Experiment No.1 Flow through a sluice gate
The discharge coefficient of sluice gates in free and submerged conditions plays an
important role in determining the flow rate past such structures. The effects of relative
gate opening and submergence ratio have been widely considered by several
investigators, mainly based on experimental work. Most of this work, however, lacks
an analytical approach to include the variation of discharge coefficient as influenced
by gate opening and submergence ratio. This paper, using energy and momentum
conservation theory, presents an analytical method to determine the contraction ratio
and discharge coefficient of sluice gates under free and submerged flow conditions.
Based on suggested relationships for the contraction ratio, variations in energy loss
under free and submerged flow and the submergence limit are determined and some
graphical demonstrations are adapted. The results are compared with experimental
data reported by several investigators and show good agreement.
1.Objective
1.1 To study the behavior of flow though a sluice gate in various conditions
1.2 To study the Coefficient of discharge (Cd )
1.3 To construct the Calibration curves of sluice gate.
2. Experimental apparatus
The experimental apparatus for this experiment consists of rectangular flume with the
sluice gate inside, depth gauge, and stop watch.
Figure1 Rectangular flume with sluice gate
Figure2 Depth gauge
3. Theory
Sluice gate are used for flow control and discharge measurement.
Pressure at water surface is atmospheric or zero gage pressure Water surface =
piezometric head level. i.e. level registered by manometer with a piezometric tap
Open channel flow, in general, has two possible flow depths for each energy level:
Subcritical and supercritical Sluice gate changes flow from subcritical to supercritical.
Figure3 Flow under sluice gate (Roberson, John & Clayton Crowe,1990)
Like Flow Through Orifice minimum cross-sectional area (vena contracta) is slightly
downstream from the gate
Ideal Flow Theory (No Energy Losses)
Q V
(1)
A1
Experimental Studies discharge coefficient Flow is never really “ ideal” . Coefficient
is related to relative size of gate opening Brater&King summarize some of these
general from
Q = 퐶 × 퐴× (2푔 × 푑퐻)
(2)
Specific energy: energy in an open channel measured relative to the channel bottom
E=푦
(3)
For two values of y with the same value of E
E=푦
1
=푦
1
(4)
Combine this with the continuity equation,
푉
(5)
1 × 푏× 푦
1 = 푉 × 푏× 푦
Now we can eliminate one of the velocities and compute the other velocity without
using Q. This gives some experimental data for a two-dimensional plot of specific
energy to compare with the theoretical equation. To use the specific energy plot, we
measure y2 at the vena contracta. As use the specific energy function
E=푦
is actually cubic in y
(6)
i.e.
푦3
퐸푦 =
(7)
The subcritical and supercritical flows are two of the three areas for the solution. The
third area of the solution has a negative value of y, which is meaningless for open
channel flow. (Henderson 1966)
Figure 4 Graph is shown relationship between specific energy and flow depth
(Roberson, John & Clayton Crowe,1990)
Sluice gate experiment study the application of one-dimensional flow analysis
involving continuity, energy and momentum equation to a sluice gate in a rectangular
channel Flow Under a Sluice Gate. As stated, there are two flow depths, subcritical
and supercritical, for each energy level. The easiest approach is to compare the
measured values of y2 with values computed for observed y1
Force By Momentum Equation
퐹
푥 = 훾× 푉
푥× 푄
(8)
Becomes
퐹= 훾(푄× (푉
1
푉)
(
−
)
(9)
Where
γ
= density of water
g (in the drawing) = gravity constant
Q
= flow rate
v1,y1
= upstream velocity and depth
v2,y2
= downstream velocity and depth
b
= width of rectangular channel
Figure5 Force by Momentum Equation (Roberson, John & Clayton Crowe,1990)
3.1 Free Flow conditions
This condition is the flow which is freely jet flow through the sluice gate without
compression and the surface contact with atmosphere so, the water surface has the
pressure equal to atmospheric pressure. This flow can occurs Vena contracta; is the
point in a fluid stream where the diameter of the stream is the least, and fluid velocity
is at its maximum, such as in the case of a stream issuing out of a nozzle.
Figure6 Free flow conditions (Thompson 1980; Thompson and Warsi 1982;
Masliyah et al. 1985).
Vena contracta
Figure7 Free flow conditions (Vena contracta)
3.2 Submerged Flow Conditions
This condition, the water flow through a gate and it’ s compressed by water at
downstream and submerged under the surface. The submergence is called Vortex or
Eddy current; is the swirling of a fluid and the reverse current created when the fluid
flows past an obstacle. The moving fluid creates a space devoid of downstreamflowing fluid on the downstream side of the object. Fluid behind the obstacle flows
into the void creating a swirl of fluid on each edge of the obstacle, followed by a short
reverse flow of fluid behind the obstacle flowing upstream, toward the back of the
obstacle. This phenomenon is most visible behind large emergent rocks in swiftflowing rivers. This flow has energy losses.
Figure8 Submerged flow condition (Thompson 1980; Thompson and Warsi 1982;
Masliyah et al. 1985).
Eddy current
Figure9 Submerged flow condition (Eddy current)
3.3 Basic equation
Bernoulli’ s Equation is energy equation for an ideal fluid (friction and energy losses
assumed negligible.) which is derived to the question for using to calculation in this
laboratory as follow:
+
푃
=
+
푃
velocity→ discharge, Q, Q=AV
(10)
(
푍1
푦1
)
(
(
=푍
)
)
(11)
(
=푦
)
(12)
unit discharge, 푞=
퐵
From (3.1);
푦
푦
1
(13)
)= 푦
푦1
(14)
=
1
( )(
( )(
)
=푦
( )( (
(
푞=
푞=
)(
(
푦
1
)
)= 푦
)×
)(
)
×
(
(15)
푦1
(16)
(17)
(18)
)
×
Q=
(19)
√
Q=
(20)
Q = 퐶푊√ 2푔푦1
(21)
Cd = Coefficient of discharge
q (act u al )
q (t h eo r y )
퐶=
= Cd< 1
(22)
√
Bernoulli’ s Equation
푦1
=
푦
(23)
푦1
=푦
(24)
Momentum Equation
F = ma
(25)
=
(26)
Free Flow
Q = 퐶" 푊√ 2푔푦1
(27)
Submerged Flow
q = 퐶푊√ 2푔푦1
(28)
4 Experiment Procedure
4.1 Open the sluice gate for 15 mm.
4.2 Turn on the water pump and then open the valve.
4.3 Wait until the water level does not change, measure the water depth y1 and y2 for a
free flow.
Figure10 Measure the water depth y1 and y2
4.4 Measure the discharge by using the notched-weir downstream of the basin. Use
the equationQ = [1.166Hw]2.5 to calculate the discharge.
Figure11 Discharge by using the notched-weir downstream of the basin
4.5 Adjust the weir on the downstream of the flume until the Eddy current is occurred
downstream of the gate. Wait until the water level does not change, measure the water
depth y1 and y3 for a submerge flow.
Figure12 Eddy current
4.6 Adjust the weir to get the different 3 more point of y1 and y3.
4.7 Increase the water discharge by adjusting the valve. Repeat the step number 4.34.6 again. Use totally 4 discharges.
4.8 Open the sluice gate about 25 mm.
4.9 Repeat the step number 3-7 again.
Figure13 Weir gets the different 3 more point of y1 and y3