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The Broad Crested Weir
For additional information on broad crested weirs, including the Crump weir, take a look here.
Before we look at the laboratory procedure, it would be prudent to look at the principles applicable to broad crested weirs and the following is an extract from Understanding Hydraulics by Les Hamill.
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 depth meter, the broad crested weir has the advantage that it operates effectively with higher downstream water levels than a sharp crested weir.
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 assuming that the breadth of the weir (b) spans the full width (B) of the channel and that the cross-sectional area of flow is rectangular, then:
Ac = b x Dc and Vc = (g x Dc)1/2 (See your notes regarding Froude No.)
Thus from the continuity equation,
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 just upstream of the weir to measure the head of water, H1, above the crest than to attempt to measure the critical depth on the crest itself. In order to eliminate Dc from the equation, we can use the fact that in a rectangular channel . 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:
If you substitute this expression into Eqn 1, it gives:
The term in the above equation is the velocity head of the approaching flow. As with the rectangular sharp crested weir, the problem arises that the velocity of approach, V1 cannot be calculated 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 energy losses. C varies between about 1.4 and 2.1 according to the shape of the weir and the discharge, but frequently has a value of about 1.6. Thus:
The broad crested weir will cease to operate according to the above equations if a backwater from further downstream causes the 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 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. Once the weir has submerged, the downstream water level must also be measured and the discharge calculated using a combination of weir and orifice equations. However, this requires the evaluation of two coefficients of discharge, which means that the weir must be calibrated by river gauging during high flows. This can 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 calculate the head that will occur over a weir at a particular discharge without considering at all the height of weir required to obtain critical depth on the crest. For example, suppose the depth of flow 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?
The answer is obtained by applying the energy equation to two sections (See diagram below). One some distance upstream 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 used as the datum level. Assuming that the channel is horizontal over this relatively short distance, that both cross-sectional areas of flow are rectangular, and that there is no loss of energy, then:
This is usually sufficient to enable equation 4 to be solved for p when Q and D1 are known. Alternatively, the depth, D1, upstream of the weir can be calculated if Q and p are known. When calculating the 'ideal' height of weir, it must be appreciated that it is only ideal for the 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.
Water flows along a rectangular channel at a depth 1.3 m when the 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
= ((8.74)2/(9.81 x 5.52))1/3
= 0.636 m
= (9.81 x 0.636)1/2
= 2.498 m/s
Substitute these values into Eqn 4 and then solve for 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 level.
Characteristics of flow over a Broad Crested Weir.
To determine the relationship between upstream head and flow-rate for water flowing over a Broad Crested weir (long base weir), to calculate the discharge coefficient and to observe the flow patterns obtained.
Multi-Purpose Teaching Flume (Armfield C4)
Broad Crested Weir
Hook and point gauge, 300mm scale,- 2 required
Stopwatch if measuring flow rate using the volumetric tank
SUMMARY OF THEORY/BACKGROUND
Provided that the weir is not submerged (downstream water level is low) the actual flow over a Broad Crested weir is given by:
Qt = 1.705 b H3/2 where H = hu + V2/2g
The velocity V is the average velocity upstream of the weir, found from V = Qa/A
A = yo x b
Qt = Theoretical flow rate (m3/s)
b = Breadth of weir (m)
hu = Head above the crest of the weir (m)
Actual flow rate, Qa = Volume flow-rate (m3/s)
= Volume/time (using volumetric tank)
The coefficient of discharge (Cd) for the weir can be determined by dividing the actual flow rate, Qa by the theoretical flow rate, Qt.
Cd is (Dimensionless)
The coefficient for the weir is thus 1.705 x Cd which frequently has a value of 1.6.
The weir can be used for flow measurement using a single measurement of level upstream provided that a standing wave exists downstream of the weir. The condition at which the standing wave ceases is called the modular limit and is not investigated in this experiment.
Ensure the flume is level, with no stop logs installed at the discharge end of the channel. Measure and record the actual breadth b(m) of the broad crested weir.
Install the weir in the flume with the rounded corner upstream. Ensure that the weir is secured using a mounting hook through the bed of the flume. For accurate results the gaps between the weir and the channel should be sealed on the upstream side using Plasticine. Position two hook and point level gauges on the channel sides, adjacent to the weir, each with the point fitted.
The datum for all measurements will be the bed of the flume. Carefully adjust the level gauges to coincide with the bed of the flume and record the datum readings. Using one level gauge carefully measure the height of the weir above the bed P(m) taking care not to damage the surface of the weir. Position this level gauge over the weir at the discharge end. Position the second level gauge some way upstream from the weir. Usually at least 4x maximum height of water above the weir.
Adjust the flow of water into the flume to obtain heads hu increasing in about 0.010m steps. For each step measure the flow-rate Q, the upstream depth of flow yo and the depth of flow over the weir yc (where the flow becomes parallel to the weir). The flow-rate Q can be determined using the direct reading flow-meter or the volumetric tank with a stopwatch. For accurate results the level gauge must be far enough upstream to be clear of the drawdown over the weir.
At each setting also observe and sketch the flow patterns over the weir.
Gradually increase the depth of the water downstream of the weir by adding stop logs at the discharge end of the channel. For each step measure the flow-rate Q, the upstream depth of flow yo and the depth of flow over the weir yc. Observe and sketch the flow patterns over the weir.
RESULTS AND CALCULATIONS
Tabulate your readings and calculations as follows:
Breadth of Weir b = ……………………(m)
Height of weir P =…………………….(m)
Plot graphs of Q against H, log Q against log H and Cd against H.
From the straight-line graph of log Q against log H, find the intercept log k on
the log Q axis and the gradient m.
The relationship between Q and H is then Q = k Hm.
Where k = 1.705 Cd Cv b
Does the magnitude of the flow-rate affect the discharge coefficient Cd?
Does Cd increase or decrease with increasing flow-rate?
What is the pattern of the water as it passes over the weir?
Would you expect the length of the weir crest to affect the discharge coefficient Cd?
What is the effect of drowning the weir (increasing the downstream depth)?
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Last Edited : 04 August 2011 13:33:33