PK.FKK.PPM.MANUAL MAKMAL CHE465 (0)
UNIVERSITI TEKNOLOGI MARA FAKULTI KEJURUTERAAN KIMIA CHEMICAL ENGINEERING LABORATORY I (CHE465) NAME
: WAN ZULKARIM BIN WAN NADZRI
STUDENT NO.
:
EXPERIMENT
: FLOW OVER WEIRS
DATE PERFORMED
:
SEMESTER
: NOV 2004 – MAC 2005
PROGRAMME / CODE
: Bachelor of Engineering Engineering/ EH220
No. 1 2 3 4 5 6 7 8 9 10 11 12 13
Title Abstract/Summary Introduction Aims/Objectives Theory Procedures Apparatus Results Calculations Discussions Conclusions Recommendations References Appendices TOTAL
2004624899
4 FEBRUARY 2004
(Hons.)
Allocated marks % 5 5 5 5 3 5 20 10 20 10 5 5 2 100
Remarks:
Checked by: EN. RUSMI
Rechecked by: TABLE OF CONTENT
1
in
Chemical
Marks %
Summary Introduction Objectives Theory Procedures Apparatus Results Sample of calculations Discussions Conclusions Recommendations Reference Appendices
SUMMARY
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What we can summarized about this experiment are we want to know the characteristics of open-channel flow over a rectangular notch and a triangular (vee) notch and the values of the discharge coefficient for both notches. In this experiment we use the difference notch, which is rectangular and triangular. Here, we can observe the difference of flow rate of water that flows into both of channel. After we get the reading for volume flow rate we can we can know what the coefficient of the discharge of the notches. The coefficient values can be determined from measurement of the height of the free surface of water above the notch and the corresponding volume flow rate. We applied the Bernoulli Equation to get the flow over notches. The importance is the equipment must be set up carefully to observe appropriate results, where as volume, time and for calculating flow rate. All this observation values will be applied in the coefficient of discharge equation to determine whether our observation is right or not. For the triangular (vee) notch, here we must carefully to adjust the increment of its height with 5-6 mm. Fetching its known volume because we want to get more observation of its time collects this. The experiment result will be compared with theory
INTRODUCTION
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Fluid mechanics has developed as an analytical discipline from the application of the classical laws of static’s, dynamics and thermodynamics, to situations in which fluids can be treated as continuous media. The particular laws involved are those of the conservation of mass, energy and momentum and, in each application, these laws may be simplified in an attempt to describe quantitatively the behavior of the fluid. The Hydraulic Bench Description service module, F1-10, provides the necessary facilities to support a comprehensive range for the hydraulic models each of which is designed to demonstrate a particular aspect of hydraulic theory. The specific hydraulic model that we were concerned with for this experiment was the Basic Weir Apparatus, F1-13. This consists of two simple weirs, a rectangular notch and a vee notch.
OBJECTIVES
•
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.
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THEORY Because the depth of flow above the base of notch is related to the volume flow rate through it, the notch forms the useful flow measurement device. The classical results for flow over notches are obtained by an application of the Bernoulli Equation, from a point well up-stream to a point just above the notch. This approach requires a number of very substantial assumptions and it yields the following results: For a rectangular notch Qt = Cd 2/3 b √(2gH3/2) For a vee notch Qt = Cd 8/15 tan(θ/2)√(2gH5/2) 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, which has to be determined by experiment (The coefficient Cd is required to accommodate the effects of the simplifying assumptions in the theory.) These can be arrange to give: Cd = 3Qt 2b√(2gh3/2) for a rectangular notch, and Cd =
15Qt 8 tan θ√(2gH5/2) 2
for a vee notch.
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THE MEASUREMENT OF DISCHARGE COEFFICIENTS, Cd When flow occurs in a pipe or channel we are usually interested in the total rate discharge rather than in the velocity, which varies considerably across the section of the conductor; this amounts to saying that we are interested in the mean value of velocity taken over normal section rather than velocities at particular points. The rate of discharge is usually taken as a volume per unit when the fluid is liquid. When the flow is steady the rate of discharge of a liquid is easily determined by collecting the liquid, which passes in measured interval time. The volume may be obtained directly from the observed depth of liquid in the collecting tank by use of a calibration curve or indirectly by weighing the liquid and division by the specific weight. For measurement of large discharges the most useful devices are the 90o V-notch and the rectangular weir. In accordance with equation, the discharge over a V-notch is given by Q = 8 Cd tan θ √(2gh5/2) 15
2
where θ is the total included angle of the notch and h is the head. For a 90o V-notch Cd has a value of about 0.59. The coefficient Cd is subject to slight variations as the head varies and B.S. 3680: Part 4A : 1965 contains tables giving values of Cd for 0.05m< h< 0.38m. Head h is measured as the head of free surface at a stagnation point above the apex of the notch. Stagnation points occur in the corners where the notch bulkhead meets the sides of the channel. When the discharge exceeds 0.021 m3/s a rectangular weir may be used. For rectangular weirs having complete contractions, B.S. 3680: Part 4A: 1965 gives the following relationship
in which
Q = 2 √(2gCdbh3/2) 3 Cd = 0.616(1 - 0.1h/b)
where b is the length of the weir and h is the observed head above the crest for negligible velocity approach. This equation may be used for the heads from 0.075m to 0.60m provided that b/h is greater than 2. Care must be taken to have the approach channel sufficiently large, as detailed in the specification. The method of determining the theoretical flow through a notch is the same as that adopted for a large orifice.
For a notch of any shape shown in figure, consider a horizontal strip of width b at a depth h below the free surface and height h.
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Area of strip = bh. Velocity through strip = (2gh) Discharge through strip, Q = Area x velocity = bh (2gh). Integrating from h = 0 at the free surface to h = H at the bottom of the notch, Total theoretical discharge(Q),
1 Before the integration of equn.1 can be carried out, b must be expressed in terms of h. Rectangular Notch:
For a rectangular notch, put b = constant = B in equn.1 giving,
2 V-Notch:
For a V-notch with an included angle p ut b = 2(H-h)tan( /2) in equn.1, giving
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Inspection of equns.2 and 3 suggests that, by choosing a suitable shape for the sides of the notch, any desired relationship between Q and H could be achieved. As in the case of orifice, the actual discharge through a notch or weir can be found by multiplying the theoretical discharge by a coefficient of discharge to allow for energy losses and the contraction of the cross-section of the stream at the bottom and sides. In the forgoing theory, it has been assumed that the velocity of the liquid approaching the notch is very small so that its kinetic energy can be neglected; it can also be assumed that the velocity through any horizontal element across the notch will depend only on its depth below the free surface. This is a satisfactory assumption for flow over a notch or weir in the side of a large reservoir, but, is the notch or weir is placed at the end of a narrow channel, the velocity of approach to the weir will be substantial and the head h producing flow will be increased by the kinetic energy of the approaching liquid to a value x = h + v12/(2g), Where v1 is the mean velocity of the liquid in the approach channel. Note that the value of v1 is obtained by dividing the discharge by the full cross sectional area of the channel itself, not that of the notch. As a result, the discharge through the strip will be Q = bh (2gx).
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PROCEDURES
Equipment Set Up 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. 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, I founded it useful to pre-set the height gauge position to give a rough guide.
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Taking a Set of Results 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 outflow did this and then the volume collected would be determined from the sight-glass. 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. For this notch I need to work with height increment 5-6 mm.
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APPARATUS
In order to complete the exercise we need a number of pieces of equipment: •
The FI-10 Hydraulics Bench which allows us to measure flow by timed volume collection.
•
The F1-13 Stilling baffle
•
The F1-13 Rectangular and Vee Notches
•
Vernier Height Gauge (supplied with F1-13)
•
Stop Watch
•
Spirit Level
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The apparatus has five basic element used in conjunction with the flow channel in the moulded bench top of Hydraulics Bench Description. A stilling baffle and inlet nozzle combine to promote smooth flow condition in the channel A Vernier hook and point gauge is mounted on instrument carrier, to allow measurement of the dept of flow above the base of the notch. Finally, the weir notches are mounted in a carrier at the outlet end of the flow channel. To connect the delivery nozzle, the quick release connector is unscrewed from the bed of the channel and the nozzle screwed in place. The stilling baffle is slid into slots in the wall of the channel. These slots are polarized to ensure correct orientation of the baffle. The instrument carrier is located on the side channels of the moulded top. The carrier may be moved along the channel to the required measurement position. The gauge is provided with a coarse adjustment locking screw and a find adjustment nut. The vernier is locked to the mast by screw and is used in conjunction with the scale. The hook and point is clamped to the base of the mast by means of a thumbscrew. The weirs may be clamped to the weir carrier by thumbnuts; the weir plates incorporate captive studs to aid assembly.
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RESULT
RECTANGULAR NOTCH Height of datum ho: 0 m Height of water level, h, (m)
Volume
H3/2
Rate Qt
Rectangular
Time of
Collected collection, T,
x 10-3 4.0 8.5 11.2 14.5 19.0
NO 1 2 3 4 5
Volume Flow
(m3) 0.003 0.003 0.003 0.003 0.003
(m3/sec) x 10-5 2.91 7.69 10.3 15.0 21.4
(sec) 103.0 39 29 20 14
Rectangular
Height above Notch (m3/2) Notch discharge notch H (m) 4.0 8.5 11.2 14.5 19.0
X 10-4 2.53 7.84 11.85 17.46 26.20
Coefficient Cd 0.02 0.03 0.03 0.04 0.04
VEE NOTCH Height of datum ho: 0 m
SAMPLE OF CALCULATIONS Height of
NO 1 2 3 4 5
water
Volume
level (m)
Collected
x 10-3 7.5 13.0 16.0 19.0 21.0
(m3) 0.003 0.003 0.003 0.003 0.003
Time of
Volume Flow
Height
collection Rate, Qt (m3/s) above notch (s) 69 30 25 15 12
x 10-5 4.35 10.0 12.0 20.0 25.0
RECTANGULAR NOTCH
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H (m) 7.5 13.0 16.0 19.0 21.0
VEE Notch VEE Notch H5/2 (m)
discharge
x 10-6 Coefficient Cd 4.8714 0.008 19.2689 0.0096 32.3817 0.009 49.7604 0.012 63.9069 0.013
Cd = 3Qt 2b√(2gH3/2) Qt = 2.91 x 10-5 m3/s b = 0.03 m H3/2 = 2.53 x 10-4 m Cd = 3(2.91 x 10-5 m3/s) 2(0.03m)(√2*9.81m/s*2.53 x 10-4 m) = 0.021
VEE NOTCH
Cd =
15Qt 8 tan θ√(2gH5/2) 2
Qt = 4.35 x 10-5 m3/s θ = 90o g = 9.81 m/s2 H5/2 = 4.8714 x10-6 m
Cd = 15 (4.35 x 10-5 m3/s) 8tan45o√(2 x 9.81m/s2 x 4.8714 x 10-6 m) = 8.34 x 10-3
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Calculation of error the Discharge Coefficient (Cd)
From the theory, the Cd value is 0.685 =
Experimental value of Cd - theoretical value
x 100%
Theoretical value of Cd
Rectangular notch; From the rectangular notch table, take the value of Cd, = 0.021 =
0.685-0.021 x 100% 0.685
=
97%
Vee notch ; From the vee notch table, take the value of Cd = 8.34 x 10-3 =
0.685- 8.34 x10-3 x 100% 0.685
= 99%
DISCUSSIONS
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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 can’t 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. CONCLUSIONS
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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.
The Cd values for both notches.
1 2 3 4 5
Rectangular Notch 0.02 0.03 0.03 0.04 0.04
Triangular Notch 0.008 0.0096 0.009 0.012 0.013
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RECOMMENDATIONS
1. The data that was observed in the experiment that was time gain should be taken twice. This can avoid the very wide deviation because of only take once of each observation 2. Take care not to allow spillage to occur over the plate top adjacent to the notch. If this happened, it would effect the collection of known volume. 3. Once the data were taken, the procedure cannot be reverse to find the value of time collection by adjusting the height. This would affect the value of height datum. The height datum must be constant and the observation should be done once round for the little increment of height especially for V-notch. 4. The readings of height should be taken carefully by avoiding sight error. The time collection should be taken much appropriately.
REFERRENCES
1.
Bruce R Munson, Donald F. Young, Theodore H. Okiishi, Fundamental Of Fluid Mechanics, fourth edition, page 650-651, John Wiley & Sons, Inc
2. Laboratory manual 1(CHE 465)
APPENDICES
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NOMENCLATURE Column
Units
Heading Notch Type Height m
Nom.
Type
Description
ho
Measured Measured
Vee Notch or Rectangular Notch Datum height, which is the base of the notch.
Datum
This is read from the vernier and used to calculate height of water level above the notch. The height datum is measured in millimeters. It has been converted to meters
Water
m
h
Measured
Level
for the calculations. This is read from the vernier. The water level is measured in millimeters. It has been converted to meters for the calculations.
m3
Volume
V
Measured
Collected
Taken from the scale on hydraulic bench. The volume collected is measured liters. It has been converted to cubic meters for the
Time
for s
t
Measured
Collection
calculations (divide reading by 1000). Time taken to collect the known volume of water in the hydraulic bench. The time is
Volume
m /sec Qt
Calculated
measured in seconds. Qt = V/t = Volume collected/Time for
Flow Rate Height
m
Calculated
collection H = h-ho = Height of Water Level – Height
2
H
Above
Datum.
Notch H3/2
Calculated
Rectangular Notch Rectangular
Used to describe relationship between flow rate and height for a rectangular notch.
Cd
Calculated
Cd = 3Qt 2b√(2g3/2)
Notch Discharge Coefficient H5/2 Vee Notch Vee Notch
Cd
Calculated
Used to describe relationship between flow
Calculated
rate and height for a Vee notch Cd = 15Qt
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8 tan θ√(2gH5/2)
Discharge Coefficient
20
