir.
•The discharge coefficient, Cd, will be a function of:

C d = φ(Vo , H, W , L, g, μ, ρ, σ )
•→ 8 variables
•→ 3 basic dimensions, M,L,T → 5 dimensionless quantity
ρ,
If we choose ρ Vo, H as primary (repeating variables); the dimensional
analysis would give us:
RR e e ρ V 0 H        RR e e           nn u u m m b b e re
, H ,      , , ⎞ = μ =                              y n old s
⎛ H
Cd  = f⎜              R e F r W ⎟F
⎝ W L                      ⎠ r = V0 = F ro u d e n u m b e
gH
σ
W     =            = W e b er n u m b er
ρ Vo H2

Q        F r o u d e n u m b e r         d ir e c t m e a s u r e o f C
Cd =            =                          ⇒                                          d

A 2gH
Therefore, the discharge coefficient is a function of:

⎛ H , H   , ⎞ Reynolds and Weber numbers
C D = f⎜       Re W ⎟
⎝ W L                                              H
⎠ become important at small values of H.
Weirs for Open-Channel Flow Measurement
Effective use of water for crop irrigation requires that flow rates and
quantitatively
volumes be measured and expressed quantitatively. Measurement of
flow rates in open channels is difficult because of nonuniform
channel dimensions and variations in velocities across the channel.
Weirs allow water to be routed through a structure of known
dimensions, permitting flow rates to be measured as a function of
depth of flow through the structure. Thus, one of the simplest and
most accurate methods of measuring water flow in open channels is
weirs                 form
by the use of weirs. In its simplest form, a weir consists of a bulkhead
of timber, metal, or concrete with an opening of fixed dimensions cut
in its top edge. This opening is called the weir notch; its bottom edge
is the weir crest; and the depth of flow over the crest (measured at a
(H). The overflowing sheet of water is known as the nappe.
•
Types of Weirs
• Two types of weirs exist: sharp-crested weirs and broad-crested
weirs. Sharp-crested weirs are normally the only type used in the
measurement of irrigation water. The sharp edge in the crest causes
the water to spring clear of the crest, and thus accurate
incorporated in hydraulic structures of various types and, although
,            y
sometimes used to measure water flow, this is usually a secondary  y
function. The components of a sharp-crested weir are shown in
following figure: .
Profile of a sharp-crested weir
3.3     Sharp-Crested Weirs
A sharp crested weir normally consists of a vertical plate mounted at right
angles to the flow and having a sharp-edged crest, as shown in the figure

A         EGL
2
V0   2g
h
2                C
V0     H               V0   2g
B

W                                      P/γ
45o      D

Sharp crested
Sharp-crested weirs are commonly used as means of flow measurement.
Sharp-crested                                              Hydraulics,
• Sharp crested weir has an importance in Open Channel Hydraulics
simply because, its theory forms a basis for the design of spillway.
,        g        p                 y y           p
Because, the edge is sharp. → no boundary layer development only      y
on the vertical surface on which the velocities are small
• Therefore no viscous effects → no energy dissipation
• Let’s consider the simplest form of weir; consisting of
g
• a plate set perpendicular to the flow in a rectangular channel,
• its horizontal upper edge running the full width of the channel
y
• 2 dimensionality → no lateral contraction effects.
• Since the lateral contraction effects are suppressed by the channel
sidewalls, this type of weir is sometimes termed the SUPPRESSED
weir.
Let’s make an elementary analysis by assuming;
• no contraction over the weir
• pressure it atmospheric across the whole section AB.

• The total head at a point C is:

P+V ⇒ = 2
2

h=        V    gh
γ 2g
=0

• The discharge per unit width then;
/                          /
H +V o 2 g                    H +V o 2 g
2                          2

q=            ∫
/
vdh =         ∫
/
2gh dh
Vo          2g                Vo 2g
2                          2
• The discharge per unit width becomes;
/                   /

2     ⎡⎛ V 2   ⎞
3 2
⎛ V o2   ⎞
3 2
⎤
q =   2 g ⎢⎜ o + H ⎟
⎜2      ⎟         −⎜
⎜2       ⎟
⎟         ⎥
3     ⎢⎝
⎣    g   ⎠          ⎝ g      ⎠         ⎥
⎦

• Here h is measured downwards from the EGL, not from the free
surface.
• Now, the effect of the flow contraction may be expressed by a
t ti            di to the      lt
contraction Cc, lleading t th result:
/                       /

2        ⎡⎛ V 2   ⎞
3 2
⎛ V o2      ⎞
3 2
⎤
q = C c 2 g ⎢⎜ o + H ⎟
⎜       ⎟          −⎜
⎜2          ⎟
⎟          ⎥
3        ⎢⎝ 2 g
⎣        ⎠           ⎝ g         ⎠          ⎥
⎦
• We can make this expression more compact by introducing a
discharge coefficient Cd;
/
2
q = Cd 2g H
3 2

3     /                                 /
• where;
⎡⎛    Vo
2
⎞
3 2
⎛ Vo    2
⎞
3 2
⎤
C d = C c ⎢⎜1 +
⎜ 2              ⎟
⎟         −⎜
⎜2          ⎟
⎟         ⎥
⎢⎝
⎣     gH          ⎠          ⎝ gH        ⎠         ⎥
⎦

• we should expect both Cc and the ratio of Vo2 2gH to be dependent
alone
on the boundary geometry alone, in particular on the ratio of H/W;

• when W is large Vo is small ⇒ V o ⇒ 0
2

Cd ≅ Cc
2gH
REHBOCK found experimentally that
H   1
C d = 0.611 + 0.08 +
W 1000H

Shows the viscous and the surface tension effects.                             π
Neglect unless H is very small. H is in meter.                         Cc =
π+2

As W becomes very large → Cd=0.611, and              This is the only fluid flow
since  Vo2 / 2 g becomes very small,                 problem in ideal fluid for
which the contraction
Cc≈Cd≈ 0.611.                                        coefficient is obtained
π
This happens to be the numerical value of            theoretically.
π +2
shown last century by Kirchoff to be the
contraction coefficient of a jet issuing without
l        d ith     li ibl deflection by
energy loss, and with negligible d fl ti b
gravity from a long rectangular slot in a large
tank, two-dimensional problem.
tank a two dimensional problem
•                                    0.611                                weirs.
By many investigators the value 0 611 have been conformed for high weirs
•   On the other hand, when W becomes small, H/W becomes large, and this formula
cannot be true for high values of H/W. In fact, experimental work has shown that it is
true only for the values of H/W up to approximately 5. Therefore:

H   1                         H
C d = 0.611 + 0.08 +                              ≤5
W 1000H                       W
H < 10
,
• For 5 <
W

formula
• Cd begins to diverge from the value given by the formula, reaching a
value of 1.135 when H/W=10.
• If W vanishes completely, so that H/W becomes infinite, we have the
case of free over fall. In this case H=yc, critical depth, and q is
determined accordingly.
p            y
• In fact, it has been shown experimentally that critical flow also occurs
just upstream of a very low weir. In this case the weir is called a sill,
i.e in the range H/W > 20.

EGL
2
V0   2g

V0                        h
H

W

yc = H + W      Vc =   gyc   qc = ycVc
/
/
W ⎞
3 2        /
⎛
qc = ( H + W ) g( H + W ) =        g(H + W )         =   g⎜ 1+   ⎟         H
3 2                             3 2

⎝    H ⎠
/                                    /
W ⎞                            .
/                          3 2        /
2                         ⎛                                       ⎛   W ⎞
3 2
q=     C 2g H         =      g ⎜1 +     ⎟         H
3 2                                   3 2

3 d                       ⎝      H ⎠                    C d = 1 06⎜1 + ⎟
⎝   H ⎠
H
• The range                                    explored.
has not yet been completely explored
10〈
W
〈 20

• But Kanda Swany and Rouse showed that:

Cd

4              8                10   0.08         0.04
H/W                                   W/H
• Max. Cd occurs at H/W=10, which is the border line for weir and sill.
• For completely free overfull, W = 0, the equation for Cd becomes

⎡⎛
/
3 2
/
3 2
⎤
.
V
2
⎞          ⎛ Vo  2
⎞                 C d = 1 484 C c
C d = C c ⎢⎜1 + o
⎜         ⎟
⎟         −⎜
⎜2            ⎟
⎟         ⎥
⎢⎝ 2 g H
⎣          ⎠          ⎝ gH          ⎠         ⎥
⎦

1.837                0.354
/
.
W ⎞
3 2
. ⎛                                .         1 06    .
C d = 1 06⎜1 + ⎟                      = 1 06 ⇒ C c = .    = 0 715
⎝   H ⎠                                   1 404

• Cc=0.715 will be discussed later at free overfall.
• Two important features of the pressure distribution down the vertical
section ABC;
• Pressure distribution is nonhydrostatic, because of distinct curvature
plane,
of the streamlines in the vertical plane
• Pressure is not atmospheric, contrary to the assumption in the
elementary analysis that :
e pressure     e a osp e c pressure
• the p essu e > the atmospheric p essu e
• Consistent with the contraction and acceleration downstream of AB.
Clearly         f     i            t        thi      l ti
Cl l a pressure force is necessary to cause this acceleration iin
the region of atmospheric pressure.
• It has been assumed throughout that the pressure is atmospheric
along the lower surface of the jet, or “nappe” as well as upper
f      this j t i j t     fi d b t              ll    ll d     t
surface if thi jet is just confined between parallell walls downstream
of the weir, air will be trapped and this all will be gradually removed
by the flow, pressure in this region is reduced.
• For a given head as Q increases, there is risk of cavitation, then
ventilation is necessary.
• Any other type of weir will be three dimensional because of the
lateral contraction from the sides, as well as in the vertical plane.
contracted
Typical examples are the “contracted” rectangular weir and the
triangular weir.
Contracted Weirs
• A contracted weir involves a 3-dimensional flow problem, because of:
• the contraction from the sides as well as in the vertical plane.
• Typical examples:
• contracted rectangular weirs
• triangular weir
• Such weirs are commonly used for flow measurement, normally in
infinite,
tanks large enough to be effectively infinite so that the contraction
coefficient, Cc,has its minimum value. In this case, general equations
il bl l ti di h          to head; but for      ll tanks i
are available relating discharge t h d b t f small t k weirs
should be calibrated for each particular problem.
Contracted Rectangular Weirs
• Francis found experimentally that the amount of lateral contraction at
each end of the contracted weirs was equal to 0.10 H, p
q             , provided that
the length L of the weir was greater than 3H. On the basis of this
result, it is commonly accepted that the discharge Q is given by;
2       .                  /    ,         .
Q = C c(L-0 2 H   )   2g H             C c = 0 611
3 2

3

Ls                      Ls

W

L > 3H, Ls > 4H and W > 3H
The triangular weir (V-Notch)
• The triangular weir can be analyzed in the same elementary way as
pp               g               g
the suppressed rectangular weir leading to the result:
8    t a n α            /
Q =    Cc         2g H      5 2

15          2
• The most commonly used value of the notch angle α is 90o. For this
case Cc=0.585 →somewhat less than for rectangular weir.

α
0 59 general
• Although the value of Cc is near to 0.59 in general, it is affected by
viscosity, surface tension, and weir plate roughness;
• A comprehensive study of triangular weir flow has been made by
Lenz, He used many liquids in order to discover the effects of
viscosity and surface tension on weir coefficients, thus extending the
decree.
utility of the triangular weir as a reliable measuring decree
• For α = 90o, Lenz proposed that
.
.              0 70
C c = 0 56 +        .            .
R           W
0 165       0 170

• Applicable to all liquids providing that the failing sheet of liquid does
not ding to the weir plate and that H > 0.06 m, Re > 300, W > 300.
• As Re and Weber number decrease, Cc will increase.
V-notch weir
A V-notch weir with stilling wells is shown in figure below
Compound Weirs
• Unusual situations may require special weirs. For example, a V-notch
weir might easily handle the normal range of discharges at a
occasionally,
structure; but occasionally much larger flows would require a
rectangular weir. A compound weir, consisting of a rectangular notch
with a V-notch cut into the center of the crest, might be used in this
situation.
situation
• The compound weir, as described, has a disadvantage. When the
g     g                     p y
discharge begins to exceed the capacity of the V-notch, thin sheets
of water will begin to pass over the wide horizontal crests. This
overflow causes a discontinuity in the discharge curve (Bergmann,
)            ,
1963). Therefore, the size and elevation of the V-notch should be
selected so that discharge measurements in the transition range will
be those of minimum importance.
• Determining discharges over compound weirs has not been fully investigated
either in the laboratory or in the field. However, an equation has been
y                         ,     q
developed on the basis of limited laboratory tests on a 1-ft-deep, 90-degree
V-notch cut into rectangular notches 2, 4, and 6 ft wide to produce horizontal
extensions of L=0, L=2, and L=4 ft, respectively (Bergmann, 1963). The
i         fully   t t d d heads to 2.8 b                 the t h i t
weirs were f ll contracted, and h d up t 2 8 ft above th notch point
were used. The equation is as follows:
.     .       .       .       .
Q = 3 9 h11 72 - 1 5 + 3 3 L h2 5
1

• where:
• Q = discharge in ft3/s
• h1 = head above the point of the V-notch in ft
• L = combined length of the horizontal portions of the weir in ft
• h2 = head above the horizontal crest in ft
• When h1 is 1 ft or less, the flow is confined to only the V-notch portion of the
weir, and the standard V-notch weir equation is used.
,                                   q
• Further testing is needed to confirm this equation before it is used for weirs
beyond the sizes for which it was developed.
Compound weir with 90-degree notch and suppressed rectangular
crest used by U.S. Forest Service.
North Fork 120-degree compound V-notch weir and sampling bridge
• The finish of the edge and upstream surface of a weir is important,
since the roughness of the surface or rounding of the edge tends to
flow
suppers the lateral components of flow, increase Cc and hence
increase the discharge.
3 4H
• H should be measured 3-4H upstream of weirweir.
3.4         Free Fall
Actual pressure distribution              EGL
0.215yb
C
yc

yb

A                                  B
3-4yc

,            p               p              p     g
• In this situation, flow takes place over a drop which is sharp enough
that the lowermost streamline separates from the channel bed.
sharp crested
It is a special case of sharp-crested weir; W = 0 but it needs a special
treatment, because of its use as
• a form of spillway
• a means of flow measurement because of unique relationship between
the brink depth and Q.
Clearly,           t t feature f th fl i th t           d
Cl l an iimportant f t of the flow is the strong departure f   t from
hydrostatic pressure distribution which exist near the brink, induced by
strong vertical components of acceleration in the neighborhood.
The form of this pressure distribution at the brink B will evidently be
somewhat as shown in the figure, with a mean pressure considerable
h hydrostatic.
lless than h d       i
At some short distance back from the brink, the vertical accelerations will
hydrostatic
be small and the pressure will be hydrostatic. This is experimentally
verified that from A to B there is pronounced acceleration and reduction
in depth as shown in figure.
• Consider a long channel of two sections, one of mild upstream and
one of steep slope downstream. If the upstream channel is steep, the
flow at A will be supercritical and determined by the upstream
conditions.
conditions
• If on the other hand the channel slope is mild, horizontal or adverse,
the flow will be subcritical at A.
Recall th t th t     iti f         ild (h i t       d      ) l    t
• R ll that the transition from mild (horizontall or adverse) slope to a
steep slope.
NDL

CDL                     M2
yc          y01               yc
S2
A
Sf > S0
O
Sf = S0
Sf < S0
B
The flow will gradually change from subcritical at a great distance
upstream to supercritical at a great distance downstream passing
point.
through critical state at same intermediate point
In the transition region upstream of (0),
S f
y < y0 → V > V0 ⇒                            > S0
Similarly, downstream of (0)
V                      S
y > y0 →              < V0 ⇒                 f   < S0   (1 - F ) d y
r
2
= S0 - Sf
dx
If we consider the point 0 to be a short curve joining two long slopes,
dy
there must be some point on this curve at which Sf=S0 and since    ≠0
dx
neighborhood, follows           1            flo     critical
in this neighborhood it follo s that Fr=1. Therefore flow is critical.
• Imagine now that in this case the steep slope is gradually made even
steeper, until the lower streamline separates and the overfall condition
is reached. The critical section cannot disappear, it simply retreats
e A.
upstream into a region of hydrostatic pressure ii.e to A

g       ; p
• The local effects of the brink is confined to the region AB; experiments
shows this section to quite short, of the order 3-4 times yc.
The Head of the free overfall
• The simplest case is that of a rectangular channel with side walls
jet,
continuing downstream on either side of the free jet so that we have
the effect of atmosphere only on the upper & lower streamlines, not
2D
to the sides. This is a 2-D case and it is only in this form of the
problem that many investigators worked on for a theoretical solution.
,                                        g
• Consider the section C, a vertical section thru the jjet far enough
downstream for the pressure throughout the jet to be atmospheric,
and the horizontal velocity to be constant.
• Assume that
• -the channel bottom is horizontal and
• -no resistance
C
y1

yb            V2x

y’2       y
A                                   B    α
3-4y
34 c

• Apply momentum eq. b/w A and C, along the x direction.
1 2                           , Q
Q   V
V 1
γ y1 b + ρ Q V1 = ρ Q V 2 x       = A1
2
1 2
γ y 1 b + ρ V 12 A1 = ρ V 1 A1 V 2 x
2
1 2
γ y 1 b + ρ V 12 y 1 b1 = ρ V 1 y 1 b1 V 2 x ------------------- E (1)
Eq.(1)
2
From Equation of Continuity:

′
V1 y 1 b = V 2 y 2 b            y ′ = y 2 cos α
2

V1y 1 = V2 y 2 cos α = V2 x y 2                              y1
V2 x   =    V1
y2

V2x
1                    y
Substituting into Eq.(1)            g y1 + V 12 = V 12 1
2                    y2
Dividing by
Di idi b gy1                    1 V 12      V1 y1
2
+      =
2 g y1      g y1 y 2
1             y
+ F12 = F12 1 rearranging we get             y 1 = 1 + 2 F1
2
• Or                                                                     or
2             y2                               y2      2 F12

y 2 = 2 F1
y 2 〈 y1
2

y 1 1 + 2 F1
2

if the flow is critical at section A, then y1=yc, then we have F1 = 1 and

y2 = 2        sets a lower limit on the brink depth yb:
,

since there is some residual pressure at the brink,
yc 3          yb must be greater than y2; it follows that
2 yb
〈 〈1
3 yc
The experiment of Rouse showed that the brink section has
depth f 0 715
a d th of 0.715 yc.
Rouse also pointed out that combination of th weir E
• R      l     i t d t th t      bi ti     f the i Eq.
/                   /

2        ⎡⎛ V 2  ⎞
3 2
⎛ V o2   ⎞
3 2
⎤
⎜2 + H ⎟
q = C c 2 g ⎢⎜   o
⎟              -⎜
⎜2       ⎟
⎟         ⎥
3        ⎢⎝ g
⎣       ⎠               ⎝ g      ⎠         ⎥
⎦
• with the critical flow equation:
a n d
qc = Vc yc = yc    gyc       w =0→ H = yc                                   Vo = Vc
/                            /

2        ⎡⎛ V 2      ⎞
3 2
⎛ V c2            ⎞
3 2
⎤ /
⎜ 2 g y + 1⎟
q c = C c 2 g ⎢⎜    c
⎟          -⎜
⎜2gy              ⎟
⎟         ⎥ y3 2
3        ⎢⎝
⎣       c   ⎠           ⎝      c          ⎠         ⎥
⎦
/
2        ⎡ . 3/2 ⎛1⎞                     3 2
⎤ 3/2                       /
q c = C c 2 g ⎢(1 5) − ⎜ ⎟                          ⎥ yc =                  g yc
3 2

3        ⎢
⎣        ⎝2⎠                          ⎥
⎦
C c = 0.715
.
• Therefore               y b = C c y c = 0 715 y c
There h      b                   h thi       d the    l i
• Th have been may research on this and th conclusion suggested      t d
by all these investigations is that a brink depth yb=0.715yc can safely
be used for flow measurements in rectangular channels with a likely
error of only 1 to or 2 %.

• We have seen that the control structures are necessary in design of
structures
hydraulic structures, because they fix a relationship between the
depth and the discharge.

• We have seen weirs and free-overfall as control structures. But in
certain hydraulic problems, they may not be useful due to certain
Two important disadvantages of weirs are:
1.they involve fairly large head loss when the available head may be very
important to be conserved.
2.The existence of a dead-water region behind the weir where silt can
accumulate and greatly change the head-discharge relationship of the
weir.
weir
Also we have seen that the critical flow establishes a fixed relationship
between the depth and the discharge. But in order to apply this principle,
it is necessary to create some device or use some feature that sets up
critical flow at a known section in its vicinity. Then the measurement of
calculated.
the depth at this section enables the discharge to be calculated
In case of free-overfall, in which, we have seen that the critical section
ill defined
retreats upstream to some ill-defined location; at the brink the depth is a
well-defined fraction of critical depth but the rapid variation in depth calls
for precise location of the depth-measuring device.
•Before considering any particular device, we first consider certain general
principles. We know that the critical flow occurs at the change of channel
slope at point O, provided that the pressure distribution is hydrostatic.
NDL                  M2
CDL
yc         y01              yc             S2
A
O

B
This will be true if the downstream slope, although steep, is not excessively
so-say of the order 0.01. In this case, section O would an ideal critical-
meter,                               critical
depth meter the depth here is definitely critical, and is not changing so
rapidly that the slight errors in locating the depth-measuring device would
g                                                    p
give rise to serious errors in estimates of the depth.
However, the long downstream slope is not usually available in
practice.
Then we have make the downstream slope short but steep but this
brings the inconveniences of free-overfall, in which we have seen
that th iti           ti     t t       t     to       ill-defined i
th t the criticall section retreats upstream t some ill d fi d region;
at the brink the depth is a well-defined fraction of critical depth, but
depth
the rapid variation in depth calls for precise location of the depth-
measuring device.
i has         tb d           ht      i t i hydrostatic
If a weir h a crest broad enough to maintain h d t ti pressure
distribution in the flow across it, the flow will apparently be critical, as
Figure.
show in Figure

H is the upstream total energy line above the weir crest.
appreciable,          eq.
If the velocity of approach is appreciable the above eq will have to
be used with successive approximations which yield H as well as q.
• Broad crested weirs are robust structures that are generally
constructed from reinforced concrete and which usually span the full
width of the channel. They are used to measure the discharge of
rivers, and are much more suited for this purpose than the relatively
flimsy sharp crested weirs. Additionally, by virtue of being a critical
meter,
operates effectively with higher downstream water levels than a
sharp crested weir.
• Only rectangular broad crested weirs will be considered, although
y possible shapes: triangular, trapezoidal and
there are a variety of p             p         g        p
round crested all being quite common. If a standard shape is used
then there is a large body of literature available relating to their
design,       ti       lib ti      d     ffi i t f discharge (
d i operation, calibration and coefficient of di h            (see
BS3680). However, if a unique design is adopted, then it will have to
be calibrated either in the field by river gauging or by means of a
scaled-down model in the laboratory.
A rectangular broad crested weir is shown above. When the length,
L, of the crest is greater than about three times the upstream head,
the weir is broad enough for the flow to pass through critical depth
somewhere near to its downstream edge. Consequently this makes
the calculation of the discharge relatively straightforward. Applying
the continuity equation to the section on the weir crest where the flow
is at critical depth gives:
•                                                         Q = Ac Vc.
•   Now            i that the b dth f the i                 the f ll idth
N assuming th t th breadth of th weir (b) spans th full width (B)
of the channel and that the cross-sectional area of flow is
rectangular,
rectangular then:
•                     Ac = b x Dc and Vc = (g x Dc)1/2
•                               equation,
Thus from the continuity equation
q       y c
Vc =      gyc/           =         Vc
q=       g yc
3 2
Eqn. 1

• However, equation 1 does not provide a very practical means of
calculating q. It is much easier to use a stilling well located in a
gauging hut jjust upstream of the weir to measure the head of water,
g g g
H1, above the crest than to attempt to measure the critical depth on
the    t it lf In d to li i t           from th equation, we can use
th crest itself. I order t eliminate yc f    the    ti
the fact that in a rectangular channel . y c   =
2
E   c
3
• Using the weir crest as the datum level, and assuming no loss of
energy, the specific energy at an upstream section (subscript 1, Fig.
above) equals that at the critical section:

V1 = = 3
2
y c        2⎛      V1 ⎞
2

H1 +     Ec   yc                     = ⎜ H1 +
⎜          ⎟
2g     2                         3⎝      2g⎟ ⎠
• Substitute this expression into Eqn 1:
/                           /
.
3 2
⎛2⎛                  ⎞⎞
3 2
⎛          ⎞
⎜ ⎜ H 1 + V1                                    V1 ⎟
2                               2

q=      g⎜ ⎜                  ⎟⎟
⎟⎟          = 1 705⎜ H 1 +
⎜       2g⎟
Eqn 2.
⎝3⎝       2g         ⎠⎠                 ⎝          ⎠
• The term     V1            in the above equation is the velocity head of the
2

2g
approaching flow. As with the rectangular sharp crested weir, the
problem arises that the velocity of approach, V1 cannot be calculated
,                                                   y
until Q is known, and Q cannot be calculated until V1 is known. A way
around this is to involve an iterative procedure, but in practice it is often
found that the velocity head is so small as to be negligible. Alternatively,
a coefficient of discharge, C, can be introduced into the equation to allow
for the velocity of approach, non-parallel streamlines over the crest, and
energ losses. C varies between abo t 1 4 and 2 1 according to the
energy losses    aries bet een about 1.4     2.1
shape of the weir and the discharge, but frequently has a value of about
1.6. Thus:
/
Q = C B ( H 1 )3       2
Eqn 3.

The broad crested weir will cease to operate according to the above
ti         b k t from further d
equations if a backwater f           t            the i t
f th downstream causes th weir to
submerge. Equations 2 and 3 can be applied until the head of water
above the crest on the downstream side of the weir, HD, exceeds the
crest.
critical depth on the crest This is often expressed as the
submergence ratio, HD/H1. The weir will operate satisfactorily up to a
submergence ratio of about 0.66, that is when HD = 0.66H1.
• For sharp crested weirs the head-discharge relationship becomes
inaccurate at a submergence ratio of around 0.22, so the broad
crested type has a wider operating range.
yp               p      g g

• Once the weir has submerged, the downstream water level must also
be measured and the discharge calculated using a combination of
q                ,        q
weir and orifice equations. However, this requires the evaluation of
two coefficients of discharge, which means that the weir must be
lib d by i           i during high flows. Thi can b
calibrated b river gauging d i hi h fl      This    be
accomplished using a propeller type velocity (current) meter.
Minimum height of a broad crested weir
• A common mistake made by many students in design classes is to
l l t the head that ill                    i t       ti l discharge
calculate th h d th t will occur over a weir at a particular di h
without considering at all the height of weir required to obtain critical
depth the          t For        l             the depth f flow
d th on th crest. F example, suppose th d th of fl
approaching the weir is 2 m. If the height, p, of the weir crest above
the bottom of the channel is only 50 mm, the weir is so low that the
flow would be totally unaffected by it and certainly would not be
induced to pass through critical depth. Equally ridiculously, if the
weir is 4 m high it would behave as a small dam and would raise the
upstream water level very considerably and cause quite serious
flooding.
• So how can we work out the optimum height for the weir? What
height will give supercritical flow without unduly raising the upstream
water level?
y pp y g            gy q
• The answer is obtained by applying the energy equation to two
sections (See diagram below). One some distance up-stream of the
weir (subscript 1) and the second on the weir crest where critical
depth occurs (subscript c). In this case the bottom of the channel is
level.
used as the datum level Assuming that the channel is horizontal
over this relatively short distance, that both cross-sectional areas of
rectangular                               energy,
flow are rectangular, and that there is no loss of energy then:
q = + = +3
2

y1 +          P Ec P  y
2 g y 12        2 c
q       2
y
y c       3               T h e r e f o r e
=           g

2
q
q = +3
2
3               E q n . 4
y1 +         P                               g
2 g y12
2

• This is usually sufficient to enable equation 4 to be solved for p when
q and y1 are known. Alternatively, the depth, y1, upstream of the weir
known.
can be calculated if q and p are known When calculating the 'ideal' ideal
height of weir, it must be appreciated that it is only ideal for the
g           g                       j           g
design discharge. The weir cannot adjust its height to suit the flow,   ,
so at low flows it may be too high, and at high flows it may be too
low. Consequently 'V' shaped concrete weirs are often used, or
compound crump weirs that have crests set at different levels.
Example:
• Water flows along a rectangular channel at a depth 1.3 m when the
8.74 /s.                                 5.5 m,
discharge is 8 74 m3/s The channel width (B) is 5 5 m the same as
the weir (b). Ignoring energy losses, what is the minimum height (p)
of a broad crested weir if it is to function with critical depth on the
crest?
• V1 = Q/A        = 8.74 / (1.3 x 5.5) = 1.222 m/s
q   2
y           3
•         c   =
g
g     = ((8.74)2/(9.81 x 5.52))1/3
•                                         = 0.636 m
V
•        c =
g y c = (9.81 x 0.636)1/2
•                                     = 2.498 m/s
q
• Substitute these values into Eqn 4 and then solve for p
•          1.2222/19.62 + 1.300 = 2.4982/19.62 + 0.636 + p
• 1.2222/19.62 + 1.300 = 2.4982/19.62 + 0.636 + p
•         0.0761 + 1.300 = 0.318 + 0.636 + p
•                     p = 0.422 m
• Thus the weir should have a height of 0.422 m measured from the
bed      l
b d llevel.
In      ti             t be bl to bt i         h id li d i t
• I practice we may not b able t obtain such an idealized picture. If
the weir is short:
•
• There will be no clearly defined region of critical flow, because the
whole weir length will be occupied by the regions of rapidly changing
depth produced by the two ends of weir.
•
• If the weir lengthened, then the resistance effects become
pp
appreciable.
•
q (*)
• In both cases we can not use the eq. ( )
•
• The most satisfactory action in practice is to use a long weir and use
Eq.(*) with a correction for the resistance or we the brink depth .
• If yb is used for flow measurement:

.y b          g y b = 1 . 65
.
•            q=                              yb ρyb
0 715 0 715

• If a correction is made to take into account the b.e. then it is reduced
by the max. displacement thickness γ1. The discharge q given by Eq.
(*) is then multiplied by a correction factor:
/                             /
⎛ δ ⎞
3 2
2 2 ⎛ δ1 ⎞
3 2        /
C = ⎜1 − 1 ⎟              q =    g ⎜1 − ⎟          H
3 2

⎝    H ⎠                  3 3 ⎝    H ⎠
The      l i f H ll for         d d i (not        d d
• Th analysis of Hall f a square-edged weir ( t rounded as iin
figure) gives C as:
.
.⎛ L      .      .
0 25 ⎞
08      .
−0 2
1 − C = 0 069⎜ − 1 + 2 84 R e ⎟                Re
⎝ H                 ⎠
• Where

V1 H                       2             2  2     /
Re =                    V1 =      gH        q= C   gH
3 2
υ                         3             3  3

The     ffi i t 2.84 ithi the b k t l t t               i f i fi it
• Th coefficient 2 84 within th brackets relates to a weir of infinite
heights, W with a vertical face. If H/W is appreciable and if the
valve.
upstream face is inclined towards the vertical C has a lower valve
These C values gives q f ± 1 5% f 3<H/ <34
• Th         l        i     for 1.5% for 3<H/w<34.
• When the weir is of finite width B, the boundary layer growth along
the sides will introduce another coefficient equal to
2                             2δ1
δ1 = (1 − C ) H                 C B = 1−
3 /                             B
⎛ δ1 ⎞                 3 δ1                     4 H (1 − C )
3 2

C = ⎜1 − ⎟            ≈ 1−                 C B = 1−
⎝   H ⎠                2 H                          3B

2  2     /    Q   C
q= C   gH     ⇒   = B qB
3 2

3  3
• A rounded u/s edge on the weir would presumably have some
C.
influence on the growth of boundary layer and on C But it has need
to be investigated.
Parshall Flume
• Parshall Flume
• A Parshall flume has a special shaped open channel flow section
which may be installed in a ditch ,canal, or lateral to measure the
flow rate. The Parshall flume is a particular form of venturi flume and
developer,          Mr.       L.
is named for its principal developer the late Mr Ralph L Parshall
(Water Measurement Manual, U.S. Bureau of Reclamation, 1984)."

Ralph L. Parshall saw problems with stream measurements when he
began working for the USDA in 1915, as an irrigation research
engineer. In 1922 he invented the f  flume now known by his name.
When this flume is placed in a channel, flow is uniquely related to the
depth                                        depth flow
water depth. By 1953 Parshall had developed the depth-flow
relationships for flumes with throat widths from 3 inches to 50 feet.
j                    q
The Parshall flume has had a major influence on the equitable
distribution and proper management of irrigation water
• Parshall flumes are apparently the most widely used types of flumes
now for fixed flow monitoring installations. They have wide flow
ranges, resistance to submersion,and are simple to calibrate..
Parshall flumes are sized by throat width and conform to
standardized dimensions published in the U.S. Department of the
Interior Bureau of Reclamation.
Interior,          Reclamation

http://www.usbr.gov/wrrl/fmt/wmm/ which ASTM and ISO standards
have also been written for them (ASTM, 1991; ISO, 1992 contains
the Burea of reclamations water measurement manual.
there are several types of popular flumes to choose from including
Palmer-Bowlus, Trapezoidal HS/H/HL Type Cutthroat, RBC
the Palmer Bowlus Trapezoidal, HS/H/HL-Type, Cutthroat RBC,
Montana, and SANIIRI and plenty of custom flumes. Computer
p p          g g
simulation software has been written to assist people in designing
optimum flume types and computer assisted calculations assist many
engineers (some of whom may not be aware of the technical
li i ) d i i Fl                   d       h         i
iimplications) iin designing Flumes and open channell equipment
3.7 Undeflow Gates
Underflow gates are used for many purposes such as:
•                                          p
Controls at the crest of an overflow spillway,y,
•   Control at the outlet from a lake to a river or irrigation channel.
g
Undeflow gates

Vertical Gates      Radial Gates         Drum Gates

(Tainter G t )
(T i t Gates)
Flow in underflow gates might be
1.
1    free tfl
f outflow or,
2.   submerged (drowned) outflow.
Free Outflow -Vertical Gates:
2
U1
EGL
2g

U2
2
2g
y1

45o                                  y2

(1)                                        (2)
q2               q2
E1 = E 2 ⇒             y1+       2   = y2 +         2   Solving for q :
2gy 1            2gy   2

2                     21                                      2g
q = 2 g( y 1 y 2 )              or            q = y 1y 2                = C d w 2 gy 1
(y 1 + y 2 )                            (y 1 + y 2 )
q       y                          2g                  o r
y2 = C c w                    =       1
Cc w
y1 + C c w
q                         2 gy1                   o r     q
= Cc w                                                 = C d w 2 gy1
1+ C c w
y1
w h e r e   C   d    =
Cc
1+ C c w
y1

C d = f⎛ w                ⎞=      dis c h a r g e           c o e ffi c i e n          t
⎜            y 1   ⎟
⎝                  ⎠
w/E1       0                 0.1               0.2           0.3               0.4        0.5
Cc         0.611 0.606 0.602 0.600 0.598 0.598

06
Cc=0.6
Vertical Sluice Gate
Radial t            id l      d           h k t t          to    t
• R di l gates are widely used iin canall check structures t controll
canal flows and water levels. By measuring upstream water level,
level           position,
downstream water level, and gate position radial gate checks can
also be used to compute flow. Computing flow at check structures
devices such as flumes, weirs, or flow meters.
• Radial gate flow is a type of variable-area orifice flow, which may be
either free or submerged. However, accurate computation of radial
gate flow requires complex analysis. Discharge under a radial gate is
dimensions.
influenced by numerous parameters and structure dimensions The
following figure shows a typical radial gate with some of the variables
g                 g
that affect gate flow. The angle of the g                  g (gate p)
gate's bottom edge (g lip)
varies with the gate opening, Go, the pinion height, PH, and the gate's
radius, r. Flow contraction is sensitive to the angle , the type of gate
lip seal, and water levels.
• The general equation for flow through an undershot gate can
be derived from the Bernoulli equation and expressed as:

Q = C d G0 B 2 g H
• where:
• Q = discharge (gate flow)
Cd = coefficient of discharge
Go = vertical gate opening
B = gate width
g = gravitational constant
term, H,
• The head term H in the above equation can be either the upstream
depth, Yu, or the differential head across the gate, Yu - Yd (see
9 8).                                           93
figure 9-8). When differential head is used, equation 9-3 becomes the
well-known "orifice" equation. The development of the coefficient of
discharge, Cd, depends on the definition of the head term as well as
the various other parameters that affect gate flow. Cd has been
predicted using a number of different methods, but most of these
accuracy.
methods have limited application and accuracy
• In 1983, a research program at Reclamation's Hydraulics Laboratory
developed gate flow algorithms that represent the complete discharge
characteristics for canal radial gate check structures.
These algorithms are a complex set of equations th t cover th range
• Th       l ith                l       t f    ti    that        the
of water levels and gate geometry normally encountered at canal
structures.                correctly,
check structures When applied correctly they can be as accurate as
any canal flow measurement device or procedure. The main
disadvantages to using these algorithms are their complexity and the
requirement to accurately measure two water levels, Yu and Yd, and
the gate position, Go. Additionally, sedimentation or check structure
s bsidence can change gate flo characteristics at e isting str ct res
subsidence                     flow                   existing structures
and require recalibration over time.
Consider the radial gate shown below

y1                                                a

w                                y2 =Ccw
Cc
q = C d w 2 g y1                  Cd =
1+ Cc w
y1
,      , ,
C d = f ( y1 w a r )
.        .
C c= 1 − 0 75β + 0 36β
2

θo           g i v e s q w it h       5 % e rr o r p r o vid e d t h a t        1
β=        o
±                                        β≤
90

Reference: A. Toch, “Discharge Characteristics of Tainter Gates”,
g,         ,      , p.290
Trans. Amer. Soc. of Civil Eng., Vol.120, 1955, p
Drown Outflow

2
U1
EGL
2g

y1

y2

(1)                   (2)
y
y                       q = + q
2                                             2
,           y
y
E1 = E 2 ⇒                                                   1       +         y                                                                        2   = Cc w
2 g y12
2 g y2
2

S olv e               f o r     q        a s                     :

2
q
⎛ 1   1 ⎞
⎜ 2 − 2 ⎟ = y1 − y                                                                          ..........               .....
(1 )
2 g ⎜ y2
⎝
⎟
y1 ⎠
1                                                 1
q =                                             q
2                                                    2

F 2 = F3 ⇒                                                           y +                                          y +
2                                             2
2                                                 2
gy2                                             gy3
3

S olv e               f o r     q        a s                     :

2
q
⎛ 1   1 ⎞ 1 2
⎜   −    ⎟ = ( y3 − y 2 )                                                                            ..........               .....
(2 )
g ⎜ y2 y 3 ⎟ 2
⎝        ⎠
T w o              u n k n o w n s                                    : q   a n d          y.

E li m i n a t e                     q   b e t w e e n                              E q u a ti o n s                            1          a n d               2   ,   a n d   s olv e   f o r   y,
︵
︶

︵
︶
a n d           t h e n        q .
Drum Gate
3.8 Energy Dissipators

In general, two methods to dissipate excessive kinetic energy of the
flow:
1. Abrupt transitions or features which induce severe turbulence
• İncluding sudden changes in direction (base of free fall)
• Sudden expansion (eg: hydraulic jump)
2. Throwing the water a long distance as a free jet (ski jump or
bucket type of energy dissipators)
3.8.1 Hydraulic Jump As An Energy Dissipator

Q2             Q2
F1 = F2   →      y1 A1 +     = y2 A 2 +
gA1            gA 2

E1 = E 2 + h l
Hydraulic Jump in Rectangular Channels
For a rectangular channel, above equations reduce to simple forms

(
y2 = 1 1+ 8 2 −1
F r1     )       Energy loss: h f =
y 2 - y1
3

︵

︶
y1 2                                                       4 y1 y 2
y 2 -1 3
hf = y 1              r e l a ti v e l o s s
︵

︶

=
y1       4   y2
y1
y2 i s a m e a s u r e o f s t r e n g t h o f t h e j u m p .
:     y1
F o r F
r >> 1 ⇒ y 2 ≈
2
2 Fr −
y1 1
y1                      2
Classification of Jump
3.8.2
3 8 2 Hydraulic Jump on Steep Slopes
3.8.3 Stilling Basins
tilli basin        h t       th f      d h         l d t the foot f
A stilling b i iis a short llength of paved channell placed at th f t of a
spillway or any other source of supercritical flow to dissipate the energy
of the flow.

The i f h d i          i       k hydraulic          form within the
Th aim of the designer is to make a h d li jjump to f     i hi h
basin, so that the flow is converted to subcritical before it reaches the
exposed and unpaved river bed downstream.

features of stilling basin are those that:
The desirable f         f

1.   To tend to promote the formation of the jjump,
p                                p,

2.   To make the jump stable in one position,

3.   To make it as short as possible.
Usually, if the jump is to be formed unaided, the floor of the stilling basin
p
must be placed a substantial distance below the tailwater level. But the
required excavation may of course make the basin very expensive. The
i depth f         i       be   id d
excessive d h of excavation may b avoided

1.    y        g          ,
By widening the basin,

2.   By installation of baffles to increase the resistance to flow,

3.   By a raised sill.
Hydraulic-Jump Basins
Where the energy of flow in a spillway must be dissipated before the
channel,    hydraulic
discharge is returned to the downstream river channel the hydraulic-
jump stilling basin is an effective device for reducing the exit velocity to
a tranquil state. The jump that will occur in such a stilling basin has
, p       g
distinctive characteristics and assumes a definite form, depending on

the relation between the energy of flow that must be dissipated and the
depth of the flow.

f                    f                     f
A comprehensive series of tests have been performed by the Bureau of
Reclamation to determine the properties of the hydraulic jump.
The      f      d the flow h  t i ti        be l t d to
Th jjump form and th fl characteristics can b related t

•the kinetic flow factor V
2
the              factor,        gd       , of the discharge entering the basin;

•to the critical depth of flow, dc ;
V
• or to the Froude number ,                gd     .

Forms of the hydraulic-jump phenomena for various ranges of the
below.
Froude number are illustrated on figure below
Characteristic forms of hydraulic jump related to
th F d number.
the Froude      b
g                                p
When the Froude number of the incoming flow is 1.0, the flow is at critical depth and a
hydraulic jump cannot form.
For Froude numbers from 1.0 to about 1.7, the incoming flow is only slightly below critical
depth,
depth and the change from this low stage to the high stage flow is gradual and manifests
itself only by a slightly ruffled water surface.

As the Froude number approaches 1.7, a series of small rollers begins to develop on the
surface. These become more intense with increasingly higher values of the number. Other
phenomena relatively
than the surface roller phenomena,relatively smooth flows prevail throughout the Froude
number range up to about 2.5.
2.5        4.5,
For Froude numbers between 2 5 and 4 5 an oscillating form of jump
occurs. The entering jet intermittently flows near the bottom and then
g                                                         g
along the surface of the downstream channel. This oscillating flow
causes objectionable surface waves that carry far beyond the end of the
basin. The action represented through this range of flows is designated
as form B on figure below:
For Froude numbers between 4.5 and 9, a stable and well-balanced
occurs                                                jump
jump occurs. Turbulence is confined to the main body of the jump, and
the water surface downstream is comparatively smooth. Stilling action
for Froude numbers between 4.5 and 9 is designed as form C on figure
below.
As the Froude number increases above 9, the turbulence within the jump and the
surface roller becomes increasingly active, resulting in a rough water surface with
jump
strong surface waves downstream from the jump. Stilling action for Froude numbers
above 9 is designated as form D.
Basins for Froude Numbers Less Than 1.7:
For Froude           b f 1 7 th        j t d th d,,
F a F d number of 1.7, the conjugate depth, d iis about t i th b t twice the
incoming depth, or about 40 percent greater than the critical depth. The
velocity,V                                     velocity,
exit velocity V2, is about one-half the incoming velocity or 30 percent
less than the critical velocity. No special stilling basin is needed to still
g
flows where the Froude number of the incoming flow is less than 1.7,
except that the channel lengths beyond the point where the depth starts
to change should be not less than about 4d,. No baffles or other
dissipating devices are needed.
di i ti d i                   d d
These basins, designated type I.
Basins for Froude Numbers Between 1.7 and 2.5
Flow phenomena for these basins will be in the form designated as the
prejump stage, as shown on figure . Because such flows are not
tt d d by ti t b l           baffles     ill      t     i d
attended b active turbulence, b ffl or sills are not required.
The basin should be long enough to contain the flow prism while it is
retardation.
undergoing retardation
The basin lengths given below will provide acceptable basins. These
basins,
basins designated type I I.
Basins for Froude Numbers Between 2.5 and 4.5
Flows for these basins are considered to be in the transition flow stage
because a true hydraulic jump does not fully develop. Stilling basins that
y        j p                y       p        g
accommodate these flows are the least effective in providing
satisfactory dissipation because the attendant wave action ordinarily
cannot be controlled by the usual basin devices. Waves generated by
the flow phenomena will persist beyond the end of the basin and must
ft be dampened by means apart f
often b d           db                      th basin.
t from the b i
Where a stilling device must be provided to dissipate flows for this range
number,                              B-1,
of Froude number the basin shown on figure B 1 which is designated a
type IV basin, has proved relatively effective for dissipating the bulk of
gy
the energy of flow.
Type IV Basin Dimensions
Minimum Tailwater Depths for Type IV Basins
However,
However the wave action propagated by the oscillating flow cannot be
entirely dampened. Auxiliary wave dampeners or wave suppressors must
p
sometimes be used to provide smooth surface flow downstream.
Because of the tendency of the jump to sweep out and as an aid in-
suppressing wave action, the water depths in the basin should be about 10
percent greater than the computed conjugate depth.
Often, the need to design this type of basin can be avoided by selecting
stilling basin dimensions that will provide flow conditions that fall outside
the range of transition flow. For example, with an 22.65-m3/s capacity
ill      h the         ifi          t th     t        d f th b i
spillway where th specific energy at the upstream end of the basin iis
about 4.6 m and the velocity into the basin is about 9.14 m/s, the Froude
3.2                        m.
number will be 3 2 for a basin width of 3 m The Froude number can be
raised to 4.6 by widening the basin to 6 m. The selection of basin widening
the basin to 6 m. The selection of basin width then becomes a matter of
economics as well as hydraulic performance.
Alternative Low Froude Number Stilling Basins
Type IV basins are fairly effective at low Froude number flows for small
canals and for structures with small unit discharges.
However, recent model tests. have developed designs quite different
from the type IV basin design, even though the type IV basin design was
included in the initial tests.
Palmetto Bend Dam stilling basin is an example of a low Froude number
structure, modeled in the Bureau of Reclamation Hydraulics Laboratory,
whose recommended design is quite different from type IV design.
The type IV design has large deflector blocks, similar to but larger than
chute blocks, and an optional solid end sill; the Palmetto Bend design
blocks                                                  sill.
has no chute blocks, but has large baffle piers and a dentated end sill
Dimensions for Alternative Low Froude Number
Basin
Minimum Tailwater Depths for Alternative Basins
Length of Jump
The foregoing generalized designs have not been suitable for some
Bureau applications, and the increased use of low Froude number
g                                                        yp
stilling basins has created a need for additional data on this type
of design. A study was initiated to develop generalized criteria for the
design of low Froude number hydraulic-jump stilling basins. The criteria
and guidelines from previous studies were combined with the results of
this study to formulate the design guidelines recommended for low
However,
Froude number stilling basins . However it should be noted that a
hydraulic-jump stilling basin is not an efficient energy dissipator at low
is,                    hydraulic jump
Froude numbers; that is the efficiency of a hydraulic-jump basin is less
than 50 percent in this Froude number range. Alternative energy
p    ,                      p                p     y,
dissipators, such as the baffled apron chute or spillway, should be
considered for these conditions. The recommended design has chute
blocks, baffle piers, and a dentated end sill. All design data are
presented on f  figure B4..
g                    pp          y              (the     j g
The length is rather short, approximately three times d, ( conjugate
depth after the jump). The size and spacing of the chute blocks and
baffle piers are a function of d, (incoming depth) and the Froude number.
The dentated end sill is proportioned according to d, and the Froude
number. The end sill is placed at or near the downstream end of the
basin.
stilling basin Erosion tests were not included in the development
of this basin. Observations of flow patterns near the invert downstream
exist.
from the basin indicated that no erosion problem should exist
However, if hydraulic model tests are performed to confirm a design
based on these criteria, erosion tests should be included. Tests should
be made over a full range of discharges to determine whether abrasive
p
materials will move upstream into the basin and to determine the erosion
potential downstream from the basin. If the inflow velocity is greater than
15 m/s, hydraulic model studies should be performed.
Basins for Froude Numbers Higher Than 4.5
and V<15 m/s
basins,                           form.
For these basins a true hydraulic jump will form The elements of the
jump will vary according to the Froude number. The installation of
accessory devices such as blocks, baffles, and sills along the floor of
the basin produce a stabilizing effect on the jump, which permits
shortening the basin and provides a safety factor against sweep out
caused b inadeq ate tailwater depth.
ca sed by inadequate tail ater depth
The basin shown on figure B2, which is designated a type III basin, can
m/s.
be adopted where incoming velocities do not exceed 15 m/s The type
III basin uses chute blocks, impact baffle blocks, and an end sill to
j p g                   p          g        y
shorten the jump length and to dissipate the high-velocity flow within the
shortened basin length. This basin relies on dissipation of energy by the
impact blocks and on the turbulence of the jump phenomena for its
effectiveness.
Type III Basin Dimensions
Minimum Tailwater Depths for Type III Basins
Height of Baffle Blocks and End Sill
and
Length of Jump
Because of the large impact forces to which the baffles are subjected by
the impingement of high incoming velocities and because of the
possibility of cavitation along the surfaces of the blocks and floor, the
use of this basin must be limited to heads where the velocity does not
exceed 15 m/s.
C i                t be taken f the dd d d l d the t t
Cognizance must b t k of th added lloads placed on th structure
floor by the dynamic force brought against the upstream face of the
blocks.
baffle blocks This dynamic force will approximate that of a jet impinging
upon a plane normal to the direction of flow. The force, in Newtons, may
p          y
be expressed by the formula:
,    w h e r e   E 1          V1
2

F = 2γ A E 1                      1   = d1 +
2g
h
where:
γ = unit weight of water, in N/m3
f the    t
A = area of th upstream f        f the block,
face of th bl k iin m2, andd
E1= the specific energy of the flow entering the basin, in m.
Negative               th b k face of the bl k will f th
N ti pressure on the back f             f th blocks ill further
increase the total load. However, because the baffle blocks
0.8d
are placed a distance equal to 0 8d2, beyond the start of
the jump, there will be some cushioning effect by the time
g jet                         ,
the incoming j reaches the blocks, and the force will be
less than that indicated by the above equation. If the full
force computed by using the above equation is used, the
negative pressure force may be neglected.
Basins for Froude Numbers Higher Than 4.5
and V>15 m/s
Where incoming velocities exceed 15 m/s, or where impact baffle blocks
are not used, the type II basin (fig. B3) may be adopted.
Because the di i ti iis accomplished primarily b hydraulic jjump
B         th dissipation              li h d i il by h d li
action, the basin length will be greater than that indicated for the type III
basin.
basin
However, the chute blocks and dentated end sill will still effectively
length.
reduce the length Because of the reduced margin of safety against
sweep out, the water depth in the basin should be about 5 percent
greater than the computed conjugate depth.
Type II Basin Dimensions
Minimum Tailwater Depths for Type II Basins
Length of Jump
Rectangular Versus Trapezoidal Stilling Basin
The use of a trapezoidal stilling basin instead of a rectangular basin may
often be proposed where economy favors sloped side lining over vertical
wall construction. Model tests have shown, however, that the hydraulic-
jump action in a trapezoidal basin is much less complete and less stable
than it is in the rectangular basin. In a trapezoidal basin, the water in the
triangular areas along the sides of the basin adjacent to the jump does
high-velocity jet.
not oppose the incoming high velocity jet
The jump, which tends to occur vertically, cannot spread sufficiently to
areas Consequently
occupy the side areas. Consequently, the jump will form only in the
central portion of the basin, while areas along the outside will be
occupied by upstream-moving flows that ravel off the jump or come from
the lower end of the basin.
The eddy or horizontal roller action resulting from this phenomenon
tends to interfere and interrupt the jump action to the extent that there is
p          p                  gy                     g
incomplete dissipation of the energy and severe scouring can occur
beyond the basin. For good hydraulic performance,
the sidewalls of a stilling basin should be vertical
or as close to vertical as practicable.

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 views: 549 posted: 7/20/2010 language: English pages: 124