TABLE OF CONTENT

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.

PAGES

1 SUMMARY 1

2 OBJECTIVE 2

3 THEORY 2 - 4

4 EQUIPMENTS 4 - 5

5 PROCEDURES 5

6 DATA AND OBSERVATIONS 6 - 8

7 DISCUSSION 9 - 10

8 CONCLUSION 10

9 REFERENCES 10

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SUMMARY:

This experiment is conducted to determine the coefficient discharge (Cd) for different notches where

Hydraulics Bench was used. Flow Over a Notch was used together with Hydraulics Bench to measure the flow rate

against height of liquid over a Rectangular Notch or a V-Notch. Three types of notches were used in this experiment,

namely the Rectangular Notch, V-Notch 60˚ and V-Notch 90˚. All notches are 100mm in depth.

In the beginning, water was let flow in the Hydraulics Bench until it overflowed through the notch. Then, the

flow control valve was closed. When the flow was in a steady state, the water surface was made sure at the level with

the opening of the notch. The water level, Ho was measured and recorded by using the hook and point gauge. After

that, the flow control valve was opened and water with flow rate of 15L/min was allowed to flow and the water level

in the channel was recorded after the flow rate has reached a steady state. At the same time, the flow rate of water was

determined by recording the period for the water in the water meter to reach 4litre. The experiment was repeated for

flow rate of 30, 45, 60 L/min. After that, type of notch was changed and the whole experiment was carried out by

using 3 types of notches as mentioned above.

Lastly, calculation was done to determine the coefficient of discharge, Cd for different notches. Graph of

Discharge (Q) versus Height of Notch (H) and graph of log Discharge (Log Q) versus log Height of Notch (Log H)

were plotted. In sum, the experiment was conducted successfully.

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GENERAL DESCRIPTION:

Flow over a Notch is equipment for use together with Hydraulics Bench to measure flow rate against height of liquid

(water) over a rectangular notch or a V-notch. It allows water to be routed through a structure of known dimensions,

permitting flow rates to be measured as a function of depth of flow through the structure. Thus, this is the simplest and

most accurate method of measuring water flow in an opened channel. In its simplest form, a weir consists of a

bulkhead of steel with an opening of fixed dimensions cut in its top edge. The opening is called the weir notch; its

bottom edge is weir crest and the depth of flow over the crest (measured at a specific distance upstream from the

bulkhead) is called the head (H). Besides, the hydraulic bench we used has been divided into three sections: the first

section corresponds to a plenum chamber, in order to obtain a laminar for flow; the second corresponds to a shallower

channel section, where the notch is located; the third corresponds to the water outlet tank.

As a brief introduction, the main component of the equipment are stainless steel V-notch (60˚and 90˚) with the depth

of 100m, stainless steel rectangular notch 50mm or 30 mm wide and 100mm deep, and also stainless steel vernier

hook and point gauge with range of 0-150mm and 0.05mm reading. Through the experiment, we can measure the flow

rate of different type of notch and calculate the coefficient of discharge for a variety of different shape notches. After

all the data have been recorded and calculated, we are now able to plot the graph of discharge (Q) versus Height of

Notch (H) and also the graph of log Discharge (Log Q) versus log Height of Notch (Log H).

OBJECTIVE:

To measure the flow rate and determine the coefficient of discharge and head of variation for variety kinds of notches.

THEORY:

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

Point 1 = A point at a distance upstream from the notch (usually 4 times the height from the notch bottom)

Point 2 = A point above of the notch.

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Assume there is no energy loss between point 1 and 2

V 1 2 / 2 g + P 1 / γ + Z 1 = V 2 2 / 2 g + P 2 / + Z 2 (EQN 1)

V = velocity of water, m / sP = pressure, N / m 2

Z = height of water above lowest point of the depth, m

γ = specific gravity, N / m 3

g = acceleration due to gravity, 9.81 m / s 2

h = height of water above point 2, mH = height of water above lowest point of the notch, m

Since the Hydraulics Bench channel is much wider than the notch width, we can assume V 1 is very slow, thus V 1 = 0.

Total head at point 1 = Ht = 0 + P 1 / γ + Z 1 (EQN 2)

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

Hence V 2 2 / 2 g + P 1 / γ + Z 2 = Ht = H (EQN 3)

At point 2, P 2 = atmospheric pressure = 0

H = V 2 2 / 2 g + Z 2 (EQN 4)V 2

2 / 2 g = H - Z 2 = h

V 2 = √ ( 2 g h ) (EQN 5)

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

RECTANGULAR NOTCH:

b = width of notch

dQ = 2 √ ( 2 g h ) ( H – h ) tan θ

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Q = ∫o H √ ( 2 g h ) b d h

Q = ( 2 / 3 ) √ ( 2 g ) b H 3 / 2 (EQN 6)

V – NOTCH:

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

dQ = 2 √ ( 2 g h ) ( H – h ) tan θ dH, 2 θ = V –notch angle

Q = 2 ∫o H √ ( 2 g h ) ( H – h ) tan θ dH

Q = ( 8 / 15 ) √ ( 2 g ) H 5 / 2 tan θ (EQN 7)

In actual flow, the cross section of water after passing the notch will be slightly reduced due to vena contracta. Thus the actual flow will be slightly below that of theory.

Rectangular notch, Q = C D ( 2 / 3 ) √ ( 2 g ) b H 3 / 2 (EQN 8)

V – notch ( 90 o ), Q = C D ( 8 / 15 ) √ ( 2 g ) H 5 / 2 tan 45 o (EQN 9a)

V – notch ( 60 o ), Q = C D ( 8 / 15 ) √ ( 2 g ) H 5 / 2 tan 30 o (EQN 9b)

Where C D = Coefficient of discharge

In practice, calculations may be made through logarithm

For rectangular notch, log Q = log K 1 + ( 2 / 3 ) log HFor V – notch, log Q = log K 2 + ( 5 / 2 ) log H(K 1 and K 2 = constant)

EQUIPMENT / DESCRIPTION OF EXPERIMENTAL APPARATUS:

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Description of equipment:

The hydraulic Bench supplies water to the wide end of the tank. Water flows through the channel and over

the notch, where the deep tank exit allows students to clearly observe the discharge. Students measure the

free water surface by using an adjustable depth gauge attached to a beam across the channel. The tank outlet

fits over the weighing tank of the hydraulic bench.

Specification of equipment:

1.1 Stainless steel V-notches: 90 and 60. Depth of notches are 100mm

1.2 Stainless steel rectangular notch 50mm or 30mm wide and 100mm deep

1.3 Stainless steel vernier hook and point gauge with range of 0-150mm and 0.05mm reading.

PROCEDURES:

1. The pump (hydraulic bench) is turned on and the flow control valve is slowly opened until water

flowing over the notch. Then the pump is stopped. It is waited until the flow has stopped and then the

water level in the channel (H0 ) is recorded by level gauge at the side of the channel or hook and

point gauge, which is more accurate.

2. The discharge valve of the measuring tank is opened.

3. The pump is started again and the flow control valve opened until the flow rate in the flow meter is

around 15L/min. The flow is allowed to continue for at least 1 min to obtain a steady state, then the

level in the flow channel is recorded by hook and point gauge (H1 ).

4. The measuring tank discharge valve is closed and the clock is started when the level reaches “0” and

the clock is stopped when water reaches required level (volume =4L).

5. Step 3 to 4 are repeated at flow rate of about 30, 45, 60 L/min or until water level in the open channel

is near the maximum.

6. The notch is changed to other type or size and step 3 to 5 are repeated.

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Note:

Types of the notches:

Rectangular notch weir 5cm wide

V- notch 60°

V- notch 90°

DATA AND OBSERVATIONS:

Flow rate in flow

meter (L/min)

Volume of

Measuring Tank

(L)

Time (sec)

Flow Rate,

Q (L/min

)

Level above

the Notch

H1 (cm)

H (cm)

Log Q (L/min

)

Log H (cm)

Cd

Rectangular notch

Weir 5cm wide

10 441.8

45.74 10

1.260

0.759 0.100 0.458

15 429.5

68.12 10

1.259

0.910 0.100 0.649

20 421.3

511.24 10

1.254

1.051 0.098 0.904

25 4 16 15.00 101.25

21.176 0.098 1.209

V-notch 90

10 4 57.4 4.18 7.41.34

60.621 0.129 1.403

15 435.0

66.85 7.4

1.348

0.836 0.130 2.291

20 429.1

58.23 7.4

1.348

0.915 0.130 2.752

25 4 29 8.28 7.41.35

00.918 0.130 2.759

V-notch 60

10 453.3

14.50 9.8

1.060

0.653 0.025 4.753

15 4 22.5 10.67 9.81.06

01.028 0.025

11.271

20 421.8

710.97 9.8

1.058

1.040 0.02411.64

3

25 418.3

113.11 9.8

1.059

1.118 0.02513.88

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GRAPHS:

0 1 2 3 4 5 6 7 805

1015202530354045

Graph of Q vs H

rectangular notchV-notch 90V-notch 60

H (cm)

Q (L

/min

)

For graph Q vs. H we are going to get most likely a curve line graph as above. As we can see, the flow rate,

Q for each notch is the same initially for the rectangular notch and V-notch 90. While the height, H is

increasing start from rectangular notch, then v-notch 90 and last v-notch 60.

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.91.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.65

Graph Of Log Q vs Log H

rectangular notchV-notch 90V-notch 60

Log H

Log

Q

For graph Log Q vs. Log H we are going to get most likely a straight line graph as above.

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CALCULATIONS:

For Rectangular notch:

We use the flow rate of 15L/min in flow meter as the example:

Flow rate, Q = 4Lt x 60 41.84 s

= 5.74 L/min

Coefficient of discharge Cd =

32

Q

√2 g bH 3/2 = 0.458

For V-Notch 90o:

We use the flow rate of 15L/min in flow meter as an example:

Flow rate, Q = 4Lt x 60 57.40s

= 4.18 L/min

Coefficient of discharge Cd =

Q×15

8√2 g tan 45ο H5 /2 = 1.403

For V-Notch 60o:

We use the flow rate of 15L/min in flow meter as an example:

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Flow rate, Q= 4Lt x 60 53.31s

= 4.50 L/min

Coefficient of discharge Cd =

Q×15

8√2 g tan 30ο H5/2 = 4.753

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DISCUSSION:

This experiment was conducted to determine the coefficient discharge (Cd) for different notches. The types of

notches used in the experiment were the Rectangular Notch, V-Notch 60˚ and V-Notch 90˚. All notches are 100mm in

depth. Two graphs were plotted based on the results of the experiment. The first graph was Graph of Q versus H.

Based on the graph, it was found that the flow rate of the water is directly proportional to the height of the water above

the notch. When the flow rate of the water increases, the height of the notch also increases. This implies for all the

three types of notches. Among all the notches, the rectangular notch has the highest flow rate at the same height.

Other than that, the values of the coefficient of discharge,Cd was calculated for all the notches at every height.

The value for the coefficient of discharge,Cd varies every height. Based on the theory, the expected value for the

coefficient discharge is expected to be around 0.6. Based on the experiment, the value for the coefficient of

discharge,Cd was either more or less than 0.6. This result could be due to mistakes and errors occurred in the

experiment.

Few errors might have occurred while conducting the experiment. The results of the experiment are inaccurate

due to the mistakes and errors that occurred during the experiment. These mistakes and the errors could be due to

human error, errors in the equipment and environment effects. One of the human errors was parallax error. When the

readings are being taken, the eye sight of the observer should be parallel with the readings in the equipment. When it

is not, the observer tends to take wrong readings. Hence, the results of the experiment are affected. The unsteadiness

of the water flow through the notches could be one of the errors of the experiment. When the water flow was not in the

steady state, we tend to obtain inaccurate value for the H1. This will cause a big difference in the theoretical and the

experimental values. Thus, this was the reason for a huge difference in the c d value for V-Notch 90˚ because the h1

value is so much smaller compared to readings for other flow rate in flow meter.

Besides that, it was difficult to make sure that the hook can accurately touch the surface of the water, as it is

not easy to detect with human eyes. Moreover, improper screwing of the screws which have caused water leakage also

might have led to the errors of the experiment. Other than that, water reflection was another reason for the inaccurate

results of the experiment. When the readings are being taken, there might be an occurrence of reflection between the

water surface and the readings. Thus, inaccurate readings are taken by the observer.

We need to take few precaution steps in order to avoid mistakes and errors in experiment. One of them is to

make sure that the equipment is in very good condition. The equipment’s must be supervised for any leakage and

should be in good condition in order to obtain accurate results. Besides that, the eye sight of the observer should be

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parallel with the reading of the apparatus in order to avoid the parallax error. Other than that, the water flow should be

in a steady condition before the readings are being taken. The hydraulic bench should be located on a level floor as it

may be affect if the bench top is not levelled. Lastly, the height gauge should be set to the datum reading by placing

the point on the crest of the weir. These entire precaution steps should be taken in the experiment conducted in future

in order to obtain accurate results.

CONCLUSION:

In conclusion, we are able to achieve the objective of this experiment where the flow rate and the coefficient of

discharge and head of variation for variety kinds of notches were determined. Based on the data observation, graph of

flow rate vs. height of notch and the graph of Log Q vs. Log H were plotted. It was found that the flow rate is

proportional to the height of the notch. The coefficient of discharge, Cd was calculated for all the three types of the

notches. The rectangular weir is more suitable for the area with high flow rate while V-shape weirs are only applicable

for area with limited flow rate. The values that are obtained are slightly more than the expected theoretical value

which should be around 0.6. This might be due to the mistakes and the errors that occurred in the experiment. Thus,

precaution steps should be taken in order to improve the accuracy of the results of the experiment.

REFERENCES:

1) Lab Manual for Hydrology & Hydraulic Engineering I Laboratory, 4th edition.

2) Hydrology & Hydraulic Engineering I Notes by Prof.Dr.Ir.Lariyah Mohd.Sidek

3) Applied Fluid Mechanics by Robert L.Mott

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