TABLE OF CONTENT

NO. PAGES

1 SUMMARY 1

2 EQUIPMENTS 2

3 OBJECTIVE (4.1) 3

4 THEORY(4.1) 3

5 PROCEDURES (4.1) 4

6 DATA AND OBSERVATIONS (4.1) 4 - 5

7 OBJECTIVE (4.2) 6

8 THEORY(4.2) 6 - 11

9 PROCEDURES (4.2) 11

10 DATA AND OBSERVATIONS (4.2) 12 - 13

11 OBJECTIVE (4.3) 14

12 THEORY(4.3) 14 - 15

13 PROCEDURES (4.3) 15

14 DATA AND OBSERVATIONS (4.3) 16

15 DISCUSSION 17 - 18

16 CONCLUSION 19

17 REFERENCES 20

0

SUMMARY:

This experiment is divided into three parts; first is The Critical Depth-Derivation of the Specific Energy

Equation, second part of the experiment is the Hydraulic Jump and the third part is Flow over Broad Crested Weir. In

the first part of the experiment we were required to determine the critical depth (yc ) and the specific energy (E) of an

open channel flow. The flow rate of the water used was constant through out the experiment. The sluice gate was

adjusted to allow the water flow over it and it was not disturbed for few minutes in order to obtain a more stable and

steady flow reading. Then, the height of the sluice gate (y g ) and the reading of ( y1 ) were taken. After that, the flow

rate of the water was recorded by taking down the time which needed to collect 40-liter water. Finally, the value ofyc ,

E1 and Emin was calculated from the collected data.

The second part of the experiment was conducted by adjusting the valve to allow the water passing through the

weir without adjusting the sluice gate. Different height of Y 2 and Y 3 was obtained by varying the flow rate of the

water. Since the hydraulic jump just occurs for a couple of moments, it was very important to mark the height of the

water level before and after the hydraulic jump. Then, the flow rate of the water was obtained by taking the time for

water in manometer to reach 40-liter. The value of energy loss and the value of froude number were obtained from the

collected data. The type of the hydraulic jump was determined based on the Froude number.

In the third part of the experiment, we were required to determine the discharge in a rectangular channel and

compare the theoretical and experimental flow rate over a broad crested weir. At first, the valve was opened to allow

the water flow. Then, the height (Z) was recorded and the depth (D) of water from the bottom of the channel was

determined after few minutes. After that, the flow rate was measured by taking down the time needed to collect 40-

liter water by using the manometer and stopwatch. From the data obtained, the theoretical (Qtheo ), and experimental (

1

Qexp ) discharge were calculated based on the collected data and finally, the coefficient of discharge (Cd ) was

calculated by using the formula given.

2

EQUIPMENTS / DESCRIPTION OF THE EXPERIMENTAL APPARATUS:

Description of Equipment:

Adjustable undershot weir

Instrument carrier

Hook and point gauge

Stop watch

Rulers

This is a self-contained open channel with rectangular cross section supported by rectangular steel frame. Sidewalls

are transparent to allow full visual observation and are supported by adjustable steel frames to ensure accurate wall

alignment. A screw can adjust the middle section of the bed manually upward or downward. Tilting can also be

adjusted by a manual screw jack.

3

1. THE CRITICAL DEPTH –

DERIVATION OF THE SPECIFIC ENERGY EQUATION

OBJECTIVE:

To determine the critical depth of the flow passing the weir.

THEORY:

The specific energy E in an open channel is equal to:

E = y + V2/ 2g = y+ Q2/ 2gb2y2

E reaches its minimum for critical y = yc or

dE/dy = 0 = 1 – 2Q2/2gb2y3

Therefore,

y = yc = 3√ (Q/gb) … (1)

And,

Emin = 1.5yc

4

PROCEDURES:

1) The adjustable weir was placed vertically in position with its bottom edge 15 mm above the flume bottom.

2) The values of E1 and y1 were measured.

3) The procedures from step 1 to 2 were repeated by changing the values of yg with 20mm, 25mm, 30mm, and

plot E1 and Q1 against y1.

4) The corresponding yc and Q was derived from the plotting Emin and these values were compared with the

calculated yc using formula (1).

DATA AND OBSERVATIONS:

THE CRITICAL DEPTH

Width of channel = 0.10 m

Yg

(m)

Y1

(m)

V

(L)

T

(s)

Q

(m3/s)

E1

(m)

Yc

(m)

Emin

(m)

0.15 0.012 40 39.20 1.02 x 10-3 0.018 0.022 0.033

0.20 0.018 40 40.90 9.78 x 10-4 0.027 0.021 0.032

0.25 0.022 40 37.50 1.07 x 10-3 0.033 0.023 0.035

0.30 0.028 40 10.70 3.74 x 10-3 0.042 0.052 0.078

CALCULATIONS:

5

For yg = 0.15; 40 L = 0.04 m3

Q = V/T = 0.04/39.2 = 1.02 x 10-3 m3/s

E1 = 1.5 y1 = 1.5 x 0.17 m = 0.018 m

y = yc =

3√ Q2gb 2 = [ (1.02x10-3)2 / (9.81)(0.10)2]1/3 = 0.022m3

Emin = 1.5 yc = 1.5(0.022) = 0.033m3

6

2. THE HYDRAULIC JUMP

OBJECTIVE:

To observe the phenomena called the hydraulic jump and to identify the characteristics and types of hydraulic jumps.

THEORY:

Vο² fluctuating water surface

2g

e

total head line

e V42

conjugate 2g

depth line e ΔE

V ₁ ² H1 e e

2g or critical depth

Hο yo E1 line

7

or

Eο Y4 H4

yc y3 or

Vg V1 Y1 Y2 V2 V3 E4

V4

Section ⓞ section ① section ② section ③ section④

Water within control volume.

The hydraulic jump is a phenomena where the water mass dissipates energy

NEWTON’S law gives us:

Q1V1 + A1 Z1 = Q2V2 + A2 Z2

g g

( no loss of momentum)

For square channels (Q = bq)

q + y 2 = q + y 3

8

gy2 2 gy3 2

or

q = y2y3

g 2(y2 + y3 ) ……………………………………….(1)

Bernoulli’s equation:

Y2 + V22 = y3 + v3

2 + ΔE

2g 2g

With Q = bq

ΔE = (y2 –y3) + q 2 1 – 1

2g y2 y3 …………………………………………………….(2)

(1) and (2) gives us:

ΔE = ( y3 – y2 ) ……………………………………………(3)

4y2 y3

or ΔE = E2 – E3 = y2 + V22 - y3 + V3

2 = (y3 –y2)3 …………….(4)

2g 2g 4y2 y3

Types of Hydraulic Jump

9

Froude = √ V 2

gh

With V = velocity (m/s), g = gravity acceleration = 9.81m/s2 and h = height (m)

1. Fr < 1.7: Undular jump

h2 is mostly lower than the critical depth.

2. 7 < Fr < 2.5: Weak jump

The energy dissipation is small.

E = 10, 15% of total energy

3. 2.5 < Fr < 4.5: Oscillating jump

10

h2

This is a very dangerous jump, which causes a lot of damage down streams.

4. 4.5 < Fr < 9: Steady jump

This is the most favored jump: string energy dissipation with almost no damage (40, 70%).

5. 9 < Fr: Strong jump

The jump includes very strong energy dissipation.

6. The submerged jump: occurs under gate

11

PROCEDURES:

1. Water flow was allowed to flow over the sluice with the desired flow rate.

2. The weir was then adjusted to form an ideal hydraulic jump.

3. The value of flow depth upstream and downstream, y2 , y3 and time, t was measured.

4. The above procedures were repeated for 3 times.

5. E was calculated by referring to data obtained.

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DATA AND OBSERVATIONS:

THE HYDRAULIC JUMP

Width of Channel = 0.1 m1 2 3 4 5 6 7 8 9 10 11 12 13 14

Volume

of

Measuri

ng tank

(L)

Time

(s)

Flow

Rate

Q = V

T

(m3/s)

Y2

(m)

Y3

(m)

A2 =

Y2b

(m2)

A3 =

Y3b

(m2)

V2=

Q/A2

(m/s)

V3=

Q/A3

(m/s)

Fr2 Fr3 E2

(m)

E3

(m)

Δ E

(m)

413.78 2.90 x

10-4

5 8 0.50 0.80 5.8 x

10-4

3.6 x

10-4

8.28

x10-5

4.06x

10-5

1.01

9

0.637 0.382

412.90 3.10 x

10-4

5 8 0.50 0.80 6.2 x

10-4

3.9 x

10-4

8.85

x10-5

4.40x

10-5

1.01

9

0.637 0.382

417.75 2.25 x

10-4

5.5 8.2 0.55 0.82 4.1 x

10-4

2.7 x

10-4

5.58

x10-5

3.01x

10-5

0.92

7

0.622 0.305

4 L = 0.004 m3

13

CALCULATIONS:

Given, Volume of measuring tank, V = 4 L or 0.004 m3

T = 13.78 s b = 0.10 m Y2 = 5 m Y3 = 8 m

Q = V / T

= 2.90 x 10-4 m3/s

A2 = Y2 b

= 0.50 m2

A3 = Y3 b

= 0.80 m2

Fr2 = (V2 / gy)1/2

= 8.28x10-5

Fr3 = (V3 / gy3) 1/2

= 4.06x10-5

V2 = Q / A2

= 5.8 x 10-4 m3

V3 = Q / A3

= 3.6 x 10-4 m3

E2 = 1.5Y2

= 1.019 m

E3 = 1.5Y3

= 0.637 m

ΔE = E2 - E3

= 0.382 m

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3. FLOW OVER BROAD CRESTED WEIR

OBJECTIVE:

To compare the Qtheo and Qexp for flow over broad crested weir.

THEORY:

Subcritical Critical Supercritical

H

Flow D

Z

A broad crested weir can be used as a flow measuring device to determine the discharge Q in a

rectangular channel. The theoretical discharge for critical flow over a broad crested weir of width B

is given by;

Qtheo = Cd (1.705) BH3/2

15

The actual flow in the channel is obtained by a coefficient of discharge Cd. The actual flow in the

channel is ;

Qact = Cd (1.705) BH3/2

The coefficient of discharge is dependent on the type of shape of the broad crested weir.

Measure the height of weir Z and width of flume B.

Cd = Qexpt / Qtheo

PROCEDURES:

1. The widths of flume, B and the height, Z and of the weir were measured.

2. The water flow was allowed to pass through the broad crested weir.

3. The flow rate was calculated by recording the time interval for volume of 40L.

4. The flow rate of the experiment was adjusted and the water depth was measured and recorded.

5. The theoretical and experimental discharge were calculated and compared.

6. This experiment was repeated for another 3 times.

16

DATA AND OBSERVATIONS:

FLOW OVER BROAD CRESTED WEIR

Z = 0.105 m

Volume

(m3)

Time

(sec)

Depth,

D

(m)

H=D-

Z

(m)

Qexp

(m3/s)

Qtheo

(m3/s)

Cd=

Qexpt/Qtheo

Qact

(m3/s)

0.04 32 0.142 0.037 1.25x10-3 1.21 x10-3 1.033 1.25x10-3

0.04 52 0.134 0.029 7.69x10-4 8.42 x10-4 0.913 7.69 x10-4

0.04 38 0.138 0.033 1.05x10-3 1.02 x10-3 1.029 1.05 x10-3

CALCULATIONS:

Given, V = 0.04m3 , T = 32s , D = 0.142m , Z = 0.105 m , B = 0.100 m

Qexp = V / T = 1.25x10-3 m 3/s H = D –Z = 0.037 m

Qtheo = 1.705 BH3/2 = 1.21 x10-3 m 3/s

Cd = Qexp / Qtheo = 1.033

Qact = Cd 1.705 BH3/2 = 1.25x10-3 m 3/s

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DISCUSSION:

In the first part of the experiment (The Critical Depth-Derivation of the Specific Energy Equation),

we were required to adjust the undershot weir in a flow channel to 15mm above the flume bottom. Then,

obtained Y1, which was the depth of the water level after flowing through the sluice gate. The volume of

water has been set to 40L through put the experiment. The time was recorded for storage 40L water. The

procedures were repeated for the height 20, 25, and 30mm above the flume. After that, E (i.e. the specific

energy of the channel) and the flow rate, Q were calculated. Then, the critical depth Y c and Emin was

calculated. The data in the table was mainly to derive the specific energy equation. Then, the graph of Y 1

versus E1 (Specific Energy Curves) was plotted.

In second part of experiment (Hydraulic Jump), we were required to perform the task of adjusting the

flow to form a hydraulic jump in the channel. The hydraulic jump is the phenomenon where the water mass

dissipates energy. In the experiment, the Froude no. was calculated as a guide to determine the type of

hydraulic jump formed. As the first part of the experiment, the water volume was fixed as 40L to calculate

the flow rate, Q. The flow rate, Q was slightly increased by turning the valve controlling the flow of fluid in

the hydraulic network. Then, the depth of water before the jump (Y2) and after the jump (Y3) was measured

and recorded in the table. The cross sections of both heights were calculated by using the width of channel,

B times the values Y2 and Y3. As a result, velocity before jump (V2) and after jump (V3) was calculated. By

using the formula given in the lab manual, the Froude No. (Fr) was calculated. The Froude No. before the

jump was used to classify the type of hydraulic jump. There are two different types of Froude numbers,

which is the Fr2 is always greater than one and Fr3 is less than 1. If the Froude number is less than 1, it

indicates the flows as sub-critical and the water flow has no opportunity to accelerate beyond the critical

velocity. But, when the Froude number is greater than 1, it is indicate as super-critical and the water flow

has been able to accelerate (over a hydraulic drop). The energy also was calculated by using the Bernoulli’s

Equation. The energy before the jump, E2 is always higher than the energy after the jump E3. Then, we found

the difference between E2 and E3, ΔE = E2 –E3.

In the third part of the experiment (Flow Over Broad Crested Weir), the weir was placed inside the

channel and it was screwed to avoid moving during the experiment. The height of the weir was measured as

Z, which was 0.105m, and base was 0.100m. In this experiment, we were required to determine the place of

sub critical, critical, and supercritical flows over the weir. We have found that the flow is usually sub critical

at the flow in front of the weir. Besides that, as the fluid hits the weir, it flows above the weir. It is known as

18

the critical portion of the flow.Tthe supercritical region was actually at the back of the weir where the flow

drops to a lower depth.

The Qtheo and Qact were then calculated using. The coefficient of discharge, Cd was calculated; Cd =

Qexp/Qtheo. The values we obtain for Cd in this experiment were quite close and similar to one another. These

values were Cd; 1.033, 0.913 and 1.029. Then, the values of Qtheo and Qexp were compared. In our results,

Qtheo and Qexp were slightly different. The value of experimental flow rate is always smaller than the

theoretical flow rate, this might due to the errors occurring during the experiment. Following are the results

of our Qtheo and Qexp.

Qtheo(m3/s) 1.21 x10-3 8.42 x10-4 1.02 x10-3

Qexp(m3/s) 1.25x10-3 7.69x10-4 1.05x10-3

One of the errors occurred in the experiment was the parallax error. The observer’s eye might have

not in parallel with the correct reading. Beside this, the slow response of the students when taking the

reading of time for the volume of the measuring tank to reach 40L could be another source of the errors.

Other than that, the adjustable undershot weir might have not in the right position at that particular distance

above the flume bottom. The following error could be the systematical error in which the rubber holding the

gate, has already lost its grip. In order to conduct the experiment without any errors, we must ensure the

laboratory equipments are in good condition. Besides that, we also must ensure that the weir is properly

controlled otherwise it will cause water leakage.

19

CONCLUSION:

1. The Critical Depth – Derivation Of The Specific Energy Equation

-As for the conclusion, the objective of this part of experiment which was to determine the critical depth

passing through the open channel was achieved. It is very useful in controlling the flow of water energy.

The specific energy of water that released can be determined by formula as shown before. It is very

important in designing the open channel. From the data tabulated and the plotted graph, the minimum

energy is 0.047m and the average critical depth obtained from this experiment is 0.031m.

2. The Hydraulic Jump

-As for the conclusion, the objective of this part of experiment which was to determine the type of

hydraulic jump and it characteristics was achieved. When a supercritical flow meets a sub-critical flow

of sufficient depth, a hydraulic jump occurs. During the hydraulic jump, energy loss will occur and the

Froude number will directly affected. The hydraulic jumps can be divided into few types according to

its flow rate. The Froude Number at the particular water flow can be determined by calculation. Based

on the experiment, two types of hydraulic jumps were found which were the undular jump and the weak

jump.

3. Flow Over Broad Crested Weir

-As for the conclusion, the objective of this part of experiment which was to compare the Q theo and Qexp

for flow over broad crested weir was achieved. Based on the experiment, we have found that higher

flow rate will rise the depth of flow on the board crested weir. However, there have the theoretical and

experimental value varies slightly. The theoretical value is always greater than experimental value

because there is a energy loss from the sub critical section to another section. It also caused by the

errors as mentioned earlier in the discussion part. Other than that, we also found that the velocity is

different for each section, but the coefficient discharge is always the same for the same weir.

20

REFERENCES:

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

ZetyizwanaZalaluddin.

2. Hydrology & Hydraulic Engineering I Notes by Prof.Dr.Ir.LariyahMohd.Sidek

3. Applied Fluid Mechanics by Robert L.Mott

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