weirs and notches

The topic of fluid mechanics

1. IN THE NAME OF ALLAH THE MOST
BENEFICENT, THE MOST MERCIFUL.

2. Dr. Ateeq-ur-Rauf
Fluid Mechanics-I
(CE-206)
Department of Civil Engineering,
U.E.T Peshawar (Bannu Campus)

3. Dr.Ateeq-ur-Rauf
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus) 3
Lecture # 4
Lecture # 11
Weirs & Notches
Fluid/Flow Measurements

4. 6/21/2022 4
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
NOTCH:
Anotchmaybedefinedasanopeninginonesideofatankor
areservoir,likealargeorifice,withtheupstreamliquidlevel
below the top edge of the opening.
Notches & Weirs
Upstream

5. 6/21/2022 5
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Thebottomedge,overwhichtheliquidflows,isknown
assillorcrestofthenotchandthesheetofliquidflowing
overanotch(oraweir)isknownasnappeorvein.
Anotchis,usuallymadeofa
metallicplateandisusedto
measurethedischargeofliquids.
Sincethetopedgeofthenotchabovetheliquidlevelserves
nopurpose,thereforeanotchmayhaveonlythebottom
edgeandsides.
Sill or Crest
Nappe

6. 6/21/2022 6
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
TYPES OF NOTCHES:
1.Rectangular Notch
2.Triangular Notch
3.Trapezoidal Notch
4.Stepped Notch

7. 6/21/2022 7Engr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Notches molded in
Metal Plates

8. 6/21/2022 8
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
DISCHARGE OVER A RECTANGULAR NOTCH
Consider a rectangular notch in one side of tank over
which water is flowing as shown in fig;
Where;
H = Height of water above
sill of notch
b = Width or length of the
notch
C
d= Coefficient of
discharge

9. 6/21/2022 9
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Discharge through the strip,
dq = C
dx Area of strip x Theoretical velocity
= C
dx b.dh x √2gh
Now total discharge, over the whole notch, may be found out by
integrating them above equation

10. 6/21/2022 10
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
H
H

11. 6/21/2022 11
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Lecture # 11
Fluid/Flow Measurements
Sometimes,thelimitsofintegration,intheaboveequation,are
fromH1toH2(i.etheliquidlevelisatheightofH1abovethe
topofthenotchandH2abovethebottomofthenotch,instead
of0toH.Thenthedischargeoversuchanotchwillbegivenby
theequation.

12. 6/21/2022 12
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Engr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
(Va is the velocity not yet reached to the notch)
The additional head caused due to the placement of the notch in the
channel is given by the gvHa
2
2 , Total Head at the notch = H+ Ha

13. 6/21/2022 13
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements

14. 6/21/2022 14
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
a
d
B
b
bn
0.1H 0.1H
H 
23
23
1.02
3
2
2
3
2
HnHbgCdQ
HbgCdQ
act
nact

     
23
23
1.02
3
2
HaHaHHaHnbgCdQ
act 
Where n = no of end
contractions (n=2)
By considering the
effect of velocity of
approach and end
contraction
simultaneously
End Contraction or Franci’s Formula for Discharge
Asthewidthofthenotchiskeptsmallerascomparedtothe
channel,sothestreamlineswillconvergeandtheendsofthe
nappewillgetcontracted.Experimentallyitisfoundthatthisend
contractedfromonsideisH/10

15. 6/21/2022 15
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
TRINGULAR NOTCH
A triangular notch is also called V-notch.
Consider a triangular notch, in one side of the tank,
over which water is flowing as shown in fig

16. 6/21/2022 16
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
DERIVATION:
x
x/2

17. 6/21/2022 17Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Let us consider a narrow rectangular strip of water flowing through the
triangular notch at a height (H-h) from the apex of the triangle having
width x and depth dh.
Therefore the Area of strip = x. dh
Area of strip = 2(H –h) tan θ /2 .dh
We know that theoretical velocity of water through strip = (2gh)
1/2
And discharge over the notch,
dq= C
d xArea of strip xTheoretical velocity
dq = Cd x2(H –h) tan θ /2 .dh x( 2gh)
1/2
The total discharge, over the whole notch, may be found out by integrating
the above equation within the limits 0 and H

18. 6/21/2022 18
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Lecture # 11
Fluid/Flow Measurements

19. 6/21/2022 19
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements

20. 6/21/2022 20
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Atrapezoidalnotchisacombinationofarectangular
notchandtwotriangularnotches.
Thedischargeoversuchanotchwillbethesumof
thedischargeovertherectangularandtriangular
notches.
Discharge over a Trapezoidal Notch

21. 6/21/2022 21
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
ConsideratrapezoidalnotchABCDasshownin
figure.Forthepurposeofanalysis,splitupthenotch
intoarectangularnotchBCFEandtwotriangular
notchesABEandDCF.Thedischargeoverthesetwo
triangularnotchesisequivalenttothedischargeover
asingletriangularnotchofangleθ

22. 6/21/2022 22
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements

23. 6/21/2022 23
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Two Stepped Notch
Discharge over a Stepped Notch

24. Stepped Notch
6/21/2022 24
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements

25. 6/21/2022 25
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements

26. 6/21/2022 26Engr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Example

27. 6/21/2022 27
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
WEIRS
Weirsarestructuresconsistingofanobstruction
suchasadamorbulkheadplacedacrosstheopen
channelwithaspeciallyshapedopening.Theweir
resultsanincreaseinthewaterlevel,orhead,
whichismeasuredupstreamofthestructure.The
flowrateoveraweirisafunctionoftheheadon
theweir.
Types
1.Rectangularweir 2.Cippolettiweir
3.Broad-crestedweir 4.NarrowCrestedweir
5.Sharp-crestedweir 6.Ogeeweir

28. 6/21/2022 28
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Consider a rectangular weir over which the water is
flowing as shown in figure -
Let,
H = Height of the water above the crest of the
weir
L = Length of the weir and
C
d= Coefficient of discharge
Discharge Over A Rectangular Weir

29. 6/21/2022 29
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Letusconsiderahorizontalstripofwaterof
thicknessatadepthfromthewatersurfaceas
showninfigure.
Areaofthestrip=L.dh
Weknowthatthetheoreticalvelocityofwater
throughthestrip=√2gh
Dischargethroughthestrip=Areaofstrip
xTheoreticalVelocityQ=Cd.L.dh.√2gh
Thetotaldischarge,overtheweir,maybefound
outbyintegratingtheaboveequationwithinthe
limits0andH.

30. 6/21/2022 30
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements

31. 6/21/2022 31
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Discharge Over A Cippoletti Weir
The"Cippoletti"weirisatrapezoidalweir,having1horizontalto4
verticalsideslopes,asshowninfigure.Thepurposeoftheslope,
onthesides,istoobtainanincreaseddischargethroughthe
triangularportionsoftheweir,which,otherwisewouldhavebeen
decreasedduetoendcontractionsinthecaseofrectangular
weirs.ThustheadvantageofaCippolettiweiristhatthefactorof
endcontractionisnotrequired,whileusingtheFrancis'Formula.

32. 6/21/2022 32
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Letussplitupthetrapezoidalweirintoarectangularweirand
atriangularnotch.
Nowdischargeoverarectangularweir,
anddischargeoveratriangularnotch
So total discharge,
SincethemainideaofCippolettiwastoavoidthefactorofend
contraction,andassuchhegavetheformulaforthedischarge,

33. 6/21/2022 33
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Discharge over a Narrow Crested Weir
Letbisthewidthofthecrestoftheweirand
Histheheightofthewateraboutthecrestoftheweir
If2b<H,theweiriscalledasanarrow-crestedweir.
Butif2b>H,thentheweiriscalledasbroad-crestedweir.
RelationforDischargeissameasthatfortherectangularweir.

34. 6/21/2022 34
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Discharge over a Broad Crested Weir
▼
b
H
A B
h
Where
H = Head of water on the upstream side of the weir
h = Head of water on the downstream side of the weir.
V = velocity of the water on the downstream side.
Cd= Co-efficient of discharge
L = Length of the weir
b = thickness of the weir

35.  
 
32
2
ththact
2
2AVQ
hHhghLC
hhHghLCVhLC
d
dd

 0+0+H=0+h+
6/21/2022 35
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Applying the energy equation at A & B.B
B
B
A
A
A
Z
γ
P
2g
V
Z
γ
P
2g
V
22
 gv
2
2 hH2gv
2

From above Equation Qact is maximum when  
32
hHh
is maximum. Therefore differentiating the equation and equating
to zero. Gives ush = 2/3 H.

36. 6/21/2022 36
Department of Civil Engineering U.E.T
Peshawar (BannuCampus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Putting the valve of h in above equation
Qmax = 1.71Cd. L . H^3/2
Sharp Crested Weir
b ˂ H/2
Ogee Crested Weir
▼

37. 6/21/2022 37
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Apitottubeisapressuremeasurementinstrument
usedtomeasurefluidflowvelocity.
ThepitottubewasinventedbytheFrenchearly
18
th
centuryandwasmodifiedtoitsmodernformin
themid-19
th
centurybyFrenchscientistHenryDarcy.
Pitot Tube
Pitottubesareanothertypesofdifferential
pressureflowmeters.
TheyarenamedafterHenryPitotwhocamewith
hisinventionintheyear1732

38. 6/21/2022 38
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements

39. 6/21/2022 39
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
There are three types of pitottube which are as
under;
Simple pitottube
Static source
Pitotstatic source
Types
Pitottubeisemployedinavarietyofflowmeasurement
applicationlikeairspeedinracingcarsandAirForce
fighterjets.Inindustries,pitottubesareinvariablyput
intouseformeasurementof;
Airflowinpipes,ductsandstacksand
Liquidflowinpipes,weirsandopenchannels

40. 6/21/2022 40
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements

41. 6/21/2022 41
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
In pitot-static tube, the kinetic energy of the
flowing fluid is transformed into potential
energy for measurement of fluid flow
velocity.
Since pitot tubes are trouble free and offer
consistent performance.
Pitot tubes ought to be used in applications
where the minimum Reynolds number is
more than 2ooo.

42. 6/21/2022 42
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Major advantages of pitot tubes include;
Cost effective measurement
No moving parts
Simple to use and install
Low pressure drop

43. 6/21/2022 43
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus)
Dr.Ateeq-ur-Rauf
Lecture # 11
Fluid/Flow Measurements
Problems

44. Engr.Ateeq-ur-Rauf
Department of Civil Engineering U.E.T
Peshawar (Bannu Campus) 44

45. T H E E N D