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- 2. 2 Why water measurement is required???? To determine the amount of water to be applied to the crops. Accurate measurement of irrigation water is necessary in field experiments on soil-water-plant relationship. Required in testing wells for their yield. Measurement of runoff from particular area and measurement steam flow are required in planning suitable soil and water conservation measure.
- 3. 3 Units of measurement Water at rest (as a tank, reservoir or standing water in field) are cubic metre, litre and hectare centimetre, cubic feet, gallons, acre-inch, acre-feet . Flowing water (as in a channel or pipeline) are m3/s, lps, ft3/s, gpm.
- 4. 4 Fundamental equation Based on the principle of conservation of mass and energy. Considering water as an incompressible liquid,the principle of conservation of mass leads to the continuity eqn Where; Q=discharge A=c/s area V=velocity(assumed constant across the section) Q = AV
- 5. 5 Conservation of energy is stated by the bernoulli’s as that along a stream line Where; P= pressure. V=velocity. z=elevation above a datum level. g=acceleration due to gravity. =sp.weight of the liquid
- 6. 6 Water measurement are the flow through open channels and flow through pipes. Measurement of flow in open channels 1. indirect discharge methods. a. velocity-area methods. I. Float method II. Current meter b. Dilution technique c. Electromagnetic method d. Ultrasonic method
- 7. 7 2. Direct discharge methods. a. Hydraulic structure A. Orifices B. Mouthpieces C. Weirs D. Notchs E. Flumes b. slope-area method
- 8. 8 a. velocity-area methods 1. Indirect discharge methods. The velocity of flow in the channel is measured by some mean and the discharge is calculated from the velocity and area of c/s I. Float method A float is a small object made of wood or other suitable material which is lighter than water. criteria A small stream in flood Small steam with rapidly changing water surface Preliminary or exploratory surveys.
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- 10. 10 A simple float moving on stream surface is called surface float. affected by surface wind and easy to use. Rod float consist of a vertical wooden rod which is weighted at the bottom to keep it vertical with its top end emerging out of free water surface when floating. It will travel with a velocity equal to mean velocity of flow.
- 11. 11 Velocity is estimated by timing how long a floating object takes to travel a pre-determined distance. Observed velocity is adjusted by some factor to estimate average velocity. Determine cross-sectional flow area. Use continuity equation to estimate Q.
- 12. 12 Advantages economical and simple Disadvantages not very accurate gives only approximate measure of the rate of flow
- 13. 13 II. Current meter It consist of a wheel having several cups or wheel, attached to a Streamlined weight and the assembly suspended by means of cables or mounted on straight rods. The wheel in current meter is rotated by the action of flowing water. The number of revolutions of the wheel per unit time are proportional to the velocity of the flowing water. It can be used for measuring velocities in irrigation channels, stream or large river.
- 14. 14 Types of current meter 1. Anemometer and propeller velocity meter 2. Electromagnetic velocity meters 3. Doppler velocity meters 4. Optical strobe velocity meters 1. Anemometer and Propeller Current Meters used for irrigation and watershed measurements. It use anemometer cup wheels or propellers to sense velocity. It does not sense direction of velocity, which may cause problems in complicated flow where backflow might not be readily apparent. For irrigation needs, this problem can be avoided by proper gage station or single measurement site selection.
- 15. 15 Anemometer type current meter
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- 17. 17 2. Electromagnetic Current Meters It produce voltage proportional to the velocity. The working principle of these meters is the same as the pipeline electromagnetic flow meter. measure crossflow and are directional. Advantage :- direct analog reading of velocity; counting of revolutions is not necessary. Limitation:- use near metallic objects
- 18. 18 3. Doppler Type Current Meters It determine velocity by measuring the change of source light or sound frequency from the frequency of reflections from moving particles such as small sediment and air bubbles. Laser light is used with laser Doppler velocimeters (LDV), and sound is used with acoustic doppler velocimeters (ADV). Acoustic Doppler current profilers ADCP measurements are becoming more frequent for deep flow in reservoirs, oceans, and large rivers. Most of the meters in this class are multidimensional or can simultaneously measure more than a single directional component of velocity at a time.
- 19. 19 4. Optical Strobe Velocity Meters It is developed by the U.S. Geological Survey (USGS) and the California Department of Water Resources use optical methods to determine surface velocities of streams (USGS, 1965). This meter uses the strobe effect. Mirrors are mounted around a polygon drum that can be rotated at precisely controlled speeds. Light coming from the water surface is reflected by the mirrors into a lens system and an eyepiece. The rate of rotation of the mirror drum is varied while viewing the reflected images in the eyepiece. At the proper rotational speed, images become steady and appear as if the surface of the water is still. By reading the rate of rotation of the drum and knowing the distance from the mirrors to the water surface, the velocity of the surface can be determined.
- 20. 20 Advantages:- No parts are immersed in the flowing stream. it can be used for high-velocity flows and for flows carrying debris and heavy sediment. It can measure large flood flows from bridges. Limitation:- However, the meter measures only the water surface velocity. It dependent upon the selection of the proper coefficient.
- 21. 21 b. Dilution technique/chemical method
- 22. 22 The material balance eqn QC0+q1C1 = (Q+q1)C2 Then rate of flow Q is Q = q1 (C2-C1) (C0-C2)
- 23. 23 c. Electromagnetic method It is based on faraday’s principle that an emf is induced in the conductor when it cuts a normal magnetic field.
- 24. 24 Where; d= depth of flow I=current in the coil n, K1,K2 = system constant It gives the total discharge when it is has been calibrated, makes it Specially suited for field situations where the c/s properties can change with time due to weed growth in , sedimentation, etc. Specific application is in tidal channels where the flow undergoes rapid changes both in magnitude as well as in direction. Accuracy ±3% Maximum channel width is 100m,and detectable velocity 0.005m/s.
- 25. 25 d. Ultrasonic method It was first reported by swengel (1955). Velocity measured by ultrasonic signals.
- 26. 26 If C= velocity of sound in water Where ; L = length of path from A to B vp =component of the flow velocity in the sound path=vcosθ similarly Thus,
- 27. 27 Advantages It is rapid and gives high accuracy. It is suitable for automatic recording of data. It can handle rapid changes in the magnitude and direction of flow as in tidal river . The cost of installation is independent of the size of river.
- 28. 28 The accuracy is limited by the factors that affect the signal velocity and averaging of flow velocity such as i. Unstable cross-section ii. Fluctuating weed growth iii. High loads of suspended solids iv. Air entrainment v. Salinity and temperature change
- 29. 29 2. Direct discharge methods. a. Hydraulic structure A. Orifices It is a small opening of any cross section on the side or at the bottom of a tank ,through which a fluid is flowing Classification of orifice According to size a)Small orifice (head of liquid >5d; d=depth of orifice) b) Large orifice (head of liquid <5d; d=depth of orifice)
- 30. 30 According to c/s area a) Circular orifice b) Triangular orifice c) Rectangular orifice d)Square orifice According to shape of u/s edge a) Sharp-edged orifice(minimum contact with fluid) b) Bell-mouthed orifice(saturated orifice) According to nature of discharge a) Free discharging orifice b) Drowned or sub-merged orifice 1) Fully sub-merged orifice 2) Partially sub-merged orifice
- 31. 31 Flow through on orifice The section cc is approximately at a distance of half of dia. of the orifice. At this section, the stream line are straight and parallel to each other and perpendicular to the plane of the orifice This section is called venacontract.
- 32. 32 Let the flow is steady and at a constant head H. applying Bernoulli's equation But z1=z2 now and (v1 <<< v2 and tank area is very large compared to the area jet)
- 33. 33 Hydraulic co-efficient velocitylTheoretica contracta-at venajetofvelocityActual =)(cvelocityofefficient-Co v gH v 2 The value cv of varies from 0.95 to 0.99 for different orifices, depending on the shape, size of the orifice and on the head under which flow take place Co-efficient of velocity (cv)
- 34. 34 orificeofArea contracta-at venajetofArea =)n(ccontractioofefficient-Co c Co-efficient of contraction(cc) a ac The value cc of varies from 0.61 to 0.69 for different orifices, depending on the shape, size of the orifice and on the head under which flow take place
- 35. 35 th d Q Q c Co-efficient of discharge(cd) velocitylTheoreticaarealTheoretica velocityActualareaActual cvd ccc The value cd of varies from 0.61 to 0.65 for different orifices,
- 36. 36 Flow through large orifice Note:-in case of small orifice, the velocity in the entire c/s of the jet is consider constant then discharge can be calculated by ghacQ d 2 But in large orifice the velocity is not constant Discharge through large rectangular orifice Consider a orifice in one side of the tank discharging freely into atmosphere under a constant head H. Let, H1 = height of liquid above top edge of orifice H2 = height of liquid above bottom edge of orifice b = breadth of orifice d = depth of orifice = H2 - H1 cd = co- efficient of discharge
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- 38. 38 dhbstripofArea 2ghstripoughwater throfvelocitylTheoretica Discharge through elementary strip velocitystripofAreacdQ d ghdhbcd 2 dhghbcd 2 Integrating above equation betn H1 and H2 Now ,Total discharge = Q 2 1 2 H H d dhghbcQ dhhgbc H H d 2 1 2 2 1 2/3 2 2/3 H H d h gbc 2/3 2 2/3 22 3 2 HHgbcd
- 39. 39 Discharge through fully sub-merged orifice It is one which has its whole of the outlet side sub-merged under liquid. Let, H1 = height of water above the top of the orifice on the u/s side. H2 = height of water above bottom of the orifice H = difference in water level b = width of orifice cd = co- efficient of discharge
- 40. 40 Height of water above the center of orifice on u/s side 2 12 1 HH H 2 21 HH Height of water above the center of orifice on d/s side H HH 2 21 Now applying Bernoulli's eqn (z1=z2 ) 2 211 HH g p H HH g p 2 212 and And V1is negligible
- 41. 41 g v H HHHH 22 0 2 2 22121 H g v 2 2 2 ghv 2 2 2 12HborificeofArea H VelocityAreacd orificethroughDischarge ghHHbcQ d 212
- 42. 42 Discharge through partially sub-merged orifice It is one which has its outlet side partially sub-merged under liquid. The upper portion behaves as orifice discharging free & lower portion behaves as a partially sub-merged orifice. Only large orifice behaves as a partially sub-merged orifice.
- 43. 43 Total discharge = discharge through free + sub-merged portion Discharge through sub-merged portion, 2/3 1 2/3 2 2 3 2 HHgbcQ d gHHHbcQ d 221 Discharge through free portion, gHHHbcHHgbc dd 22 3 2 2 2/3 1 2/3
- 44. 44 B. Mouthpieces A mouthpiece is a short length of a pipe which is two to three times its diameter in length fitted in a tank or vessel containing the fluid Classification of Mouthpieces According to their position with respect to tank a) External Mouthpieces b) Internal Mouthpieces According to shape a) Cylindrical Mouthpieces b) Convergent Mouthpieces c) divergent Mouthpieces d) Convergent-divergent Mouthpieces
- 45. 45 According to nature of discharge at outlet/re-entrant/borda’s (only for internal) a) Mouthpieces running full If jet of liquid after expand and fills the whole mouthpiece b) Mouthpieces running free If jet of liquid after contraction does not touch the side of mouthpiece
- 46. 46 Discharge through external cylindrical mouthpiece Let, H = height of liquid above the centre of mouthpiece vc = velocity of liquid at c-c section ac = area of flow at vena- contracta v1 = velocity of liquid at outlet a1 = area of mouthpiece at outlet cc = co- efficient of contraction
- 47. 47 Applying continuity eqn at c-c and (1)-(1) 11 vava cc c c a va v 11 But ncontractioofefficient-co 1 c c c a a Taking cc = 0.62 1 1 a a v c 62.0,, 1 a a getwe c 62.0 1v vc
- 48. 48 The jet of liquid from section c-c suddenly enlarges at section (1)-(1). Due to sudden enlargement , there will be a loss of head, hL g vv h c L 2 2 1 But 62.0 1v vc g v v hL 2 62.0 2 1 1 22 1 1 62.0 1 2 g v g v 2 375.0 2 1
- 49. 49 Now applying Bernoulli's eqn to point A and (1)-(1) LA AA hz g v g p z g v g p 1 2 11 2 22 01 pressurecatmospheri g p Where, zA = z1 , vA is negligible g v g v H 2 375.0 2 000 2 1 2 1 g v H 2 375.1 2 1 375.1 2 1 gH v gHv 2855.01
- 50. 50 Theoretical velocity of liquid at outlet is = gH2 Co-efficient of velocity for mouthpiece VelocitylTheoretica VelocityActual cv 855.0 2 2855.0 gH gH Cc for mouthpiece = 1 . area of jet of liquid at outlet = area of mouthpiece at outlet 855.01855.0 cvd ccc Value of Cd for mouthpiece > Value of Cd for orifice Discharge through mouthpiece will be more.
- 51. 51 Discharge through internal or re-entrant or borda’s mouthpiece i) Borda’s mouthpiece running free If the length of the tube is equal to its dia., the jet of liquid comes out from mouthpiece without touching the sides of the tube is known as running free Let, H = height of liquid above the mouthpiece vc = velocity through mouthpiece ac = area of contracted jet in the mouthpiece a1 = area of mouthpiece
- 52. 52 hagentranceonforcepressureTotal Where, a = area of mouthpiece h = distance of c.g. of area a from free surface = H Hag According to Newton's 2nd law, net force = rate of change of momentum cv cacflowing/seliquidofmass,Now Initial velocity of fluid=0 & final velocity of fluid = vc VelocityInitial-VelocityFinalcflowing/seliquidofmassmomentumofchangeofrate 0 ccc vva 2 ccva ………(i) ………(ii)
- 53. 53 Equating eqn (i) & (ii) 2 Hag ccva Now applying Bernoulli's eqn to free surface of liquid and section (1)-(1) 1 2 11 2 22 z g v g p z g v g p Taking the centre line of mouthpiece as datum, we have 0 0 0 1 1 1 v vv p g p g p z Hz c atm ………(iii)
- 54. 54 g v H g v H cc 2 0 2 000 22 gHvc 2 Substituting the value vc in eqn (iii) Hgac 2Hag v c c c a a aa 5.0 2 1 2 There is no head loss, cv = 1 5.015.0, vcd cccNow gHacQeDisch d 2)(arg gHa 25.0
- 55. 55 ii) Borda’s mouthpiece running full If the length of the tube is about 3 times its dia., the jet of liquid comes out with dia. equal to the dia. of mouthpiece at outlet is known as running full Let, H = height of liquid above the mouthpiece vc = velocity through mouthpiece ac = area of the flow at c-c a = area of mouthpiece v1 = velocity at outlet
- 56. 56 The jet of liquid after passing through c-c, suddenly enlarges at section (1)-(1).Due to sudden enlargement ,there will be a loss of head g vv h c L 2 2 1 Applying continuity eqn at c-c and (1)-(1) 11 vava cc c c a va v 11 1 1 a a v c 5.0 11 v c v c 12vvc …………..(i) Substituting the value vc in eqn (i) g v g vv hL 22 2 2 1 2 11
- 57. 57 Now applying Bernoulli's eqn to free surface of liquid and section (1)-(1) Lhz g v g p z g v g p 1 2 11 2 22 Taking the centre line of mouthpiece as datum, g v g v H 2 0 2 000 2 1 2 1 g v g v H 22 2 1 2 1 g v H 2 1 gHv 1 (Actual velocity) gHvVelocitylTheoreticaBut th 2,
- 58. 58 VelocitylTheoretica VelocityActual cv Co-efficient of velocity cv 707.0 2 1 2 gH gH Cc for mouthpiece = 1 . area of jet of liquid at outlet = area of mouthpiece at outlet 707.01707.0 cvd ccc gHacQeDisch d 2)(arg gHa 2707.0
- 59. 59 Discharge through convergent – divergent mouthpiece If a mouthpiece converges up to vena- contracta and then diverge is called convergent – divergent mouthpiece. There is no sudden enlargement of the jet, the loss of energy due to sudden enlargement is eliminated. And cd =1 Let , H = head of liquid over the mouthpiece
- 60. 60 Now applying Bernoulli's eqn to free surface of liquid and section c -c c cc z g v g p z g v g p 22 22 Taking the centre line of mouthpiece as datum, 0,,0, cca zH g p H g p vHz 0 2 0 2 g v HHH c ca ca c HHH g v 2 2 )(2 cac HHHgv ………(i)
- 61. 61 Now applying Bernoulli's eqn at section c –c & (1) – (1) 1 2 11 2 22 z g v g p z g v g p c cc ac H g p andzzBut 1 1, g v H g v H a c c 22 2 1 2 From eqn (i) g v HHHHH acac 2 2 1 H g v 2 2 1 gHv 21
- 62. 62 Applying continuity eqn at c-c and (1)-(1) 11 vava cc gH HHHg v v a a cac c 2 (2 1 1 H H H H ca 1 H HH ca 1 gHaQeDisch c 2arg Where , ac = area at vena- contracta
- 63. 63 C. Weirs Classification of Weirs According to shape of opening a) Rectangular Weir b) Triangular Weir c) Trapezoidal Weir( Cippoletti Weir) According to shape of crest a) Sharp–crested Weir b) Broad-crested Weir c) Narrrow-crested Weir d) Ogee –shaped Weir It is generally in the form of vertical wall ,with a sharp edge at the top , running all the way across the open channel.
- 64. 64 The edge over which water flows is called the crest. The height of the weir between the crest and the channel bottom is called the crest height. The height of the discharge over the crest is called the nappe. The air space under the nappe, downstream from the weir, is called the ventilation.
- 65. 65 Factors Affecting Flow over Weirs • The head • Fluid properties and Temperature Effects • Approach and tail water conditions • Weir Geometry • Measurement inaccuracies
- 66. 66 Advantages Capable of accurately measuring a wide range of flows Tends to provide more accurate discharge ratings than flumes and orifices Easy to construct Can be used in combination with turnout and division structures Can be both portable and adjustable Most floating debris tends to pass over the structure
- 67. 67 Disadvantages Relatively large head required, particularly for free flow conditions. This precludes the practical use of weirs for flow measurement in flat areas. The upstream pool must be maintained clean of sediment and kept free of weeds and trash, otherwise the calibration will shift and the measurement accuracy will be compromised
- 68. 68 Short crested weirs In general, short-crested weirs are those overflow structures, in which the streamline curvature above the weir crest has a significant influence on the head-discharge relationship of the structure. Weir sill with rectangular control section
- 69. 69 Limits of application The practical lower limit of h, is related to the magnitude of the influence of fluid properties, to the boundary roughness in the approach section, and to the accuracy with which h, can be determined. The recommended lower limit is 0.09 m; The crest surface and sides of the control section should have plane surfaces which make sharp 90-degree intersections with the upstream weir face; The bottom width of the trapezoidal approach channel should be 1.25 b,; The upstream head h1, should be measured 1.80 m upstream of the down streamweir face. Consequently, h, should not exceed half of this distance, i.e. 0.90 m; To obtain modular flow the submergence ratio h,/h, should not exceed 0.20.
- 70. 70 V-Notch Weir it is also called Thomson Weir or Gourley Weir. This weir features a weir plate standing vertical to the flow direction with a sharp-edged triangular cutout. The backwater level in front of the weir is directly proportional to the flow volume. Due to its special cutout the V-Notch weir is especially suitable for small volume measurement (0.05 l/s - 30 l/s; 0.79 - 475.59 gpm). it is primarily suitable for the evaluation of clean media like spring water, small sewage plant’s drains or partially even for volume measuring of percolating waters in dumps
- 71. 71 Prerequisites no backwater low oncoming flow velocity no sedimentation clean media without slubs, fibers or similar
- 72. 72 Limits of application The head over the weir crest should be at least 0.03 m and should be measured a distance of 3.00 m upstream from the weir. The notch should be at least O. 15 m from the bottom or the sides of the approach channel. The approach channel should be reasonably straight and level for 15.0 m upstream from the weir. To obtain modular flow the submergence ratio h2/h1 should not exceed 0.30.
- 73. 73 Advantages low costs for the needed measurement technique accurate measurement results (even at low volumes) easy to verify Disadvantages partially high mechanical expenses needed to realize the necessary hydraulic conditions no measurement in polluted or sediment carrying media no measurement of very high volumes
- 74. 74
- 75. 75 D. Notchs It may be defined as an opening in the side of a tank or a small channel in such a way that the liquid surface in the tank or channel is below the top edge of the opening. Classification of Notch According to shape of opening a) Rectangular Notch b) Triangular Notch c) Trapezoidal Notch d) Stepped Notch According to the effect of the sides on the nappe a) Notch with end contraction b) Notch without end contraction or suppressed
- 76. 76 Big in size. Small in size. Made of concrete or masonary structure. Made of metallic plate. Weirs Notchs
- 77. 77 Discharge over a rectangular notch or weir Let , H = head of water over the crest L = length of the notch or weir Consider an elementary horizontal strip of water of thickness dh and length L at a depth h from the free surface of water. Are of strip =L * dh gHstripthroughflowingwaterofVelocitylTheoretica 2
- 78. 78 The discharge dQ through strip is velocitylTheoreticastripofAreacdQ d gHdhLcd 2 Now total discharge Q dhhgLcdhghLcQ H d H d 00 22 H d h gLc 0 2/3 2/3 2 2/3 2 3 2 HgLcQ d
- 79. 79 Discharge over a triangular notch or weir Let , H = head of water above v-notch θ = angle of notch Consider a horizontal strip of water of thickness dh at a depth of h from the free surface of water. From fig. we have, 2 tan)( )(2 tan hHAC hH AC OC AB
- 80. 80 2 tan)(22 hHACABstripofWidth dhhHstripofArea 2 tan)(2 ghstripthroughwaterofVelocitylTheoretica 2 Discharge ,dQ through the strip is )( ltheoreticavelocitystripofAreacdQ d ghdhhHcd 2 2 tan)(2 dhghhHcd 2 2 tan)(2
- 81. 81 Total discharge Q is H d dhghhHcQ 0 2 2 tan)(2 H d dhhhHgc 0 )(2 2 tan2 H d dhhHhgc 0 2/32/1 )(2 2 tan2 H d hHh gc 0 2/52/3 2/52/3 2 2 tan2 2/52/3 2 2 tan2 2/52/3 HHH gcd 2/52/5 5 2 3 2 2 2 tan2 HHgcd
- 82. 82 2/5 15 4 2 2 tan2 Hgcd 2/5 2 2 tan 15 8 Hgcd For a right angled V- notch , if cd =0.6 1 2 tan900 2/5 81.9216.0 15 8 arg HeDisch 2/5 417.1 H
- 83. 83 Advantages of triangular notch or weir over rectangular notch or weir The expression for discharge for V- notch or weir is very simple . For measuring low discharge, a triangular notch gives more accurate results than a rectangular notch. In triangular notch , only 1 reading i.e.H is required for computation of discharge. Ventilation of triangular notch is not necessary.
- 84. 84 Discharge over a trapezoidal notch or weir Total discharge = discharge through rectangular notch or weir + discharge through triangular notch or weir Let , H = height of water over the notch L = length of crest of notch 1dc = co –efficient of discharge for rectangular portion 2dc = co –efficient of discharge for triangular portion
- 85. 85 Discharge through rectangular portion ABCD 2/3 1 2 3 2 HgLcQ d Discharge through 2 triangular notches FDA & BCF = discharge through single triangular notch 2/5 2 2 2 tan 15 8 HgcQ d Discharge through trapezoidal notch or weir = Q1+ Q2 2/52/3 2 2 tan 15 8 2 3 2 HgcHgLc dd
- 86. 86 Discharge over a stepped notch Discharge through stepped notch = sum of discharge through different rectangular notch Let , H1 = height of water above the crest of notch (1) L1 = length of notch (1) H2 , L2 & H3 , L3 are corresponding value for notch (2) &(3) respectively. cd = co –efficient of discharge for all notch
- 87. 87 321)(arg QQQQedischTotal 2/3 33 2/3 3 2/3 22 2/3 2 2/3 11 2 3 2 2 3 2 2 3 2 HgLc HHgLc HHgLcQ d d d
- 88. 88 Cipolletti weir or notch Cipolletti weir is trapezoidal weir, which has side slopes of 1:4(H:V) '214 4 1 tan 2 4 14 2 tan 0 H H BC AB
- 89. 89 The discharge through a rectangular weir with two end contractions is 2/3 2)2.0( 3 2 HgHLcQ 2/52/3 2 15 2 2)2.0( 3 2 HgcHgHLc d Let the slope is given by θ/2, now discharge through V- notch is 2/5 2 2 tan 15 8 Hgcd 2/52/5 2 15 2 2 2 tan 15 8 , HgcHgcThus dd '214 4 1 tan 24 1 8 15 15 2 2 tan 01
- 90. 90 The discharge through cipolletti weir is 2/3 2 3 2 HgLcQ d If velocity of approach , va is to be taken in to consideration 2/32/3 2 3 2 aad hhHgLcQ
- 91. 91 Discharge over a broad –crested weir A weir have wide crest is known as broad –crested weir Let , H = height of water over the crest L = length of the crest h = head of water at the middle of weir which is constant v = velocity of flow over the weir If 2l > H , the weir is called broad –crested weir
- 92. 92 Now applying Bernoulli's eqn to the still water surface on the u/s side and running at the end of weir h g v H 2 000 2 hH g v 2 2 hHgv 2 The discharge over weir is velocityflowofAreacQ d hHghLcd 2 32 2 hHhgLcd ………….(i)
- 93. 93 The discharge will be maxm , if (Hh2 –h3 ) maxm 0Hh 32 h dh d hHhHh 32032 2 Hh 3 2 Substituting value of h in eqn (i) 32 max 3 2 3 2 2 HHHgLcQ d 32 27 8 9 4 2 HHHgLcd
- 94. 94 33 27 8 9 4 2 HHgLcd 27 812 2 3 H gLcd 27 4 2 3 H gLcd 2/3 3849.02 HgLcd 2/3 81.923849.0 HLcd 2/3 705.1 HLcd
- 95. 95 Discharge over a narrow –crested weir If 2l < H , the weir is called narrow –crested weir. It is similar to Rectangular weir or notch 2/3 2 3 2 HgLcQ d
- 96. 96 Discharge over a ogee weir In which the crest of the weir rises up to maxm height of 0.115 * H where H = height of water above inlet of weir The discharge through ogee weir is same as that of rectangular weir 2/3 2 3 2 HgLcQ d
- 97. 97 Discharge over submerged weir or drowned weir When the water level on the d/s side of weir is above the crest of the weir ,then the weir is called to be submerged weir drowned weir Divided in to two portion. the portion betn u/s and d/s water surface may be treated as free weir and portion betn d/s water surface and crest of weir as a drowned weir Let , H = height of water on the u/s of the weir h = height of water on the d/s of the weir
- 98. 98 Then , portionupperovereDischQ arg1 2/3 2 3 2 1 hHgLcd portiondroenedthrougheDischQ arg2 flowofvelocityflowofAreacd 2 hHghLcd 22 Total discharge, 21 QQQ hHghLc hHgLc d d 2 2 3 2 2 1 2/3
- 99. 99 E. Flumes Flumes are shaped open channel flow sections in which flow is measured DESCRIPTION 1. Flumes force flow to accelerate Converging sidewalls Raised bottom Combination 2. Flumes force flow to pass through critical depth Unique relationship between water surface profile and discharge
- 100. 100 Advantages Minimal drop in pressure. Enables measurement in a large range of flow. The flow rate in flumes is usually high enough to prevent sedimentation; they are therefore self-cleaning. Provides a reliable measurement in free flow and submerged flow conditions.
- 101. 101 Disadvantages Installation is usually expensive. Installation requires extremely careful work. Requires a secure watertight base. Flow at the entrance must be evenly distributed, with little turbulence, to produce accurate measurements.
- 102. 102 Two basic classes of flumes 1. Long throated flumes Parallel flow lines in control section Accurately rate with fluid flow analysis 2. Short throated flumes Curvilinear flow in control section Calibrated with more precise measurement devices Types of flume
- 103. 103 Long throated flumes (Replogle flume ) Long-throated flumes have one-dimensional flow in the control section -- Long-throated means long enough to eliminate lateral and vertical contraction of the flow at the control section…streamlines are essentially parallel Can be calibrated using well-established hydraulic theory No laboratory testing needed Calculations are iterative, so computer models that do the calculations have made long-throated flumes reasonable to implement in recent years
- 104. 104 Classified under the term ‘long-throated flumes’ are those structures which have a throat section in which the streamlines run parallel to each other at least over a short distance. Because of this, hydrostatic pressure distribution can be assumed at the control section. This assumption allowed the various head-discharge equations to be derived, but the reader should note that discharge coefficients are also presented for high H1/L ratios when the streamlines at the control are curved. Long-throated flumes are the measurement device of choice for most open channel applications, having significant advantages over Parshall flumes and other traditional devices.
- 105. 105 These older devices were laboratory-calibrated, because the flow through their control sections is curvilinear. In contrast, streamlines are essentially parallel in the control sections of long- throated flumes, making them ratable using straightforward hydraulic theory. The crest level of the throat should not be lower than the dead water level in the channel, i.e. the water level downstream at zero flow. The throat section is prismatic but the shape of the flume cross- section is rather arbitrary, provided that no horizontal planes, or planes that are nearly so, occur in the throat above crest (invert) level, since this will cause a discontinuity in the head-discharge relationship.
- 106. 106 The flume comprises a throat of which the bottom (invert) is truly horizontal in the direction of flow. Advantages Minimal head loss required , Economical construction techniques Adaptable to existing control sections Variety of construction materials Rating table accuracy of ±2% Choice of various shapes and configurations Calibration based on the as-built dimensions User-friendly software WinFlume Proven track record Accurate over the entire flow range Minimal problems with trash and debris Ability to pass sediment
- 107. 107
- 108. 108 Long-Throated Flumes (Ramp Flumes)
- 109. 109 Limits of application The practical lower limit of h, is related to the magnitude of the influence of fluid properties, boundary roughness, and the accuracy with which h, can be determined. The recommended lower limit is 0.07 L. To prevent water surface instability in the approach channel the Froude number Fr = v1/(gA1/B1)² should not exceed 0.5. The upper limitation on the ratio H1/L arises from the necessity to prevent streamline curvature in the flume throat. Values of the ratio H1/L should be less than 1.0 The width B, of the water surface in the throat at maximum stage should not be less than L/5. The width at the water surface in a triangular throat at minimum stage should not be less than 0.20 m.
- 110. 110 Trapezoidal Replogle flume Rectangular Replogle flume
- 111. 111 Other flumes a) H-Flumes H flumes are a hybrid between flumes and weirs. H flumes can measure a wide variety of flows, from very low to extremely high volumes. H flumes were designed in the mid-1930s by the USDA Agricultural Research Service The measuring point of the H flume, selected during development, is in the draw down effect, this means that H flumes are very sensitive to slight errors in measuring point position. A straight uniform approach must be provided that matches the inlet width of the H flume. H flumes require a non-impeded discharge so that there can be no submergence.
- 112. 112 H flumes are capable of monitoring flows that vary over wide ranges with a high degree of accuracy. H flume is capable of providing accurate measurement for applications with flow ranges of 100:1 or more. On natural streams where it is necessary to measure a wide range of discharges, a structure with a V-type control has the advantage of providing a wide opening at high flows so that it causes no excessive backwater effects, whereas at low flows its opening is reduced so that the sensitivity of the structure remains acceptable.
- 113. 113 To serve this purpose the U.S. Soil Conservation Service developed the H-type flume, of which three geometrically different types are available 1. HS flumes 2. H flumes 3. HL flumes
- 114. 114 Operating principle An H flume operates according to the Venturi principle. Due to lateral restrictions, the flume restricts the flow area, causing the water level upstream from the throat to rise. The flow can be obtained by simply measuring the water depth, because this depth varies proportionally with flow. Applications An H flume was developed to measure the flow of irrigation water from small catchment areas and surface water. it is generally used to measure the flow of irrigation water, slow- flowing watercourses and water in sewer systems.
- 115. 115 The geometry and operating principle of an H flume make it a very useful tool for measuring the flow of water that contains solids. This type of flume can measure a variety of different flows and provides good precision. Ranges of measurement H flumes can be used to measure flowrates between 0.3981 m3 per day, for an Hs flume 122 mm (0.4 ft) high, and 286,251 m3 per day, for an HL flume 1219 mm (4 ft) high.
- 116. 116 1. HS flumes Of this ‘small’ flume, the largest size has a depth D equal to 0.305 m (1 ft) and a maximum capacity of 0.022 m³/s. HS flumes are typically recommended for lower flows not exceeding 0.8 cfs.
- 117. 117 2. H flumes Of this ‘normal’ flume, the largest size has a depth D equal to 1.37 m (4.5 ft) and a maximum capacity of 2.36 m³/s. Fiberglass H flumes are available in a variety of sizes and can be used to measure flows ranging from zero to 80 cfs.
- 118. 118
- 119. 119 1. HL flumes The use of this ‘large’ flume is only recommended if the anticipated discharge exceeds the capacity of the normal H- flume. The largest HL-flume has a depth D equal to 1.37 m (4.5 ft) and a maximum capacity of 3.32 m³/s. The 4.0’ HL flume may be recommended for larger flows up to 111 cfs.
- 120. 120
- 121. 121 ADVANTAGES OF H FLUMES Three types of flumes—HS, H, and HL—are available for small-, medium-, and high-discharge rates, respectively. They have different specifications to suit various ranges of water flow. The shape of flume provides the following distinct advantages that favor its use under a variety of flow conditions (USDA 1979): 1. The increase of throat opening with the rise of stage facilitates accurate. 2. Measurement of both low and high flow of water. 3. The converging section of flume makes it self-cleaning because of increased velocity.
- 122. 122 Consequently, the flume is suitable for measuring flows having sediment in suspension and low bed-loads. 4. It is simple to construct, rigid and stable in operation, and requires minimal maintenance for retaining its rating. 5. Its installation is simple and is generally not affected by the steepness of the channel gradient.
- 123. 123 Submergence of H flume Flumes should be installed with free outfall or no submergence wherever possible. If submergence occurs, the free discharge head (H) can be computed by using the following equation, presented in non-metric units to be consistent with those given in USDA (1979): H = d1/{1 + 0.00175[exp (d2/d1)5.44]} Where, H is the free flow head (in ft) d1 is the actual head with submergence (in ft) d2 is the tail water depth (in ft) above flume zero head and 0.15 < d2/d1 < 0.90.
- 124. 124 H flumes Discharge equations FLUME SIZE EQUATION HS-Type 0.4' Q=294.50*H^2.23815 0.6' Q=322.569*H^2.2405 0.8' Q=345.10*H^2.23173 1.0' Q=366.13*H^2.22258 H-Type 0.5' Q=767.5*H^2.31 0.75' Q=830.3*H^2.31 1.0' Q=875.2&H^2.31 1.5' Q=947.0*H^2.31 2.0' Q=1000.8*H^2.31 3.0' Q=1081.6*H^2.31 4.5' Q=1166.9*H^2.31 HL-Type 4.5' Q=1156.46&H^2.31716
- 125. 125
- 126. 126 Evaluation of discharge All three types of H-flumes have a rather arbitrary control while an upstream piezometric head ha is measured at a station in the area of water surface drawdown. Under these circumstances, the only accurate method of finding a head-discharge relationship is by calibration in a hydraulic laboratory. Based on this calibration, an empirical formula, expressing the discharge in m³/s as a function of the head ha in metres, could be established of the general form log Q = A + B log ha + C[log ha]² ……………(1) Values of the numbers A, B, and C appear in Table
- 127. 127
- 128. 128 Modular limit The modular limit is defined as the submergence ratio h2/ha which produces a 1% reduction from the equivalent modular discharge as calculated by Equation …..(1) Results of various tests showed that the modular limit for HS- and H-flumes is h2/ha = 0.25, for HL-flumes this limit is 0.30. Rising tail water levels cause an increase of the equivalent upstream head ha at modular flow. Because of the complex method of calculating submerged flow, all HS- and H-flumes should be installed with a submergence ratio of less than 0.25 (for HL-flumes 0.30).
- 129. 129 Limits of application a. The inside surface of the flume should be plane and smooth while the flume dimensions should be in strict accordance with Figure. b. The practical lower limit of ha, is mainly related to the accuracy with which ha, can be determined. For heads less than 0.06 m, point gauge readings are required to obtain a reasonably accurate measurement. The lower limit of ha for each type of flume can be read from Tables 7.13 to 7.15. c. To obtain modular flow the submergence ratio h2/ha should not exceed 0.25. d. To prevent water surface instability in the approach channel, the Froude number Fr, = v1/(gA1/B)^1/2 should not exceed 0.5.
- 130. 130 b) Parshall flume The Parshall flume was designed in the later 1920s to measure the flow of irrigation water. It is often used to measure the flow of wastewater, for permanent or temporary installations DESCRIPTION A Parshall flume consists of a converging section, a throat section and diverging section. The crest of the throat section is tilted downstream. In other words, there is a sill between the horizontal crest and converging section and the crest of the throat section.
- 131. 131 For channels smaller than 2.44 m (8 ft), the inlet of the converging section may be rounded, and larger channels may have vertical walls at a 45° angle. To prevent erosion due to water fall, the diverging section is usually extended by means of vertical walls, and the angle of these walls will be steeper than the angle of the walls of the diverging section 1. Dimensions are standardized for each flume Not hydraulic scale models of each other A 12 ft flume is not simply 3 multiply by a 4 ft flume 2. Designated by throat width Measure 0.01 cfs with 1 inch flume Measure 3000 cfs with 50 foot flume
- 132. 132 3. Relate Ha (or Ha and Hb ) to discharge with rating equation, or consult appropriate chart 4. Flow rate through the critical section is a function of the upstream head, acceleration of gravity, and the control section size Operating principle A Parshall flume operates according to the Venturi principle. Due to lateral restrictions, the flume restricts the flow area, causing the water level upstream from the throat section to rise. A sudden or steep drop in water level at the throat section creates an increase in flow velocity.
- 133. 133 The flowrate can be obtained simply by measuring the water depth, because it has been established that depth varies proportionally with flow. Applications initially developed to measure flow in natural open channels such as rivers, streams, drainage ditches, etc., widely used to measure flow in man-made open channels, such as storm and domestic drainage systems, sewage treatment plant inlets and outlets, etc. Because of its geometry and operating principle, a Parshall flume is extremely effective for measuring the flow of water that contains solids. Because it creates little loss of depth, it can be easily adapted to existing sewer systems.
- 134. 134
- 135. 135 Dimensions The dimensions of a Parshall flume are defined by the width of constriction
- 136. 136 CLASSES OF PARSHAL FLUMES On the basis of the throat width, Parshall flumes have been classified into three main groups. (i) Very small - 25.4 mm to 76.2 mm. (ii) Small 152.40 mm to 2438.4 mm. (iii) Large 3048 mm to 15240 mm.
- 137. 137 1. VERY SMALL FLUMES Discharge capacity ranges from 0.09 l/s to 32 l/s. Turbulence makes difficult to read Hb – gauge Hc – gauge included downstream end of diverging section to provide readings during submergence Hc – gauge readings are converted to Hb – gauge by using a graph & used to determine discharge .
- 138. 138 2. SMALL FLUMES Discharge capacity ranges from 0.0015m3/s to 3.95 m3/s Length of side wall of converging section, A, of (1ft -8ft) throat width (m) is given as; Where; bc= throat width (m) Ha – gauge located at distance of a = upstream from the end of the horizontal crest Hb – gauge location is the same in all small flumes (X = 2inch upstream from the low point in the sloping throat floor ) & (Y= 3 inch above it) 219.1 2 cb A A 3 2
- 139. 139 3. LARGE FLUMES (10 ft up to 50 ft) Discharge capacity ranges from 0.16m3/s to 93.04 m3/s Length of side wall of converging section is longer than in small flumes Ha – gauge located at distance of m upstream from the end of the horizontal crest Hb – gauge location is the same in all large flumes (X = 12inch upstream from the floor at downstream edge of the throat ) & (Y= 9 inch above it) 813.0 3 cb a
- 140. 140
- 141. 141 ADVANTAGES Relatively low head loss (1/4 of sharp crested weir) Handle some trash and sediment Well accepted • May be mandated Many sizes are commercially available DISADVANTAGES Complicated geometry for construction Tight construction tolerances Aren’t amenable to fluid flow analysis BoR does not recommend for new construction
- 142. 142 Range of measurements Parshall flumes can measure flows varying from 70.7 m3 per day, for a 76 mm (3 in) channel, to 8,038,656 m3 per day, for a 15.24 m (50 ft) channel. For the purposes of this document, only data that apply to channels with dimensions between 76 mm (3 in) and 36.57 m (12 ft), have been included.
- 143. 143 c) Palmer-Bowlus Flume A Palmer-Bowlus flume was designed in the 1930s for use as a flume that can be inserted in an existing channel with a slope of less than 2 %. Description This flume is rounded to create a restriction and produce a greater flow velocity in the throat of the flume. It is a Venturi type flume with a uniform throat. The length of the throat is equal to the diameter of the corresponding flume. Different types of restrictions have been developed, but the restriction most frequently used is trapezoidal in shape.
- 144. 144 It is usually made of prefabricated fibreglass that is reinforced with plastic. Although rare, also made of stainless steel. A Palmer-Bowlus flume is manufactured in sizes ranging from 102 mm (4 in) to 1067 mm (42 in). Operating principle Vertical and lateral restrictions on the flume reduce the flow area, causing the water level upstream from the throat section to rise, which is followed by a drop in water level in the throat section, resulting also in an increased flow velocity. Flowrate can be determined simply by measuring water depth upstream from the flume, since it has been established that variations in depth are proportional to flow.
- 145. 145 Applications it is designed to measure flow in sewer systems and existing channels, a Palmer-Bowlus flume is not a temporary device. In fact, the difference in measurement between a minimum and maximum flow is relatively small if a system is expanded, the size of the flume must also be changed. Like all flumes, a Palmer-Bowlus flume is an effective tool for flow measurement of water that contains solids. It is also relatively easy to install because it does not require a crest differential upstream or downstream.
- 146. 146 Dimensions Dimensions of a Palmer-Bowlus flume depend on the diameter of the channel in which it is installed. SHAPE OF A PALMER-BOWLUS FLUME ACCORDING TO LUDWIG
- 147. 147 Ranges of Measurement Palmer-Bowlus flumes can measure flows varying between 2.4 m3 per day, in the case of a 102 mm (4 in) flume, and 49,200 m3 per day, in the case of a 762 mm (30 in) flume. d) Leopold-Lagco flume The Leopold-Lagco flume was developed in the early 1960s and introduced on the market in 1965 by F.B. Leopold Company Inc. of Pennsylvania.
- 148. 148 Description It has a round shape. The purpose of its rounded shape is to create a restriction in the conduit, which causes a greater flow velocity in the throat of the flume. This flume operates according to the Venturi principle. The throat is uniform and its length is equal to the diameter of the channel for which it was designed. its throat section has a rectangular shape. It consists of three sections: a converging section, throat section and diverging section
- 149. 149 There are three models: permanent installation model: there is a slight extension of the converging and diverging sections; insertion model: outer radius of the flume corresponds to the inner radius of the channel in which it is to be installed; cutthroat model: the diverging section is not as high. This flume is used on a temporary basis only. The inner surface of the flume must be made of material that is smooth and free of irregular edges. The outer surface is made of a material that facilitates adhesion to a concrete surface.
- 150. 150 The flume is made of fiberglass in standard sizes varying between 152 mm (6 in) and 1219 mm (48 in). Operating principle Due to vertical and lateral restrictions, a Leopold-Lagco reduces the flow area, causing the water level upstream from the throat section to rise, followed by a drop in water level and an increased flow velocity. Flow can be determined by simply measuring the water level upstream from the flume, since it has been established that depth varies according to flow. Literature provides no information about use of this flume in submerged flow conditions and no correction formula. Use in only free flow conditions is therefore recommended.
- 151. 151 Applications It is used as a main measuring device on a temporary or permanent basis. Like all flumes, it is an effective tool for measuring the flow of water that contains solids. Due to their relatively small volume, flumes with a diameter of 381 mm (15 in) or less can be inserted in a standard sewer manhole, without the need to modify access. It is relatively easy to install because there is no need for a required distance from the bottom of the channel in which it is inserted.
- 152. 152 Dimensions The dimensions of a Leopold-Lagco flume are a function of the diameter of the conduit in which it is installed.
- 153. 153 Range of measurements Leopold-Lagco flumes can measure flows varying between 84.2 m3 per day, for a 152 mm (6 in) flume, and 108,445 m3 per day, for a 1219 mm (48 in) flume. e) Cutthroat flume It was developed in the mid-1960s by Utah State University Water Resources Laboratory. It is used to measure flow in locations where there is no slope or very little slope.
- 154. 154
- 155. 155 Description A cutthroat flume consists of a converging section and diverging section. The control section (W) does not have parallel sides because the flume consists only of a converging and diverging section. The bottom of the entire length of the flume is flat. For flumes that are less than 1.37 m (4.5 ft) long (L) and 15.2 cm (0.5 ft) wide in the control section (W), the inlet of the converging section may be rounded. For larger flumes, the inlet of the converging section may have vertical walls at a 30° angle. To prevent erosion due to water fall, the diverging section is usually extended by means of vertical walls, and the angle of these walls is steeper than the angle of the walls in the diverging section.
- 156. 156 Operating principle Cutthroat flumes operate according to the Venturi principle. Due to the lateral shape of its walls, the flume restricts the flow area, which causes the water level upstream from the control section to rise, followed by a sudden and significant drop of the water level in the control section, accompanied by an increase in flow velocity. The flow can be determined by simply measuring the water depth, because depth varies proportionally with flow. Although this flume can be used in submerged flows, use in free flow conditions is strongly recommended
- 157. 157 Applications It was developed to measure flow in open natural channels, such as rivers, streams, drainage ditches, etc. with a small slope. It has been the subject of several studies that demonstrate its effectiveness as a measuring device in sewer systems and water treatment plants. The geometry and operating principle of a cutthroat flume make it an effective device for measuring flow in water that contains solids. Because this flume causes only a small loss of head and requires no difference in height between the bottom of the channel and base of the flume, it is relatively easy to adapt to existing sewer systems.
- 158. 158 A cutthroat flume is simple and inexpensive to manufacture. It is also perfectly suited to a temporary measurement system. Dimensions The dimension of a cutthroat flume is defined by the total length of the flume (L) and the width of the control section (constriction) (W).
- 159. 159
- 160. 160
- 161. 161 Range of measurements Cutthroat flumes can measure flows varying between 32 m3 per day, for a flume 457 mm (1.5 ft) long with a constriction of 25 mm (0.083 ft), and 210,555 m3 per day, for a flume 2,743 mm (9 ft) long with a constriction of 1,829 mm (6 ft). Disadvantages when it compared with long-throated flumes: The discharge coefficient Cd is rather strongly influenced by H1 and H2; The modular limit varies with H1 and has a lower value; The control section can only be rectangular; Cd value has high error of about 8 percent.
- 162. 162 f) Trapezoidal Flumes These are some what similar to Parshall flumes but different in shape. These were originally developed in Washington State College and as such are referred to WSC flume. Advantages 1) A large range of flows can be measured with a comparatively small change in head; 2) Sediment deposits in the approach does not change the head discharge relationship noticeably; 3) Extreme approach conditions seem to have a minor effect upon head discharge relationship;
- 163. 163 4) The flumes will operate under greater submergence than rectangular shaped ones without corrections for submergence; 5) The trapezoidal shape fits the common channel sections more closely than a rectangular one.
- 164. 164 Schematic view of truncated flume for earthen channel. Shortening of the full length structure is possible by deleting the diverging section and the tailwater section if the head loss over the section exceeds 0.4 times the head causing the flow, as measured from the crest of the throat section. Such a structure is called a truncated flume. g) Truncated Flume
- 165. 165 Triangular throated flumes are adapted to measure a wide range of discharges, including low flows like return flows to drainage system operational spillage from irrigation systems. It also permits wide variations in the flow rate. The ratio between the maximum and minimum flow is high in case of triangular throated flume. h) Triangular Throated Flume
- 166. 166 Schematic view of triangular throat flume.`
- 167. 167 b. Slope-Area Method This consists of using the slope of the water surface in a uniform reach of channel and the average cross-sectional area of that reach to give a rate of discharge. The discharge may be computed from the Manning formula: 2/13/21 sRA n Q h where: Q = discharge (m3/s) A = mean area of the channel cross section (m2) Rh = mean hydraulic radius of the channel (m) S = energy slope of the flow n = a roughness factor depending on the character of the channel lining
- 168. 168 Measurement of flow in pipe measuring the time required for the flow to fill a container of known volume. Volumetric measurement time volume flowofRate Advantages It is very simple and requires little equipment. Disadvantages where the flow rate is not uniform over a period of time, frequent measurements are to be taken to get accurate data
- 169. 169 FLOW RATE MEASUREMENTS The different methods used for measuring the rate of flow in pipes are: 1. Venturimeters 2. Orifice plate 3. Pitot tube 4. Elbow meter 5. Co –ordinate method
- 170. 170 1. Venturi Meters. It consists of converging and expanding section of short length. It is useful for measuring the flow of water in pipes under pressure. It utilises the principle that the flow passing through a constricted section of pipe is accelerated and the pressure head lowered. The drop in the pressure head is measured by providing openings in the Venturi meter at the points shown in the figure and connecting these openings to a U-tube manometer. Considering points (1) and (2) with cross-sectional areas A1 and A2 respectively and assuming horizontal pipe, from Bernoulli theorem, neglecting friction
- 171. 171
- 172. 172 g v g P g v g P 22 2 22 2 11 g P g P gvv 212 1 2 2 2 The pressure head difference is indicated by the manometer reading, h, hence, M ghvv 2 2 1 2 2 where, ρM is the density of the gauge fluid. Q = V1A1 = V2A2 By continuity,
- 173. 173 Substituting for V2 in terms of V1 yields M gh A A v 21 2 2 12 1 Solving for V1 M gh A A v 2 1 1 2 2 1 1 M ideal gh A A A vAQ 2 1 2 2 1 1 11 idealdactual QCQ Hence, dC = coefficient of discharge
- 174. 174 2.Orifice plate Its function is similar to the venturi meter. major difference between the devices lies in the fact that, downstream of the orifice piate, the flow area expands instantaneously while the fluid is unable to expand at the same rate. This creates a 'separation zone' of turbulent eddies in which large energy losses occur. Cd is considerably lower than that for the Venturi meter. Advantages its lower cost and its compactness.
- 175. 175 The orifice can be put at the end of the pipe (Fig.) and is known as pipe orifice. The ratio of the orifice diameter to the pipe diameter should be between 0.5 and 0.8 and is selected in such a way that the pipe flows full.
- 176. 176 The discharge is computed using the equation. ghaCQ d 2 Where a = area of orifice h = head of flow measured from center of pipe
- 177. 177 3.Pitot tube The pitot tube is an open L shaped tube useful for measuring velocity of flows in an open channels as well as in pipes. 000 2 21 2 PP g v h PP g v 12 2 2 ghv 2 The velocity at point 2 immediately at the nose of the tube is zero as water is at rest here. The Pitot tube gives the velocity at the point at which the open end is placed
- 178. 178 The use of the Pitot tube for measuring flow when the pipe is flowing under pressure the static pressure of the water is to be taken into consideration. Fig. 4.18 illustrates how this is done using an inverted U- tube.
- 179. 179 The velocity of flow is given by the equation. ghcv 2 Where, C is known as the Pitot tube coefficient (usually 0.95 to 1.0). 4. Elbow meter Pressure differences between the outside and inside walls of an elbow are related to volumetric flow rate. Q = CeKA(Po-Pi)l/2 where, Q = discharge (l/min); Ce = elbow meter flow coefficient A = c/s area of elbow (cm2); Po = pressure on outside of elbow (kPa); Pi = pressure on inside of elbow (kPa); k = unit constant(k=8.49)
- 180. 180
- 181. 181 5. Co –ordinate method measurements are taken of the jet of water issuing from the end of the pipe and these are used for calculating the rate of discharge.
- 182. 182 The formula to be used is obtained by combining the following equations : Q = AV………………(i) t XVVtX g Y tgtY 2 2 1 2 Substituting in Eq.(i) and introducing C, the coefficient of discharge y g CAXQ 2 Where, Q = discharge (l/s) X = horizontal distance Y = vertical distance A = area (square centimeter) g = 980 cm/sec2
- 183. 183 Y CAX Q 02.0
- 184. 184 METERS FOR MEASURING CUMULATIVE FLOW 1. Propeller Meters 2. Deathridge Meter 3. Water Meter 1. Propeller Meters record the cumulative flow of water. widely used in USA in the farm irrigation systems at the canal outlets. The flow from the canal outlet is allowed to pass through a pipe into a basin. A propeller which rotates due to the flow of water is installed at the pipe outlet.
- 185. 185 The number of rotations indicated by a counter will give the cumulative water flow. Calibration and maintenance are important to get accurate readings.
- 186. 186 Advantages Commercially available Totalizing meter Can achieve good accuracy Disadvantages Operating conditions different from manufacturer’s calibration conditions will affect accuracy Only tolerate small amount of weeds and debris Moving parts operating underwater Can require a good deal of maintenance and inspection
- 187. 187 used in Australia operates on the same principle as the propeller meter but the construction is different The size of the rotating wheel depends upon the discharges to be measured. The number of rotations are recorded on a counter. The device is to be calibrated in situ to obtain accurate readings. 2. Deathridge Meter
- 188. 188
- 189. 189 3. Water Meter designed for measuring pipe flow. generally used for measuring municipal water supplies and are rarely used for measuring water on the farm. These consist of a| multiblade propeller made of metal, plastic or rubber, connected to a counter by means of a gear system. The counter readings are calibrated to give the volumetric flow in the desired units. Water meters are made in different sizes to suit the different pipe diameters and ranges of flow.
- 190. 190 The basic requirements for using the water meters are : (1) the rate of flow should be within the designed range. (2) The pipe must always flow full. (3) the water should not contain any debris.
- 191. 191 References R. K. Bansal, A Text Book Of Fluid Mechanics And Hydraulic Machines P. N. Modi & S. M. Seth, Hydraulics And Fluid Mechanics. K. Subramanya, Engineering Hydrology. V. V. N. Murthy & M. K. Jha, Land And Water Management Engg.. M.G. Boss, Discharge measurement structure.