UNIVERSITI TEKNOLOGI MARA

FAKULTI KEJURUTERAAN KIMIACHEMICAL ENGINEERING LABORATORY I

(CHE465)

NAME : WAN ZULKARIM BIN WAN NADZRI

STUDENT NO. : 2004624899

EXPERIMENT : FLOW OVER WEIRS

DATE PERFORMED

: 4 FEBRUARY 2004

SEMESTER : NOV 2004 – MAC 2005

PROGRAMME / CODE

: Bachelor of Engineering (Hons.) in Chemical Engineering/ EH220

No. Title Allocated marks % Marks %1 Abstract/Summary 5  2 Introduction 5  3 Aims/Objectives 5  4 Theory 5  5 Procedures 3  6 Apparatus 5  7 Results 20  8 Calculations 10  9 Discussions 20  

10 Conclusions 10  11 Recommendations 5  12 References 5  13 Appendices 2  

TOTAL 100  Remarks:

Checked by: EN. RUSMI Rechecked by:TABLE OF CONTENT

1

PK.FKK.PPM.MANUAL MAKMAL CHE465 (0)

Summary

Introduction

Objectives

Theory

Procedures

Apparatus

Results

Sample of calculations

Discussions

Conclusions

Recommendations

Reference

Appendices

SUMMARY

2

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

3

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.

THEORY

4

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 = 3 Qt

2b√(2gh3/2)

for a rectangular notch, and

Cd = 15 Qt

8 tan θ√(2gH5/2)

2

for a vee notch.

THE MEASUREMENT OF DISCHARGE COEFFICIENTS, Cd

5

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 Q = 2 √(2gCdbh3/2) 3in which 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.

Area of strip = bh.

6

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 put b = 2(H-h)tan(/2) in equn.1, giving

7

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).

8

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.

9

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.

10

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

11

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.

12

RESULT

RECTANGULAR NOTCH

Height of datum ho: 0 m

VEE NOTCH

NO

Height of

water

level, h,

(m)

x 10-3

Volume

Collected

(m3)

Time of

collection, T,

(sec)

Volume Flow

Rate Qt

(m3/sec)

x 10-5

Height above

notch H (m)

H3/2

Rectangular

Notch (m3/2)

X 10-4

Rectangular

Notch discharge

Coefficient Cd

1 4.0 0.003 103.0 2.91 4.0 2.53 0.02

2 8.5 0.003 39 7.69 8.5 7.84 0.03

3 11.2 0.003 29 10.3 11.2 11.85 0.03

4 14.5 0.003 20 15.0 14.5 17.46 0.04

5 19.0 0.003 14 21.4 19.0 26.20 0.04

Height of datum ho: 0 m

NO

Height of

water

level (m)

x 10-3

Volume

Collected

(m3)

Time of

collection

(s)

Volume Flow

Rate, Qt

(m3/s)

x 10-5

Height

above notch

H (m)

VEE Notch

H5/2 (m)

x 10-6

VEE Notch

discharge

Coefficient

Cd

1 7.5 0.003 69 4.35 7.5 4.8714 0.008

2 13.0 0.003 30 10.0 13.0 19.2689 0.0096

3 16.0 0.003 25 12.0 16.0 32.3817 0.009

4 19.0 0.003 15 20.0 19.0 49.7604 0.012

5 21.0 0.003 12 25.0 21.0 63.9069 0.013

13

SAMPLE OF CALCULATIONS

RECTANGULAR NOTCH

Cd = 3 Qt

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 m 3 /s)

2(0.03m)(√2*9.81m/s*2.53 x 10-4 m)

= 0.021

VEE NOTCH

Cd = 15 Qt

8 tan θ√(2gH5/2)

2

Qt = 4.35 x 10-5 m3/s

θ = 90 o

g = 9.81 m/s2

H5/2 = 4.8714 x10-6 m

Cd = 15 (4.35 x 10 -5 m 3 /s)

8tan45o√(2 x 9.81m/s2 x 4.8714 x 10-6 m)

14

= 8.34 x 10-3

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

15

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

16

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.

Rectangular Notch Triangular Notch

1 0.02 0.008

2 0.03 0.0096

3 0.03 0.009

4 0.04 0.012

5 0.04 0.013

17

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)

18

APPENDICES

NOMENCLATURE

Column

Heading

Units Nom. Type Description

Notch Type Measured Vee Notch or Rectangular Notch

Height

Datum

m ho Measured Datum height, which is the base of the notch.

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

for the calculations.

Water

Level

m h Measured This is read from the vernier. The water level

is measured in millimeters. It has been

converted to meters for the calculations.

Volume

Collected

m3 V Measured Taken from the scale on hydraulic bench.

The volume collected is measured liters. It

has been converted to cubic meters for the

calculations (divide reading by 1000).

Time for

Collection

s t Measured Time taken to collect the known volume of

water in the hydraulic bench. The time is

measured in seconds.

Volume

Flow Rate

m2/sec Qt Calculated Qt = V/t = Volume collected/Time for

collection

Height

Above

Notch

m H Calculated H = h-ho = Height of Water Level – Height

Datum.

H3/2

Rectangular

Calculated Used to describe relationship between flow

rate and height for a rectangular notch.

19

Notch

Rectangular

Notch

Discharge

Coefficient

Cd Calculated Cd = 3Qt

2b√(2g3/2)

H5/2 Vee

Notch

Calculated Used to describe relationship between flow

rate and height for a Vee notch

Vee Notch

Discharge

Coefficient

Cd Calculated Cd = 15Qt

8 tan θ√(2gH5/2)

20