Hydraulic Exp1

DEPARTMENT OF CIVIL ENGINEERING

COLLEGE OF ENGINEERING

HYDROLOGY AND HYDRAULIC ENGINEERING LABORATORY CEWB221

Experiment 1: Flow Over A Notch

Section : 1

Group members :

1) Andy Ngiew Qi Ying CE091739

2) Pang Wen Bin CE091731

3) Ammar Taqi CE092280

4) Tariq Adi Satria Ahmat Adam CE093982

5) Fadzlihadi Bin Fadzil CE091555

Date of lab session : 10 November 2014

Lecturer : Miss Hidayah Bte Basri

INTRODUCTION:

Flow over a Notch is equipment for use together with Hydraulic Bench to measure flow rate

against height of liquid (water) over a rectangular notch or a v-notch.

In open channel hydraulic, weirs are commonly used to either regulate or to measure the

volumetric flow rate. They are of particular use in large scale situation 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.

OBJECTIVES:

The objective of this experiment is to demonstrate the characteristics of flow over weirs and to

determine the ‘Coefficient of Discharge’ for each type of weir.

LEARNING OUTCOMES:

By doing this experiment, the student will have the ability to conduct setup and conduct

experiment and collect data from coefficient of discharge. The student will also able to interpret

data from the coefficient of discharge and determine the characteristics of coefficient of

discharge.

PROBLEM STATEMENT:

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.

APPARATUS:

1. Hydraulic Bench

2. Weir channel

3. (V) Vee notch weir

4. Hook and point gauge

5. Basket of glass spheres

6. Volumetric measuring tank

7. Rectangular weir

8. Hook gauge and scale

THEORY:

Flow of water between 2 points over a notch follows Bernoulli’s equation.

Point 1 - A point at distance upstream from the notch (usually 4 times the height from the

Notch bottom) (Refer Fig. 2).

Point 2 - A point above of the notch (Refer Fig. 2).

Assume no energy loss between Point 1 and 2.

v1

2g+

p1

γ+z1=

v2

2 g+

p2

γ+z2 (1 )

v = Velocity m/sec

p = Pressure Newton/m2

z = Elevation m

γ = Specific gravity kg.f (m3)

g = Acceleration due to gravity 9.81 m/ sec2

h = Height of water above point 2 m

H = Height of water m

Since the hydraulic bench channel is much wider than the notch width, we can assume V1 is very

slow.

Thus v1 = 0

Total head at point 1 = Ht = 0+p1

γ+z1 (2)

Where Ht = H = Height of water above notch lowest point

Hence v2

2g+

p2

γ+z2=H t=H (3)

At point 2 P2 = Atmosphere pressure = 0

Thus v2

2 g+z2=H (4)

v2

2 g=H−z2=h

Thus v2=√2 gh (5)

Consider dh = A thin of slap water at the point of measurement.

Rectangular Notch

b = width of the notch

dQ = √2gh bdh

Q =23 √2g b H 3 /2

#for ESSOM HB 013 : b = 30 mm or 50 mm.

V-Notch

Width of the thin slap is 2 (H – h) tan θ

dQ = 2√2 gh ( H−h ) tanθ dH

2θ = V-notch angle

Q = ∫0

H

2√2 gh ( H−h ) tan θ dH

Q =8

15 √2 g H 5 /2 tan θ

#for ESSOM HB 013 : 2θ = 90° or 60°

In actual flow, the cross section of water after passing the notch will be slightly reduced (vena

contracta), thus the actual flow will be slightly below that of theory.

Thus Qrectangular notch=CD23 √2g b H 3/2

QV −notch(90 °)=CD8

15 √2 g tan 45° H5 /2

QV −notch(60 °)=CD815 √2 g tan 30° H5 /2

Where CD = Coefficient of discharge

In practice, calculations may be made through logarithm.

For rectangular notch, log Q=log K 1+23

log H , K1 = constant.

For V-notch, log Q=log K 2+52

log H , K2 = constant.

EXPERIMENTAL PROCEDURE:

1. The flow stilling basket of glass spheres is placed into the left end of the weir channel

and the hose is attached from the bench regulating valve to the inlet connection into the

stilling basket.

2. The specific weir plate which is to be tested first is placed and it is held by using the five

thumb nuts. The square edge to the weir is ensured to face upstream.

3. The pump is started and the bench regulating valve is opened slowly until the water level

reaches the crest of the weir and the water level is measured to determine the datum level

Hzero.

4. The bench regulating valve is adjusted to give the first required head level of

approximately 10mm. The flow rate is measured using the volumetric tank or the

rotameter. The shape of the nappe is observed.

5. The flow is increased by opening the bench regulating valve to set up heads above the

datum level in steps of approximately 10 mm until the regulating valve is fully open. At

each condition the flow rate is measured and the shape of the nappe is observed.

6. The regulating valve is closed, the pump is stop and then the weir is replaced with the

next weir to be tested. The test procedure is repeated.

RESULT:

Water level at lowest point of

a) Rectangular notch = 6.206 cm

b) V-notch 90° = 9.022 cm

c) V-notch 60° = 6.528 cm

Flow

rate in

flow

meter

(L/min

)

Volume

of

Measurin

g Tank

(L)

Tim

e

(sec

)

Flow

Rate,

Q

(L/min

)

Leve

l

abov

e the

notch

, H1

(cm)

H

(cm)

log Q

(L/min

)

log

H1

(cm)

Qtheory

Cd

=

Q/

QTheory

Rectangul

ar notch

weir 5cm

wide

10 4 6.13 39.15 3.80410.01

01.593

0.58

065.7 0.596

20 4 3.44 69.77 5.05011.25

61.844

0.70

3

100.

50.694

30 4 3.37 71.22 5.52211.72

81.853

0.74

2

115.

00.619

V-notch

90°

10 4 5.22 45.98 4.47213.49

41.663

0.65

159.9 0.768

20 4 3.63 66.12 5.27414.29

61.820

0.72

290.5 0.731

30 4 2.91 82.47 5.60614.62

81.916

0.74

9

105.

50.782

V-notch

60°

10 4 5.87 40.89 5.50212.03

01.612

0.74

158.1 0.704

20 4 3.40 70.59 6.51013.03

81.849

0.81

488.5 0.798

30 4 2.84 84.51 7.00813.53

61.927

0.84

6

106.

40.794

Examples of calculation:

Q =Volume of MeasuringTank

Time

=4

6.13

= 0.6525 L/sec

= 39.15 L/min

For Rectangular Notch,

Qtheo =23 √2g b H 3 /2

=23 √2(9.81)(5 ×10−2)(3.804 ×10−2)3 /2

= 0.001095 m3/s

= 65.7 L/min

For V-notch,

Qtheo =8

15 √2 g H 5 /2 tan θ

=8

15 √2(9.81)(4.472 ×10−2)5 /2 tan 45°

= 9.991 m3/s

= 59.9 L/min

Cd =Q

QTheory

=39.1565.7

= 0.596

0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.74 0.761.45

1.51.55

1.61.65

1.71.75

1.81.85

1.9f(x) = 1.70988949503427 x + 0.609157924185201R² = 0.959658829248049

Graph of log Q vs log H (Rectangular notch)

log H (cm)

log

Q (L

/min

)

0.64 0.66 0.68 0.7 0.72 0.74 0.761.5

1.55

1.6

1.65

1.7

1.75

1.8

1.85

1.9

1.95

f(x) = 2.50637439833485 x + 0.026824508911149R² = 0.986759759395108

Graph of log Q vs log H (V-notch 90° notch)

log H (cm)

log

Q (L

/min

)

0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.861.4

1.5

1.6

1.7

1.8

1.9

2

f(x) = 3.04246748762804 x − 0.638988145931637R² = 0.996181157841127

Graph of log Q vs log H (V-notch 60° notch)

log H (cm)

log

Q (L

/min

)

From the graph of rectangular notch,

log K1=0.6092

K1=4.066

23

Cd √2(9.81× 102× 60)(5 )=4.066

Cd=0.00356

From the graph of 90° V-notch,

log K1=0.0268

K 1=1.064

815

Cd √2(9.81× 102× 60)( tan 45 ° )=1.064

Cd=0.00581

From the graph of 60° V-notch,

log K1=−¿0.639¿

K1=0.2296

815

Cd √2(9.81× 102× 60)( tan30 ° )=0.2296

Cd=0.00217

DISCUSSION:

In this experiment, the coefficient of discharge is calculated for three types of the weirs, which

are rectangular weir, 90° V-notch weir and 60° V-notch weir. For the rectangular weir, the

coefficient of discharge obtained is 0.00356. For the 90° V-notch weir, the coefficient of

discharge is 0.00581 and 0.00217 is obtained for the coefficient of discharge for the 60° V-notch

weir. By theory, the index is approximately 1.5 for the rectangular weir and 2.5 for the V-notch

weir from the slope of the graphs of log Q versus log H for the three types of the weirs. From the

graph plotted, the slope of the rectangular weir graph is 1.7099 which is approximately 1.5 from

the theory. For the 90° and 60° V-notch weir, the slopes of the graphs are 2.5064 and 3.0425

respectively. These values are approximately 2.5 which mentioned in the theory.

Errors may occur during conducting the experiment and will cause the result become

inaccurate. When the weir is screwed on the tank, there are some leakages of water from the

sides of the weir. This may affect the flow of the water and the accuracy of the result. Besides,

parallax errors when taking the reading from the scale will also affect the result.

The nappe of rectangular notch was clinging. The end

contraction of the flow was big. The width of the flow becomes smaller compared to the width of

the notch.

The nappe of the 90° v-notch was sprung clear and the end

contraction was small. The width of the flow changed not much compared to the notch.

The nappe of the 60° v-notch was sprung clear and the end

contraction was small but bigger than the 90° v-notch. The width of the flow changed a little but

the changing was more than 90° v-notch.

CONCLUSION:

In the experiment, the coefficient of discharge (Cd) was determined for the three types of weir,

which are rectangular weir, 60° and 90° v-notch weir. From the result, the average of Cd obtained

of rectangular weir is about 0.636. The average of Cd obtained is about 0.760 for the 60° and 90°

v-notch weir. The characteristics of the water flow over weirs are observed. From the

observation, the nappe of flow over rectangular weir is clinging while the nappe of flow over v-

notch weir is sprung clear. The objectives of the experiment are met.

REFERRENCE:

1. Ms. Hidayah Bt. Basri, CEWB 221 Hydrology & Hydraulic Engineering 1 Laboratory

Manual, Department of Civil Engineering, Universiti Tenaga Nasional