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ABSTRACT
This experiment was conducted to observe the characteristics over a rectangular notch and a triangular notch. The discharge coefficient, of fluid flow was also determined by calculation. The experiment was done by using a rectangular notch and triangular notch. At the beginning of the experiment, the initial reading water level in the tank was noted and recorded. Then, the depth of water with different height was tested by recording the time taken to collect 3L of water which later will be used to calculate the flow rate of the flow. The data obtained were further tabulated by calculating the discharge coefficient, using the equation provided. Then, graphs were plotted to analyze the characteristics of the flow. Based on the graph plotted for rectangular notch, it was observed that there is a decrease in the discharge coefficient, before it finally reaches a constant value. Unlike triangular notch, the discharge decrease smoothly but the values are higher than the rectangular notch. Therefore, from this experiment, it can be concluded that triangular notch has higher discharge than rectangular notch.
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INTRODUCTION
Weir is a barrier which is usually used to alter the characteristics of the flow. It is usually located on top of the sidewall of the tank. Notch is almost similar to a weir but different in the structure where the former is built in small structure and sharp edges. A weir is basically a combination of an overflow structure with a broad crest which is built across an open channel. 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.
There are several different types of weirs but the most common weir constructions are the rectangular weir, the triangular or v-notch weir, and the broad-crested weir. Sharp-crested weirs are weirs which crests’ are constructed of thin metal plates, and broad-crested weirs are which crests’ are made of wide timber or concrete.
Rectangular weir and triangular weir are often used in water supply, wastewater and sewage systems. Weir structure is consists of a ponding basin, a stilling well, a notch, a flume and concrete wings which slightly approaches outwards uphill to catch and direct the stream and any nearby ground water into the flume and basin. The weir is anchored to the bedrock to ensure the water can flow under it. The amount of water flowing through one or two components; a notch at the downstream end of the basin for most flows or the flume for very high flows.
OBJECTIVES
To observe the flow characteristics over a rectangular weir and triangular weir.
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THEORY
In this experiment, only 2 weirs will be used which are rectangular weirs and triangular weirs. Therefore only these two weirs are focused on. Different weirs have different ways of calculating the discharge coefficient, of the flow of fluid. This is because each weir has different characteristics.
Rectangular weir or rectangular notch is used to meter flow in an open channel. The head over the rectangular weir is measured and correlated with the water flow rate through the open channel (and over the weir). A rectangular weir equation gives water flow rate as a function of head over the rectangular weir.
FIGURE 1
Referring to the figure 1, the flow in the element of height, H at a depth, h below the surface is taken in measured. It was assumed that the flow of fluid is everywhere normal to the plane of the weir and that the free surface remains horizontal to the plane of the weir. In reality, the flow through the notch will not be parallel and thus it will not be normal to the plane of the weirs. As a result, the viscosity and the surface tension will be greatly affected. There will be a considerable change in the shape of the nappe as it passes through the notch with curvature of the stream lines in both vertical and horizontal planes. In particular, the width of the nappe is reduced by the contractions at each end.
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The flow rate measurement in a rectangular weir is based on the Bernoulli Equation principles and can be expressed as:
√( ) Where; ⁄ ( )
It was said that the discharge from the rectangular notch will be less approximately 60% of the theoretical analysis due to the curvature effects. In order to obtain the discharge coefficient, the equation above is rearranged. Therefore, the equation for discharge coefficient is:
√( )
A triangular weir/notch is also known as the V-notch. The name for a v notch weir is very descriptive; refer to figure 2. A v notch weir is simply a 'v notch' in a plate that is placed so that it obstructs an open channel flow, causing the water to flow over the v notch. It is used to meter flow of water in the channel, by measuring the head of water over the v notch crest. The v notch weir is especially good for measuring a low flow rate, because the flow area decreases rapidly as the head over the v notch gets small. The head over the V-notch is measured and correlated with flow rate through the open channel. A v notch weir equation will give the open channel flow rate. The V-notch design causes small changes in discharge to have a large change in depth allowing more accurate head measurement than with a rectangular weir.
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FIGURE 2
The flow rate for V-notch can be calculated based on the equation below:
( ) √( ) Where; ⁄ Thus, the discharge coefficient can be calculated;
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APPARATUS
SOLTEQ® Flow Over Weirs (Model: FM26)
Stopwatch
PROCEDURE
Start-up Procedure
1. The hydraulic bench was positioned so that its surface is horizontal (necessary because flow over notch is driven by gravity).
2. The rectangular notch was mounted into the flow channel and the stilling baffle was positioned.
3. 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.
4. Then, carefully the gauge was lowered until the point was just above the notch base and the coarse adjustment screw was locked.
5. Then, by using the fine adjustment, the gauge was adjusted until the point just touched the notch bottom and a reading would be taken.
6. The instrument carrier was mounted and it was approximately located half way between the stilling baffle and the notch plate.
7. 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.
7 Experimental Procedure
1. The general features of the flow were observed and recorded.
2. 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.
3. 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.
4. The volume flow rate was determined by measuring the time required to collect 3L volume in the volumetric tank. Using the ball valve to close the tank outflow did this and then the volume collected would be determined from the sight-glass
5. After determined the volume collected, the valve was opened again at the end of the measurement.
6. This procedure was repeated by having opened the bench valve further to produce increase in depth of approximately 10 mm at the level was checked in stable condition before taking readings.
7. Readings with increasing flow rate were continued had been taken until the level reached the top of the notch.
8. 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.
8. The rectangular notch plate was replaced with the Vee notch plate and procedure above was repeated.
Shut-down Procedure
1. The water supply valve and venture discharge valve was closed. 2. The water supply pump was turned off.
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RESULT
Rectangular Weir Volume (L) Water Heigh t (cm) Time (s) Average Time (s) Flow rate, Q ( ) Discharge coefficient, 1st 2nd 3rd 3 1 29 33 27 29.67 1.1414 3 2 12 17 18 15.67 0.7641 3 3 6 6 9 7.00 0.9310 3 4 4 5 5 4.67 0.9064 3 5 3 4 4 3.67 0.8256
Triangular Weir Volume (L) Water Heigh t (cm) Time (s) Average Time (s) Flow rate, Q ( ) Discharge coefficient, 1st 2nd 3rd 3 1 58 58 66 60.67 2.0932 3 2 18 18 19 18.33 1.2247 3 3 5 6 7 6.00 1.3577 3 4 3 4 5 4.00 0.99219
Graph for Rectangular WeirH Cd 0.01 1.1414 0.02 0.7641 0.03 0.9310 0.04 0.9064 0.05 0.8256 0 0.002 0.004 0.006 0.008 0.01 0.01 0.02 0.03 0.04 0.05 Fl o w rate , Q ^2/3 Depth of water, H
Q^(2/3) Vs H
0 0.2 0.4 0.6 0.8 1 1.2 0.01 0.02 0.03 0.04 0.05 D isch ar ge Co e ff ic ie n t, Cd Depth of water, HCd Vs H
Series 110 Graph for Triangular Weir
H Cd 0.01895 0.01 2.0932 0.03059 0.02 1.2247 0.04782 0.03 1.3577 0.05624 0.04 0.9921 0 0.01 0.02 0.03 0.04 0.05 0.06 0.1 0.2 0.3 0.4 Fl o w rate , Q ^2/5 Depth of water, H
Q^2/5 Vs H
0 0.5 1 1.5 2 2.5 0.01 0.02 0.03 0.04 D isch ar ge c o e ff ic ie n t, Cd Depth of water, HCd Vs H
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CALCULATIONS
Rectangular Weir 1. To calculate the flow rate,Using result for the 1st reading where;
Volume, L = 3L = 0.003 and average time, s = 29.67s
( ) ( )
2. To calculate the discharge coefficient, Using the flow rate for the 1st reading where; Flow rate, Discharge coefficient, √( ) ( ) √ ( ) 1.1414
12 Triangular Weir
1. To calculate the flow rate,
Using result for the 1st reading where;
Volume, L = 3L = 0.003 and average time, s = 60.67s
( ) ( )
2. To calculate the discharge coefficient, Using the flow rate for the 1st reading where; Flow rate, Discharge coefficient, ( ) √( ) ( ) √ ( ) = 2.0932
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DISCUSSION
Back to the purpose of conducting this experiment which is to observe the characteristics over rectangular and triangular weir and to determine the discharge coefficient of the fluid flow, the results achieved enable a conclusion to be made. The raw results that were obtained were tabulated further in the forms of graphs to see a clearer relationship between the parameters of this experiments which are the discharge coefficient and the depth of the water. The discharge coefficient of each flow was calculated by using the equation given. Each weir has different ways of calculating its discharge coefficient. The discharge coefficient’s equation was originally derived from the equation of flow rate which is by dividing the actual volume flow rate and the ideal volume flow rate.
Observing the result for both weirs based on the graph plotted for flow rate versus depth of water, it shows that the flow rate of the fluid is proportional to the depth of water. Meanwhile, for the graph of discharge coefficient over depth, it is observed that the discharge coefficient decrease as the depth of the water increases. This is said to occur due to the resistance caused by the surface water tension which obstruct the flow of the water approaching the weir. Thus, affects the time taken to collect 3L of water and in return, affects the discharge coefficient because both depend on the flow rate of the fluid.
Even though the experiment was successfully conducted, there were some flaws in the value of the data obtained due to some errors created while doing the experiment. Firstly, while taking the reading of the data, there was some confusion on where the zero marks were supposed to be. It was only figured out after a few minutes of asking the previous group. Secondly, the height of datum might not be very accurate as it is hard to determine whether the needle needs to be on the surface of the water or above the surface of the water. As a result, it may cause a slight inaccuracy in the reading obtained. Lastly, there might be some external errors while taking the reading of the data. For example, vibration caused by the pump which causes the person trying to read the reading from the gauge to hesitate while taking the readings.
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CONCLUSION
As a conclusion for this experiment, it is concluded that the discharge coefficient for the triangular weir is higher than rectangular weir. This is due to the shape of the weir itself and the size of the space for the water to flow through the weir.
RECOMMENDATIONS
Make sure to check the apparatus before staring the experiment and always start by carrying out the start-up procedure and finish by carrying out the shut-down procedures.
More type of weirs should be introduced in order to see more variations in terms ofshapes, discharge coefficient and depth of the water.
Ensure that the apparatus is not vibrating for it may contribute to the inaccuracy of the results obtained.
Ensure the needle point is in zero positioning before setting the initial depth of the water.
When changing the weir, make sure the screw are tight to avoid any leakage while thewater flows.
REFRENCES
https://www.scribd.com/doc/37249588/Flow-Over-Weirs
https://www.scribd.com/doc/243828584/39520118-Flow-Over-Weirs
J.M Coulson, J.F Richardson, J.R Backhurst and J.H Harker, Chemical Engineering, (2010), Elsevier.
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