The first section in this chapter outlines the basic data required to determine the stage^discharge characteristics of gates. The discharge coefficients for radial gates used in the equations are not directly comparable because the definition of energy head varies. In some cases it may be the head upstream of the gate, in others the head to the middle of the gate opening, and in drowned discharge both the true energy head, the difference between upstream and downstream water levels, and the downstream head enter the equation. Little information has been published on the stage^discharge relationship of top-hinged flap gates. Available data have been included in this chapter.
The next section deals with hydraulic downpull forces on vertical-lift gates. This hydrodynamic effect is usually ignored when designing gates in open channels, because under these conditions it is low and is absorbed by the margin of hoisting force provided in gate installations. It becomes important for high head gates. Because of the number of variables involved in determining hydraulic downpull, calculations must be considered approximate. All research in this field has been carried out on models representing vertical-lift gates, although hydraulic downpull forces also act on radial gates.
Later sections draw attention to instability in a reach of a watercourse which can be caused by the operation of a gate when there is limited ponded up water. Problems can also arise when there is a change from 3D to 2D flow. This is the condition of flood flow from a reservoir into a sluiceway. This type of problem can be resolved by a physical model study. The occurrence of reflux at a multigate installation and observed flow oscillations are described, as well as the hysteresis effect of gate discharge during raising and lowering.
The final section begins with a discussion of vorticity at intakes. The introduction of air into a conduit can cause severe pressure fluctuations at control gates. Awareness that free vortices can occur should prompt reconsideration of the design of an intake.
Cavitation and erosion are factors whenever flow velocities of the order of 13^15 m/s are reached or exceeded. Cavitation can affect gate slots and the invert of tunnels. Information relevant to gates is included in this section and is complementary to cavitation in valves which was discussed in Chapter 3.
9
pivot above the sill. This is reproduced by Lewin. Chow gives discharge coefficients for radial gates where the radius of the gate is the denominator in the non-dimensional functions, whereas Metzler2uses the height of the pivot
above the gate sill.
For a flat vertical sluice gate Franke and Valentin5developed a discharge
formula for free flow by measuring the pressure at the floor directly below the gate lip, and relating this value to the geometry of the jet. The pressure can be determined analytically and Franke and Valentin developed an expression for the free discharge case. Young and Fellerman6extended this for the general case
of submerged flow. In many cases a direct solution can be obtained from the expression for the general case; in others, a solution has to be obtained by trial and error.
Should the floor level drop appreciably downstream of the sluice gate, the equation derived by Young and Fellerman cannot be applied and direct pressure measurements are then required. Another limitation arises when the jet efflux at the gate opening attains a subcritical value.
The general equation for discharge through an underflow gate can be expressed as:
Q Cd Go Wp 2gH 9:1
where Q discharge
Cd coefficient of discharge
Go gate opening (denoted b in Fig. 9.5)
W gate width
g gravitational constant H upstream water head
The variables affecting the discharge characteristics of a radial gate are shown in Fig. 9.1.
An example of the coefficient of discharge map for free and submerged flow under a radial gate based on Metzler2is shown in Fig. 9.2.
Buyalski7used similar maps to derive discharge algorithms which can be pro-
discharge based on measurement of water levels and gate attitude, converted to gate opening. The algorithms derived by Buyalski were based on experiments carried out with gates having a lip seal of hard rubber rectangular section. The seals were mounted upstream of the gate skin plate, whereas the preferred practice is to locate the seal downstream of the skin plate. An upstream seal causes flow disturbance and is not in accordance with the rule suggested by Lewin8and Vrijer9
stating that flow separation should be arranged at the extreme downstream edge of a gate to achieve flow conditions which are as steady as possible. Buyalski7claims
Figure 9.1. Variables affecting the discharge characteristics under a radial gate
Figure 9.2. Coefficient of discharge map for free and submerged flow under a radial gate for r/a = 1.5
Hydraulic considerations pertaining to gates
The chart produced by the US Corps of Engineers for the coefficient of submerged discharge is independent of the a/R ratio and is plotted for the ratio of raised sill downstream submergence over gate opening. It appears that the height of the sill above the approach bed is not an important factor in submerged flow controlled by gates. One of the graphs (sheet 320^8) is reproduced in Fig. 9.3.
Figure 9.3. US Corps of Engineers' chart for the coefficient of discharge under submerged flow conditions
For radial gates on spillway crests, the discharge through a partially open gate can be computed using the same basic orifice equation:
Q CAp 2gH 9:2
where C coefficient of discharge A area of opening g gravitational constant H head to the centre of opening
The coefficient is primarily dependent upon the characteristics of flow lines approaching and leaving the orifice. In turn, these flowlines depend on the shape of the crest, the radius of the gate and the location of the gate pivot.
The Hydraulic design criteria14 plot average discharge coefficients from
model and prototype data for several crest shapes and gate designs for non- submerged flow. On the chart, the discharge coefficient is plotted as a function of the angle formed by the tangent of the gate lip and the tangent to the crest curve at the nearest point of the crest curve. This angle is a function of the major geometric factors affecting the flow lines of the discharge.
Figure 9.4 gives suggested design values for discharge coefficients of 0.67^0.73 for from 50 to 110.
The sill of radial gates on spillway crests is usually located downstream of the crest axis. Provision is made for placing stoplogs upstream of the gates. Positioning the gate sill and the sill for the stoplogs close to the crest axis reduces the overall height of the gates and the stoplogs in relation to the reservoir retention level. A practice favoured by gate designers is thus to make the gap between stoplogs and gate just sufficient for work to be carried out within the space with the stoplogs located upstream of the crest axis and the gates downstream. Limited test results suggest that within the normal practical dimensions of location of the gate sill there is no effect on the discharge coefficient, but the crest pressure will be affected.15Slight negative pressures occur on the spillway crest for a G
o/Hdratio
of 0.4 or with the gate seat located on the crest axis. Crest pressures derived from the charts in reference 15 are positive for all other Go/Hdratios and gate seats
downstream of the crest axis.
The discharge coefficients in references 10, 13 and 14 are based principally on tests with several bays in operation, and it is suggested that discharge coefficients for a single bay would be lower because of side contraction. Limited experimental data16indicate that provided the gate piers project at least half a
bay width upstream of the gate sill and the approach channel is sensibly straight, each sluiceway operates as if it was independent of the adjoining bays. The requirement for projection of the piers is usually met because of the practice of locating a bridge upstream of the gates for access purposes and for mounting a gantry crane for handling of stoplogs.
To compute the discharge through each bay, the pier flow contraction coefficient17must also be considered.
The equation of discharge through a vertical-lift gate is the same as equation 9.1 for a radial gate, and using the same notation as Fig. 9.1 the variables affecting the discharge characteristics are shown in Fig. 9.5 based on Rouse.1
Hydraulic considerations pertaining to gates