Empirical stagedischarge equations of this type (Equation 166) have always been
derived for one particular structure, and are valid for that structure only. If such a
structure is installed in the field, care should be taken to copy the dimensions of the
tested original as accurately as possible.
1.12
Orifices
The flow of water through an orifice is illustrated in Figure 1.20. Water approaches
the orifice with a relatively low velocity, passes through a zone of accelerated flow,
and issues from the orifice as a contracted jet. If the orifice discharges free into the
air, there is modular flow and the orifice is said to have free discharge; if the orifice
discharges under water it is known as a submerged orifice. If the orifice is not too
close to the bottom, sides, or water surface of the approach channel, the water particles
approach the orifice along uniformly converging streamlines from all directions. Since
these particles cannot abruptly change their direction of flow upon leaving the orifice,
they cause the jet to contract. The section where contraction of the jet is maximal
is known as the vena contracta. The vena contracta of a circular orifice is about half
thedkmeter of the orifice itself.
I_c___
Ifefree
aischarging orifice shown in Figure 1.20 discharges under
the average head HI (if H,
>>
w) and that the pressure in the jet is atmospheric,
we may apply Bernoulli’s theorem


HI
=
(h,
+
vI2/2g)
=
v2/2g
(1
67)
Hence
v
=
,/2gHI
(1
68)
This relationship between v and
fi
was first established experimentally in
1643
by Torricelli.
Figure I
.20
The
free
discharging jet
42
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I
I
Figure
I
.21
Rectangular orifice
If we introduce a C,value to correct for the velocity head and a C,value to correct
for the assumptions made above, we may write
V
=
Cd
c,
J2ghI
(1
69)
According to Equation 12, the discharge through the orifice equals the product of
the velocity and the area at the vena contracta. This area is less than’the orifice area,
the ratio between the two being called the contraction coefficient, 6. Therefore
Q
=
CdCv6Am
70)
i
The product of cd, C, and 6 is called the effective discharge coefficient Ce. Equation
170 may therefore be written as
Q
=
CAm
(171)
~
~
Proximity of a boundinp surface of the approach channel on one side of the orifice
erevents the free approach of water and the contraction is partially suppressed on
e.
If the orifice edge is flush with the sides or bottom of the approach channel,
the contraction along this edge is fully suppressed. The contraction coefficient, how
ever, does not vary greatly with the length of orifice perimeter that has suppressed
contraction. If there is suppression of contraction on one or more edges of the orifice
and full contraction on at least one remaining edge, more water will approach the’
orifice with a flow parallel to the face of the orifice plate on the remaining edge(s)
and cause an increased contraction, which will compensate for the effect of partially
or fully suppressed contraction.
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 Spring '12
 yousry
 Fluid Dynamics, Orifice plate, Weir, weir crest, Control section

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