FACULTY OF CHEMICAL ENGINEERING
October 16, 2012
ABSTRACT:
This experiment is about the measurement of flow of water by notches and weirs which has been conducted on 6th October 2012 at Fluid Mechanics Laboratory, UiTM Shah Alam. Basically, the experiment that had conducted is to discuss about the flow characteristics of water over the different notches. The notches that used to examine the flow are rectangular and triangular (V) notches. Besides, the experiment here is also to define the discharge coefficient of the fluid flow. In order to achieve the objectives, all the data are recorded while while conducting the experiment. The manipulated variables from this experiment are the height of water level and also the types of notches. Thus, for the easier calculation, the amount of volume is set at the constant level which is 3 litres. Based on the data that had been recorded, we construct a graph to analyzing the characteristics of the flow. From the rectangular graphs, we can observed that the discharge coefficient decrease slowly and it almost have a constant value for the rest. Different with the rectangular notch, the discharge coefficient for the triangular notch is smoothly but the value still higher than the rectangular notch. Thus, we can conclude that the triangular notch showed the higher discharge coefficient rather than the rectangular notch.
INTRODUCTION:
Nowadays, if we can see a structure that used to dam up a stream or river, over which the water flows is known as weir and also can used notch. But the different between the weir and notch is the structure. A weir is an opening in the sidewall of the tank at the top. Besides, the notch and weir almost the same except the former is a small structure and has sharp edges. A weir is generally an overflow structure, with a broad crest, built across an open channel. The top of weir wall over which the liquid flows is known as the sill or crest. While the head under which the weir is discharging is measured from the crest to the free surface. Basically, a weir and notch is used for measuring the flow of liquids. For this experiment, the rectangular weir and triangular weirs are been used. Both of these weirs are often used in water supply, wastewater and also sewage systems. They consist of a sharp edged plate with a rectangular, triangular triangular or v-notch profile for the water flow. In dam spillways, spillways, the broad-crested weirs can be observed where the broad edge is beneath the water surface across the
FACULTY OF CHEMICAL ENGINEERING
October 16, 2012
entire stream. Flow measurement installations with broad-crested weirs will meet accuracy requirement only if they are calibrated.
OBJECTIVES:
1. To observe the flow characteristics over a rectangular and triangular (Vee) notches. 2. To determine the discharge coefficient of the fluid flow.
THEORY: With the different types of notch, then the method of calculating the discharge coefficients of the fluids flow is also different. There are some theories that will discussing about the reasoning of two different notches which are: 1) RECTANGULAR NOTCH A rectangular notch is a thin square edged weir plate installed in a weir channel as shown in figure 1 below.
Figure 1
Rectangular notch
Based on the figure above, consider that the flow in an element of height H at a depth, h below the surface. Then, assume that the fluid flow everywhere normal to the plane of the weir and that the free surface remains horizontal up to the plane of the weir. When the flow through the notch is not parallel then it will be not normal to the plane of the weir. If the free surface is not horizontal the result for the viscosity and surface tension will have an effect. There will be a considerable change in the shape of the nappe as it passes through the notch
FACULTY OF CHEMICAL ENGINEERING
October 16, 2012
with curvature of the stream line in both vertical and horizontal plane. In particular, the width of the nappe is reduced by the contraction at each end.
Figure 2 Shape of the nappe The formula for the discharge coefficient of rectangular is:
Qt
= Cd
Where; Qt
= volume flow rate (m/s)
H
= height above notch base (m)
B
= width of rectangular notch (0.03m)
Cd
= the discharge coefficient coefficient which has to be determined by the experiment
The discharge from the rectangular notch will be considerably less, approximately 60% of the theoretical analysis due to these curvature effects. A coefficient of discharge, Cd is therefore introduced so that :
Cd =
However, Cd is not a true constant tending towards a constant only for large heads and a low velocity of approach in the weir channel.
FACULTY OF CHEMICAL ENGINEERING
October 16, 2012
2) TRIANGULAR NOTCH
Figure 3
triangular notch
The formula for the triangular notch is:
Qt
= Cd
Where; Qt
= volume flow rate
H
= height above notch base
B
= width of rectangular notch
θ
= angle of the Vee in the triangular notch
Cd
= the discharge coefficient coefficient which has to be determined by experiment
Thus ,
Cd
=
For the rectangular notch the rate of discharge is proportional to the liquid depth raised to power 1.5 and for the triangular notch to a power 2.5. a triangular notch will therefore handle a wider range of flow rates. It can be shown that the notch must have curved walls giving a large width to the bottom of the notch and a comparatively small width towards the top. The weir is frequently for controlling the flow within the unit itself, for instance in a distillation column or reactor.
FACULTY OF CHEMICAL ENGINEERING
October 16, 2012
APPARATUS AND MATERIALS: 1. SOLTEX ® flow over weirs (Model: FM 26)- Appendix 2. Water 3. Hydraulics bench 4. Weir channel 5. (V) Vee notch weir 6. Hook & point gauge 7. Basket of glass sphere 8. Volumetric measuring tank 9. Rectangular weir
4 2 5
7
1
3
6
Figure 1 : flow over weirs – Vee notch weir
Figure 2 : flow over weirs – rectangular notch weir
PROCEDURES: 1. Place the flow stilling basket of glass sphere into the left end of the weir channel and attach the hose from the bench regulating valve to the inlet connection into the stilling basket. 2. Place the specific weir plate which is to be tested and hold it using the thumb nuts. Ensure that the square edge of the weir faces is upstream. 3. Start the pump and slowly open the regulating valve until the water level reaches the crest of the weir and measure the water level to determine the datum level H zero.
FACULTY OF CHEMICAL ENGINEERING
October 16, 2012
4. Adjust the bench regulating valve to give the first required head level of approximately 3m 3. Measure the flow rate using the volumetric tank until 3m 3. 5. Increase the height of the crest by 1cm and open the valve wider. Then, measure the flow rate. 6. Repeat the experiment by increasing the height by 1cm and until the water reach the maximum height. 7. Close the regulating valve, stop the pump, and then replace the weir with the next weir that need to be tested. Repeat the test procedure.
RESULT AND CALCULATION: i)
RECTANGULAR WEIR Height of datum = 0.03m Trial
Volume collected, V (m3)
Time of collection, t (s)
Volume flow rate, Qact (m3/s)
Q2/3
Log H
Log Q
Cd
4.29x10 -4
Height of water level, H (m) 0.00
1
0.003
7.0
0.000
0.000
-3.368
0.000
2
0.003
4.8
6.25x10 -4
0.01
0.007310
-2.000
-3.203
7.055
3
0.003
4.0
7.50x10 -4
0.02
0.008083
-1.699
-3.125
2.900
CALCULATION:
Q = Cd B
Width of the weir, B = 0.03m Gravity, g = 9.81 m2/s Volume flow rate, Qact =
FACULTY OF CHEMICAL ENGINEERING
Trial 1 Qact
= 4.29 x 10 -4 m3/s
Q 4.29x10-4 Cd
x x 0.03 x √ x (0)
= Cd b = Cd
3/2
=0
Q2/3
= (0 x x 0.03 x
x (0) √
3/2 2/3
)
=0 Trial 2 Qact
=
= 6.25 x 10-4 m3/s
Q 6.25x10-4 Cd
Q2/3
x (0.01) x x 0.03 x √
= Cd b = Cd
3/2
= 7.055
= (7.055 x x 0.03 x = 0.007310
x (0.01) √
3/2 2/3
)
October 16, 2012
FACULTY OF CHEMICAL ENGINEERING
October 16, 2012
Trial 3 Qact
=
= 7.25 x 10-4 m3/s
Q 7.50x10-4 Cd
Q2/3
x (0.02) = C x x 0.03 x √ = Cd b
d
3/2
= 2.9
= (2.9 x x 0.03 x
x (0.02) √
3/2 2/3
)
= 0.008083
ii)
V - NOTCH WEIR
Height, H (m) 0.00
Time, t (s) 73.00
Flow rate, Qact (m3/s) 4.11 x 10-5
Q2/3
Cd
1
Volume, V (L) 3
0
0
2
3
0.01
22.00
1.36 x 10-4
0.0284
5.757
3
3
0.02
11.45
2.63 x 10-4
0.0369
1.961
4
3
0.03
5.45
5.5 x 10-4
0.0497
1.494
Trial
CALCULATION:
( )
= 90
o
g = 9.81 m2/s Volume flow rate, Qact =
FACULTY OF CHEMICAL ENGINEERING
Trial 1
Qact
= 4.11 x 10 -5 m3/s
-5
3
4.11 x 10 m /s Cd
= =0
( )
= √ =0 Trial 2 Qact
= 1.36 x 10-4 m3/s
1.36 x 10-4 m3/s = Cd
√
= 5.757
October 16, 2012
FACULTY OF CHEMICAL ENGINEERING
( √ )
= √ = 0.0284 Trial 3
Qact
= 2.62 x 10-4 m3/s
2.62 x 10-4 m3/s Cd
=
√
= 1.961
( √ )
= √ = 0.0369
Trial 4 Qact
= 5.5 x 10 -4 m3/s
October 16, 2012
FACULTY OF CHEMICAL ENGINEERING
-4
3
= √
Cd
= 1.494
5.5 x 10 m /s
( √ )
= √ = 0.0497
October 16, 2012
FACULTY OF CHEMICAL ENGINEERING
October 16, 2012
GRAPH: i)
RECTANGULAR WEIR Log H
Log Q
0.000
-3.368
-2.000
-3.203
-1.699
-3.125
4
3.5
3
2.5
Q g o l
2 Q
1.5
1
0.5
0 0
0.5
1
1.5 log H
Slope = (3.368 – 3.200) / ( 0.0-2.0) = -0.084
2
2.5
FACULTY OF CHEMICAL ENGINEERING
ii)
October 16, 2012
V - NOTCH WEIR
Log H
Log Q
0.00
-4.386
0.01
-3.866
0.02
-3.580
0.03
-3.260
5
4.5
4
3.5
3
Q g 2.5 o L
Y-Values
2
1.5
1
0.5
0 0
0.005
0.01
0.015 Log H
Slope = ( 4.386 – 3.26) / (0-0.03) = -37.53
0.02
0.025
0.03
0.035
FACULTY OF CHEMICAL ENGINEERING
October 16, 2012
DISCUSSION A notch is an opening in the side of a measuring tank or reservoir extending above the free surface. A weir is a notch on large scale. 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. For rectangular weir, when the flow approaches the edge of the notch, there is a contraction because the velocity at the edge is not normal to the plane of the notch. This produces a reduction in the cross section and some friction in the flow. The volume flow rate, Q for rectangular weir:
Q = Cd b
The volume flow rate Q, for V – notch wier:
( ) From the result, we observed that the coefficient of discharge, C d for rectangular weir is in variations. This is because of the inconsistent low height increment. For V – notch, we observed that the higher the height of water level, the shorter the time taken to collect 3 L of water. This resulted in the coefficient of discharge, C d as it decreased when the volume of flow rate, Q increased.
FACULTY OF CHEMICAL ENGINEERING
October 16, 2012
CONCLUSION From both experiment, it were clearly shown that the coefficient of discharge is dependent on the volumetric flow rate and its height (head) of water level from the base of notch. The coefficient of discharge corresponds differently to the height of the water level (head) to the type of notch used. For triangular notch, the coefficient of discharge also depends on the angle of the v shape. Then it can be concluded that the experiment is a success.
RECOMMENDATIONS 1. In this experiment, many trials should be made so that we can observe the trend of the coefficient of discharge more accurately. 2. Each increment of the height of the water level should be made carefully and accurately. Parallax error should be avoided. 3. The time taken for the experiment
REFERENCE Yunus, A. Cengel. & John, M. Cimbala. (2006). Fluid Mechanics Fundamental and Applications. Applications. (2nd ed.). New York: MC Graw Hill
