Broad Crested Weir

 

TITLE:

LAB REPORT ON BROAD CRESTED WEIR

 JOMO KENYA KENYATT TTA A

UNIVER UNIVERSITY SITY

OF AGRICULTURE

AND TECHNOLOGY

NAME: WABURI FRANCIS GA GATUBU  TUBU 

REG NO: EN251-3428/2013

COURSE: Bsc CIVIL ENGINEERING

UNIT: HYDRAULICS 1

UNIT CODE: ECE 2304

LECTURER: DR PHD KAZUNGU MAITAIRIA

SUBMITED ON: JAN 2015

 

Lab Report 2 TABLE OF CONTENT

CONTENT

PAGE

 

ABSTRACT

3

 

INTRODUCTION

3

    AIMS / OBJECTIVE     THEORY

3

3-4

    MATERIAL

5

    METHOD

6

    RESULTS

7-9

    CALCULATION

9-11

    DISCUSSION

11

    CONCLUSION

12

    RECOMMENDATION

12

    LITERATURE CITED

14

    APPENDICES

14

2

 

Lab Report 2 A BSTRACT

Basic experiments were conducted on rectangular broad-crested . It was found that the discharge coefficient of a rectangular broad-crested weir is related to upstream total head above the crest, length of weir and Channel breadth. Multiple regression analysis equations based on the dimensional analysis concept were developed for computing the discha dis charg rge e coeffi coefficie cient nt of a re recta ctang ngula ularr broa broad-c d-cre reste sted d weirs weirs an and d disch dischar arge ge coeffi coefficie cient nt eq equat uation ion was was used used fo forr comput computing ing the discha discharge rge ov over er the broad broad-cr -crest ested ed weirs weirs.. Good Good agreements between the measured values and the values computed from the predictive eq equat uation ion are are ob obtai taine ned. d. There Therefor fore, e, a re relia liable ble eq equat uation ion for calcu calculat lating ing the discha discharge rge coefficient of rectangular broad-crested weirs in subcritical flow conditions is presented.

INTRODUCTION OBJECTIVES

1)

To obs obser erve ve the the cha chang nge eo off tth he st stat ate e of of ffllow. ow.

2)

To cali calibr brat ate e a lab labor orat ator oryy-sc scal ale e roun roundd-no nose se b bro roadad-cr cres este ted d weir weir..

3)

To comp compare are the coeffic coefficient ient of dischar discharge ge obtain obtained ed by the experi experimen mentt with with that that by by

British Standard (BS3680, Part 4f).

THEORY A weir is commonly used in open channels for controlling upstream water levels and measuring discharge. For both tasks it acts as an obstruction which promotes a condition of minimum specific energy in sub critical flow. When used for the latter purpose all weirs must be calibrated because theoretical predictions of discharge are rendered inadequate by the effects of viscosity viscos ity and the variations of flow geo geometry metry with upstream depth. Broad crested weirs are generally constructed from reinforced concrete and are widely used for flow measurement and regulation of water depth in rivers, canals and other natural open channels.

3

 

Lab Report 2 A weir weir in gene genera rall can can ta take ke on many many shape shapes, s, howe howeve verr br broa oad d crest crested ed weir weirs s operate more effectively than their sharp crested counterparts under higher downstream  water levels, and can be used use d to measure the discharge of rivers since the parallel flow caused by the weir allows it to be accurately analyzed by the use of energy principles and critical depth relationships. It works on the principle that subcritical flow upstream of the weir moves over the obstruction and this height of the weir causes critical flow, accelerating the liquid which then transition transitions s into supercritical supercritical nappe nappe after the weir is crossed downstream. downstream. This critical depth required to cause critical flow is not easily measured because its exact location is not easy to determine and may vary with flow rate. However, the upstream depth can be used to determine the flow rate through mass conservation which is a more reliable measurement. Experimentally, broad crested weirs can be used as a flow rate-measuring device and has the advantage that it is simple to construct and has no edge that can wear and thus alter the coefficient.

Using Bernoulli’s equation, it can be derived that

[(  ) ]

v 12 Q =1.705 B 2g

1.5

+ H 1

.

Furthermore, the discharge is related to a coefficient of discharge for the weir, C d,

defined by the equation   Q=CdCv

()√ 2 3

B

2g 3

 H 1

3 2

.

4

 

Lab Report 2

FIGURE 1

MATERIALS 1. Round-nose Round-nose broad-cr broad-crested ested weir with with rubber rubber packing’s. packing’s. 2. A steady steady water water supp supply ly syst system. em. 3. An adjustableadjustable-slope slope rectang rectangular ular open open channel channel with point point gauge. gauge. 4. A v-notc v-notch h with with a hook hook gauge. gauge. 5. A stee steell tape tape mea measur sure. e. 6. A th ther ermo mome mete terr.

METHOD 1) The dimensions dimensions of the the broad-cres broad-crested ted weir were were taken taken and the distances distances from from section 2A to section 2F were taken. 2) The open channel channel was then then set horizont horizontal al and the temperat temperature ure of the water water measured. 3) The crest level level of the broad-cr broad-crested ested weir weir and that of of the channel channel bed were were determined using a point gauge. 4) The level of of the v-notch v-notch pouring pouring the water water up to the crest crest level level was determined determined using a hook gauge and values got recorded. 5) The operation operation of the the steady water water supply supply system system was started started and the the discharge discharge  was set small. 6) The head above above the the v-notch v-notch was measured measured after after the the flow flow was steady steady 7) The depth depth of flow in the the upstream upstream where where the weir does does not exert exert influence influence on the  water surface was determined and recorded recorded (section 1). 8) The changes changes of state of of flow by the the broad-crest broad-crested ed weir were were observed observed and the section where the control section occurs was noted, letting a drop of water fall on the surface of flow. flow. 5

 

Lab Report 2 9) The discharge discharge was was then increas increased ed and procedur procedure e 6 and 7 repeate repeated. d. 10)One flow was selected and the depth of flow at section 2A -2F were determined. .

RESULTS TITLE: EXPERIMENT OF BROAD-CRESTED WEIR Date: 10/29/2014   No. : 02 ***FUNDAMENTAL ***FUNDA MENTAL DATA*** DATA*** Properties of Water

Temperature

21°c

Density (ϸ)

997.996 kg/m3

Width (B)

0.30 m

Length (L) Height (Z)

0.30 m 0.15 m

1-0.006L/B

0.994

Crest level (point gauge)

0.626m

Property of channel

Bed level (point gauge)

0.475 m

Properties of V-notch

Half angle of V-notch

45°

Coefficient of discharge(Cdv)

0.859

Coefficient (Kv)

1.42

Dimensions of broad crested  weir

6

 

Lab Report 2 Crest level (hook gauge)

0.216 m

***Operation Data*** V- notch Stag e

Section 1

Readi 

Hea

Dischar 

ng

d (m)

 ge (Q)

Readin

Dept 

 gs (m)

h (H 1 )

H1-Z   

L /

(m)

H 1-Z 

Specific energy Velocit

Velocit 

y of flow

 y head  ×10-5 m

Es

The oret  ical 

C dd  

C ddt t 

  (m)

×10-3m/s

t  (Q )

m/s

(m)

1

0.15 5

0.06 1

1.305

0.647

0.172

0.02 2

13.6 4

0.02 5

3.186

0.02 2

1.66 4

0.78 4

0.93 4

2

0.14 8

0.06 8

1.712

0.650

0.175

0.02 5

12

0.03 3

5.550

0.02 5

2.01 6

0.84 9

0.94 1

3

0.14

0.07

2.187

0.654

0.179

0.02

10.3

0.04

8.568

0.02

2.51

0.86

0.94

1

5

9

4

1

9

9

8

8

4

0.13 4

0.08 2

2.734

0.658

0.183

0.03 3

9. 9.09 09

0.05 0.05 0

12.74 2

0.03 3

3.05 7

0.89 4

0.95 4

5

0.12 7

0.08 9

3.356

0.662

0.187

0.03 7

8. 8.1 11

0.06 0.06 0

18.34 9

0.03 7

3.63 0

0.92 5

0.95 8

6

0.12 2

0.09 4

3.847

0.665

0.190

0.04 0

7.5

0.06 7

22.88 0

0.04 0

4.08 0

0.94 3

0.96 1

7

0.11 7

0.09 9

4.379

0.670

0.195

0.04 5

6. 6.67 67

0.07 0.07 5

28.67 0

0.04 5

4.86 8

0.90 0

0.96 4

7

 

Lab Report 2 8

0.11 1

0.10 5

5.073

0.673

0.198

0.04 8

6. 6.25 25

0.08 0.08 5

36.82 5

0.04 8

5.36 3

0.94 6

0.96 6

9

0.10 5

0.11 1

5.829

0.679

0.204

0.05 4

5. 5.56 56

0.09 0.09 5

45.99 9

0.05 4

6.40 0

0.91 1

0.96 9

10

0.09

0.12

7.689

0.688

0.213

0.06

4. 4.76 76

0.12 0.12

73.39

0.06

8.25

0.93

0.97

2

4

0

4

4

7

1

3

Cdm

Cdtm

=

=

0.89

0.95

5

7

3

*******FUND AMENTAL DATA***** *******FUNDAMENTAL DATA***** Selected stage Actual discharge [Qa] Crest level of the weir Width of the weir [B] ****** OPERATION O PERATION DATA****** DATA****** section Distance Water from level section 2A [point (m) gauge] 2A 0.0 0.680 2B 0.05 0.671 2C 0.1 0.667 2D 0.15 0.664 2E 0.20 0.663 2F 0.25 0.653

10 7.689x10 m /s 0.626 m 0 .3 m -3

Depth m

0.054 0.045 0.041 0.038 0.037 0.027

Velocity of flow[v] (m/s) 0.475 0.5696 0.625 0.674 0.693 0.949

Propagatio n velocity[u] m/s 0.728 0.664 0.634 0.611 0.602 0.515

3

Froude number [Fr] 0.653 0.858 0.986 1.103 1.151 1.843

SAMPLE CALCULATIONS All readings for distance were taken in Millimetres so a conversion factor of 0.001 was used to convert it to meters. 5

Actual Discharge, Qa

2 = Kv   Hv  

Where kv-cofficient of v notch,  

Hv- Head above v north 2.5

=1.42x0.061

8

 

Lab Report 2 −3

1.302 X 10

=

3 -1  m s

Upstream velocity, v1  Q=

  A v1

 

Q  A  

v1 =

1.305  x 10

v1 =

−3

(0.3 x 0.172 )  

= 0.02 0 .025 5 ms m s-1

[ ]   [  ] 2

 v 1

Velocity Veloc ity head =

2g

0.0252 19.62

 

=

 

=3.186 x10 -5 ms-1 2

v1 2g

Specific energy (E) = H1 – Z +

 

=0.172 – 0.15 +3.186 x10 -5 

=0.022 J

2

=

Critical Depth (HC)

=

3

 E

 

2  X 0.022   3

Theoretical Discharge, Qt =

=0.015m

1.705 B

[

2

 v 1

2g

+ H 1

]

3 2

9

 

Lab Report 2

 

=

[

2

0.025 1.705 ( 0.3 )   + 0.172 19.62

]

3 2

 

3 -1 = 1.66 1. 664x 4x 10 1 0-3   m s

Qa

Co-efficient of Discharge, Cd

=

Q t   

=

1.305 1.664  

= 0.784 Value of =

 L ( H 1− Z )

 

= 0.3/0.022

 

=13.64

1−

0.003 L

 H 1− Z  ) 3/2 Theoretical coefficient of discharge (Cdt) = ( 0.006  L   ¿¿ 1− B 0.003 x 0.3

 

= (1-0.006X0.3/0.3) (1 –

 

= 0.934

0.172−0.15

  ) ^1.5

CALCULATIONFOR SECTION 2 (selected section 10) CALCULATIONFOR 10

 

Lab Report 2 Q  A

Velocity Veloc ity of flow (v) =

−3

 

7.689 x 10 = 0.3 x 0.054

 

=0.475m/s

Propagation velocity of long waves, v=   √ gH  9.81 x 0.054   =   √ 9.81

 

=0.728m/s

v

Fr Froud oude e Numbe Numberr, Fr =

=

gH    √ gH 

0.475 9.81 x 0.054   √ 9.81

= 0.653

AGRAPH OF Cd AGANAIST H1

11

 

Lab Report 2 1 0.9 0.8 0.7 0.6 Cd

0.5 Cd vs H1

0.4 0.3 0.2 0.1 0 0.17

0.18

0.19

0.2

0.21

0.22

0.23

H1

AGRAPH OF Qa AGANIST H1 0.01 0.01 0.01 0.01 0.01 Qa

0 Qa vs H1

0 0 0 0 0.17

0.18

0.19

0.2

0.21

0.22

0.23

H1

12

 

Lab Report 2

A GRAPH OF Log Qa AGANIST Log E

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

0 -1.1 -0.5 -1 -1.5

Log Q a

Log Q a vs Log E

Linea r (Log Q a vs Log E) -2 -2.5 -3 Log E

DISCUSSION AND ANALYSIS OF RESULTS Froude Number at Broad Crested Weir Edge The Froude numbers calculated at the edge of the broad crested weir i.e. the Froude numbers fell well out of the expected range. range. Since the flow upstream of the weir  was subcritical and the flow at the edge of the weir theoretically is supposed to be critical, criti cal, a value close to 1 was expected. expected. The values obtained obtained ranged between between 0.6531.843.This 1.843. This may have been due to erroneous erroneous measurement measurement or calculatio calculation. n. The only sense that could be made of these very high Froude numbers is that the liquid achieved a very high velocity hence a high energy (both total and specific).

13

 

Lab Report 2 Magnitude of Flow Rate and Effect on Discharge Coefficient C d It was was fo foun und d th that at as th the e magn magnit itud ude e of th the e fl flow ow rate rate in incr crea eased sed,, so di did d th the e discharge discha rge coefficie coefficient. nt. This may have been due to the shape of the weir whic which h had a rectangular control section. Since the height of the water iincreased ncreased with increased flow flow,, more friction loosed may have occurred. Relationship Between Cd and Flow Rate Experimental data showed that Cd increased with increasing flow rate. Magnitude of Flow Rate and Effect on Velocity Coefficient C v It was found that as the magnitude of the flow rate increased, so did the velocity coefficient. Relationship Between C v and Flow Rate Experimental data showed that Cv increased with increasing flow rate.

Pattern of Water Over Weir  Test  Test no.1

14

 

Lab Report 2

Errors & Precautions

  Error due to parallax in reading the vernier scale and tank.   The flow may not have been fully stabilized when the readings were taken. Reaction time error when using the stopwatch.

  CONCLUSION Within Withi n the limits of experimenta experimentall error, error, it was found that both the discharge and velocity coefficient are directly directly influenced by the flow rate. Also, nappe patterns of flow  were observed.

RECOMMENDATION

i)

The The rea readi ding ngs s of heig height ht shou should ld be tak taken en car caref eful ully ly by avo avoid idin ing g sight sight er erro rorr. The The time collection should be taken much appropriately. appropriately.

ii ii))

The The expe experi rime ment nt sho shoul uld d be carr carrie ied d out out by al alll civi civill engi engine neer erin ing g stud student ents s in ord order er to appreciate the theory learnt in class.

LITERA LITERATURE TURE CITED.

1. Daug Daughe hert rty y, Rober Robertt L. Hydraulics. New York: McGraw-Hill Book Company, Inc, 1925. Print. 2. Harr Harris is,, Char Charle less W. W. Hydraulics. New York: J. Wiley, 1936. Print. 3. King, Horace Horace W, W, Chester O. Wisler, Wisler, and and James G. Woodburn Woodburn..  Hydraulics. New N ew York: York: J. Wiley, 1948. Print. 4. Simon, Simon, Andrew Andrew L, and and And Andrew rew L. Simon Simon.. Hydraulics. New York: Wiley, Wiley, 1986. Print.

15

 

Lab Report 2

5. Lecturer’ Lecturer’ss note note and lab hard outs by Dr  Dr.PHD .PHD K. Maitairia, 2014.Print.

APPEDICES

  The images show some applications of broad-crested weirs

16