(1)Flow Over Notch

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INTRODUCTION In open channel hydraulics, weirs are commonly used to either regulate or to measure the volumetric flow rate, they are of particular use in large scale situations such as irrigation schemes, canals and rivers. For small scale applications, weirs are often referred to as notches and invariably are sharp edged and manufactured from thin plate material. The flow pattern over a notch or weir is complex and there is no analytical solution to the relationship between discharge and head so that once again a semi-empirical approach has to be used. Which weirs are structures consisting of an obstruction such as a dam or bulkhead placed across the open channel with a specially shaped opening or notch. The weir results an increase in the water level, or head, which is measured upstream of the structure. The flow rate over a weir is a function of the head on the weir.

Common weir constructions are the rectangular weir, the triangular or v-notch weir, and the broad-crested weir. Weirs are called sharp-crested if their crests are constructed of thin metal plates, and broad-crested if they are made of wide timber or concrete. Water level-discharge relationships can be applied and meet accuracy requirements for sharp-crested weirs if the installation is designed and installed consistent with established ASTM and ISO standards.

Common Standards and Specifications for Weir Flow Measurements

Rectangular weirs and triangular or v-notch weirs are often used in water supply, wastewater and sewage systems. They consist of a sharp edged plate with a rectangular, triangular or vnotch profile for the water flow. Broad-crested weirs can be observed in dam spillways where the broad edge is beneath the water surface across the entire stream. Flow measurement installations with broad-crested weirs will meet accuracy requirements only if they are calibrated. Other available weirs are the trapezoidal (Cipolletti) weir, Sutro (proportional) weir and compound weirs (combination of the previously mentioned weir shapes).

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THEORY Gauging the flow in natural streams can never be precise because the channel is usually irregular and so is the relationship between stage and flow rate. Natural stream channels are also subject to change by erosion or deposition. More reliable estimates can be obtained when the flow is passed through a section where these problems have been reduced. This could be simply smoothing the bottom and sides of the channel, or perhaps lining it with masonry or concrete, or installing a purpose-built structure. There is a wide variety of such devices, mostly suitable for a particular application. A selection of those simple to install and operate are described here with reference to appropriate manuals for more expensive or complicated structures. In general, structures across the stream which change the upstream level are called weirs, and channel-type structures are called flumes, but this distinction is not always followed. A more important distinction is between standard and non-standard devices. A standard weir or flume is one where if it is built and installed to a standard published specification, the flow can be directly obtained from the depth of flow by the use of charts or discharge tables, that is the flume is pre-calibrated. A non-standard weir or flume is one which needs to be individually calibrated after installation by using the velocity/area method as when rating a stream. There is such a wide range of standard devices available, that non-standard structures are best avoided except for one-off estimates of flood flows using the velocity/area method at a bridge, or ford, or culvert. Most weirs are designed for free discharge over the critical section so that the rate of flow is proportional to the depth of flow over the weir, but some weirs can operate in the condition called submerged or drowned, where the level downstream interferes with the flow over the weir. Some types of weir can be corrected for partial submergence but this is an undesirable complication requiring additional measurements and more calculations so should be avoided where possible (Figure 26). Another variation best avoided is the suppressed weir, which is a weir set in channel of the same width as the critical section (Figure 27).

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Sharp-crested weirs The two most common types are the V-notch and the rectangular notch as shown in Figure 28. There must be a stilling pool or approach channel on the upstream side to smooth out any turbulence and ensure that the water approaches the notch slowly and smoothly. For accurate measurements the specification is that the width of the approach channel should be 8 times the width of the notch, and it must extend upstream for 15 times the depth of flow over the notch. The notch must have a sharp edge at the upstream side so that the flow is clear of the downside edge as shown in Figure 29. This is called the end contractions, which are required for the standard calibration to be applicable. To read the depth of flow through the notch a measuring scale is set in the stilling pool in a position where it can be easily read. The zero of the scale is set level with the lowest point of the notch. The scale should be set well back from the notch so that it is not affected by the drawdown curve as the water approaches the notch.

V-notch weirs are portable and simple to install in either temporary or permanent positions. The V shape means that they are more sensitive at low flows, but the width increases to accommodate larger flows. The angle of the notch is most commonly 90, but calibration charts are available for other angles, 60, 30 and 15, if more sensitivity is required. Discharge values through small 90 V-notch weirs are given in Table 4. For larger flows the rectangular weir is more suitable because the width can be chosen so that it can pass the expected flow at a suitable depth. Table 5 gives the discharge per metre of crest length and so can be applied to rectangular weirs of any size.

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OBJECTIVE i. ii. To observed the characteristics of open-channel flow over, firstly, a rectangular notch and then a triangular (vee) notch. To determine values of the discharge coefficient for both notches

APPARATUS In order to complete the exercise we need a number of pieces of equipment: i. The FI-10 Hydraulics Bench which allows us to measure flow by timed volume collection.

ii. iii. iv.

The F1-13 Stilling baffle The F1-13 Rectangular and Vee Notches Vernier Height Gauge (supplied with F1-13)

v.

Stop Watch

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PROCEDURE A. Equipment set up i. ii. The hydraulic bench is positioned so that its surface is horizontal (necessary because flow over notch is driven by gravity). The rectangular notch was mounted into the flow channel and the stilling baffle was positioned as shown in the diagram.

iii.

iv. v.

vi. vii.

In order to measure the datum height (with the height gauge) of the base of the notch, the instrument carrier was positioned in the opposite way round from that shown in the diagram. Then carefully the gauge was lowered until the point was just above the notch base and the coarse adjustment screw was locked. Then, by using the fine adjustment, the gauge was adjusted until the point just touched the notch bottom and a reading would be taken; here we must be careful not to damage the notch. The instrument carrier was mounted as shown in the diagram and it would be approximately located half way between the stilling baffle and the notch plate. The bench control valve was opened and water was admitted to the channel; the valve was adjusted to give approximately 10mm depth above the notch base. To help achieve this, and this founded it useful to pre-set the height gauge position to give a rough guide.

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B. Taking a set of results i. ii. The general features of the flow were observed and recorded. To take an accurate height reading, the fine adjustment was used to lower the gauge until the point just touched its reflection in the surface; (to achieve this, I need to have my eye level just above the surface). The flow rate was ensured large enough to prevent the outflow from the notch clinging to the notch plate; it was projected clear of the plate. The volume flow rate was determined by measuring the time required to collect a known volume in the volumetric tank. Using the ball valve to close the tank out flow did this and then the volume collected would be determined.

iii. iv.

v.

Then, measure the filling of water in volumetric tank for 10 liters

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vi.

Using the stop watch to measure the time, t, when the water achieves 10 liters.

vii. viii.

ix.

x.

xi.

After determined the volume collected, the valve was opened again at the end of the measurement. This procedure was repeated by having opened the bench valve further, to produce an increase in depth of approximately 10 mm; the level was checked in stable condition before taking readings. Readings with increasing flow rate were continued had been taken until the level reached the top of the notch; take care not to allow spillage to occur over the plate top adjacent to the notch. Before starting this test, there was sufficient water in the bench main tank checked to allow the pump to operate without drawing in air at the maximum flow rate (i.e. maximum height above notch). The rectangular notch plate was replaced with the Vee notch plate and procedure above was repeated.

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HM 150.03 FLOW OVER A NOTCH ACCESSORIES A. Preparation i. ii. iii. iv. v. vi. vii. Two weirs are provided, namely: A V-profile weir and a rectangular-profile weir These are bolted to the outlet end of the channel. The seal is to be placed between channel and weir. When moistened, the seal can easily be positioned on the channel. A weir is then to be fitted using 4 M6 x 20 cheese-head bolts. The height sensor is arranged over the channel such that it faces the weir. Filling the HM150 with water and establishing the power supply completes the preparatory work.

Seal

Weir

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B. Experiments Rectangular 1. -Profile Weir i. ii. iii. The volumetric flow rate can be derived from the weir width b and the weir head z. The width b is constant. b = 6.0 cm The weir head z is measured indirectly.

z b

2. Determination of weir head z i. ii. The height h of the water level is measured. Given the constants: h0 = 4.7 cm h1 = 5.0 cm The weir head z is calculated as follows: Z = h0 + h1 - h Make slight contact with water level

iii.

Sensor

Weir

h h1 z

h0

b 9

3. Determination of volumetric flow rate i. The theoretical volumetric flow rate V th is calculated as follows : V th = 2/3 . . b . z . 2gz Where = 0.63 for sharp-crested weir discharge ii. iii. The actual volumetric flow rate V M can be determined with the aid of the volumetric tank of the HM 150 using a stopwatch. It is advisable to measure the filling time t for 10 litres. A good volume display is obtained in the scale range between 20 and 30 litres.

4. Measured values i. The following values were obtained for comparison between calculated and measured volumetric flow rates: z ( cm ) 4.9 6.4 6.7 7.9 8.5 Time, t for 10 l ( sec ) 107 18 15 8 7 V th ( l/s) 0.192 0.181 0.194 0.248 0.277 VM ( l/s ) 0.094 0.555 0.666 1.25 1.429 Deviation (%) (9.4) 37.4 47.2 100.2 115.2

h ( cm ) 4.8 3.3 3.0 1.8 1.2

CALCULATION z = h0 + h1 h z = 4.7 + 5.0 4.8 z = 4.9 cm V th = 2/3. . b. z . 2gz = 2/3 (0.63)(6)(4.9) 2(9.81)(4.9) = 192.18 m3/s = 0.192 l/s (m3 to l = 1000) VM = 10/107 = 0.0935 l/s Deviation = 0.094 0.192 (100) = (-9.4) ii. Determination of the volumetric flow rate with a rectangular-profile weir ensures a high level of coincidence with the actual volumetric flow rate.

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V Shape 1. V-profile weir i. ii. iii. The volumetric flow rate can be derived from the weir width b and the weir head z. The width b is a function of the weir head z. b = 2z The weir head z is measured indirectly.o

90

z

b = 2z 2. i. ii. Determination of weir head z The height of the water level is measured. Given the constants : h0 = 4.7 cm h1 = 6.0 cm the weir head z is calculated as follows : z = h0 + h1 h Sensor Make slight contact with water level

iii.

Weir

h

h0

h1 z

b

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3. Determination of volumetric flow rate i. The theoretical volumetric flow rate V th is calculated as follows : V th = 8/15 . . z2 . tan /2 . 2gz Where = 0.63 for sharp-crested weir discharge and tan 45o = 1 The actual volumetric flow rate V M can be determined with the aid of the volumetric tank of the HM150 using a stopwatch. It is advisable to measure the filling time t for 10 liters. A good volume display is obtained in the scale range between 20 and 30 liters.

ii. iii.

4. Measured values i. The following values were obtained for comparison between calculated and measured volumetric flow rates : z ( cm ) 4.9 6.7 7.7 8.2 8.7 Time, t for 10 l ( sec ) 112 35 20 14 9 V th ( l/s) 0.0791 0.0864 0.1224 0.1432 0.1661 VM ( l/s ) 0.0893 0.2857 0.5000 0.7142 1.1111 Deviation (%) 1.02 1.99 3.77 5.71 9.45

h ( cm ) 5.8 4.0 3.1 2.9 1.6

z = h0 + h1 h z = 6 + 4.7 5.8 = 4.9 cm V th = 8/15 . . z2 . tan /2 . 2gz = 8/15 (0.63)(4.9)2 tan 45 2(9.81)(4.9) = 8.067(9.805) = 0.0791 l/s VM = 10/112 = 0.0893 l/s Deviation = 0.0893 - 0.0791 (100) = 1.02 %

ii.

Determination of the volumetric flow rate with a V-profile weir ensures a high level of coincidence with the actual volumetric flow rate.

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DISCUSSIONS

After we have done this experiment, we are able to determine the flow rate and the coefficient of discharge for flow over a triangular and rectangular notch using the Basic Weir apparatus. We can make a few discussion based on this experiment.

Firstly, from the result we get, we observed that the trend of the coefficient discharge for rectangular are increasing. We get the average of coefficient discharge is 0.03 m3/s. So the results we get are suitable because the most ideal volumetric flow rate for a rectangular notch is 0.021m3/s and above. For rectangular notch,Cd values at lower flow rates were in quite wide variations. This was because the difference of values of height was in wide range.

Secondly, For V-notch,Cd values at low flow rate were not in wide variations. This is because the low height increments.

For experimental values for Cd for water flowing over V-notch with central angles varying from 100 to 900. The rise in Cd at heads less than 0.5 ft is due to incomplete contraction. At lower heads the frictional effects reduce the coefficient. At a very low heads, when the nappe clings to the weir plate, the phenomenon can longer be classed as weir flow.

The values of Cd for vee notch at low flow rate were not in wide variations because the low height increments. But the values of Cd for rectangular notch at lower flow rates were in quite wide variations because the difference of values of height was in wide range. From the experimental result, the values of coefficient discharge calculated increased when the head increased for rectangular notch. From the theory, volume flow rate that is suitable for this notch is about from 0.021m3/s and above, but in the experiment we cant constant the value of volume flow rate. We only know the volume flow rate by measuring the data that we have. So the volume flow rate that we use less than the volume flow rate of theory because of that the values of Cd also less from the theory.

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CONCLUSION

What we can conclude after we have done this experiment, our objectives are to observed the characteristic of open-channel flow over, firstly, a rectangular notch and then a triangular (vee) notch and to determined the discharge coefficient for both notches.

We have also concluded that the coefficient of discharge of both; triangular and rectangular notch depends on the volumetric flow rate of the water and the height of the water level from the base of the notch. The coefficient of discharge corresponds differently to the height of the water level (H) to the type of notch used. For rectangular notch; H3/2 and triangular notch; H5/2 in there has given equation. For triangular notch, the coefficient of discharge also depends on the angle of the vee shape.

Rectangular weir has wide range variations of Cd . This is because this notch has width with 0.03 m.V-notch has small range of variations for the value of Cd. This is because this notch has an angle at its bottom where about 90o. This angle might affect the values of flow rate and Cd.

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