chapter 4 flow measurement

8/10/2019 Chapter 4 FLOW MEASUREMENT

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Chapter 4 : FLOW MEASUREMENT

4.1 Background

A control structure measures discharge by establishing a relationship between the flow depth and

discharge in its vicinity. Once the relationship is known, discharge can be calculated from themeasured depth of flow. The depth-discharge relationship is obtained by changing the flow regime

from subcritical to supercritical. When flow changes from subcritical to supercritical, it passes

through critical flow conditions. At critical flow conditions, there is a unique relationship between

the discharge and flow depth which for rectangular channels can be expressed as follows for a

rectangular channel section,

32 gyq = C (4.1)

where q is the discharge per unit width of the channel, g is the gravity constant, and y is the flow

depth. All discharge measuring structures in open channels, such as flumes and weirs, employ the

principle of change in flow regime to obtain hydraulic control. We have analyzed the concepts ofhydraulic control in Chapter 2.

A concept of particular importance in discharge measurement by weirs and flumes is that of

modular flow. The flow over a weir is modular when it is independent of variations in downstream

water level. For this to occur, the downstream head h2must not rise beyond a certain percentage of

upstream head over the weir crest h1. For weirs and flumes, the minimum required differential head

( H ) to operate in the modular flow range can be expressed as a fraction of the upstream energyhead h1as

1

2

1

21

1 h

h

h

hh

H =

= (4.2)

The last term of equation (4.2),1

2

h

his the submergence ratio for the weir crest which is used to

define the modular limit. The modular limit is the value of submergence ratio at which the real

discharge deviates by one percent from the discharge calculated by the depth-discharge equation.

The modular limit of weirs and flumes depends basically on the degree of streamline curvature at the

control section. Broad-crested weirs and long-throated flumes, which have straight and parallel

streamlines at their control section, can obtain a modular limit as high as 0.95. That is, the

broad-crested weirs and long-throated flumes maintain their accuracy even at high submergenceratios. Modular limit of a sharp- crested weir and zero throat flume will be lower as the streamlines

are more strongly curved under normal operation. The sharp-crested weir is an extreme example

where the downstream water level must remain at least seven centimeters below crest level for

modular conditions and accuracy of discharge measurement.

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4.2 Types and Management Implications

There are three types of control structures for measuring flow discharge in open channels: weirs,

orifices and flumes. Weirs and orifices produce hydraulic control by contracting the flow in vertical

plane, and flumes obtain the control conditions by contracting the flow in horizontal plane. Weirs

can be sharp-crested or broad-crested. A sharp-crested weir consists of a vertical plate with a sharpedge that is placed normal to the flow direction. The flow contracts as it passes over the plate, and

as a result the flow regime is changed from subcritical (upstream of the weir) to supercritical

(downstream of the weir).

The depth-discharge equation for a sharp-crested weir is derived by assuming atmospheric pressure

around the overflow jet. Care must be taken to insure that the underside of the jet is properly

aerated. For this purpose, the underside of the falling jet is connected to the atmosphere by means of

a vent pipe. However, these vent pipes are usually vandalized and removed. When the vent pipe is

removed, vacuum is created under the jet which increases discharge over the weir and the

depth-discharge relationship will no longer be accurate.

Weirs require larger energy head to pass a given discharge as compared to flumes, and as such the

flow depth upstream of a weir is significantly increased. For this reason, weirs should not be

installed very close to turnout or turnout structures as the "pile-up" effect may extend back up to the

turnout and reduce its discharge. Because of many improperly installed weirs, these structures tend

to be less popular with farmers. Another reason why sharp-crested weirs may not be favored by

farmers is that they require substantial labor for cleaning the sediment that accumulates upstream of

the weir structure. Because of the increased depth, flow velocity upstream of a weir is reduced

causing the suspended silt to settle in the channel. With all these potential drawbacks, however, a

properly designed and installed weir is an accurate discharge measuring device for open channels.

A broad-crested weir has a crest length (in the direction of flow) so that the streamlines can bestraight and parallel before the free overfall. Therefore, the broad-crested weir does not have the

disadvantages associated with sharp streamline curvature. Critical flow occurs at the weir crest and

this property is used to derive the depth-discharge relationships.

In orifice flow, the streamline curvature is less and as such the upstream water surface does not rise

as much as in sharp-crested weirs. When orifices are designed to be submerged by the downstream

water surface, then the head differential required to pass a given discharge is further reduced.

Submerged pipe turnouts function satisfactorily at head differential as low as 5 cm. Because of these

advantages, orifice-based regulation structures are very commonly used in irrigation canals.

Flumes obtain hydraulic control by contracting the flow in horizontal plane, and as such all flumeshave a converging section followed by a diverging section. In addition, some flumes have a straight

"throat" section in between the two sections. Some widely used examples are the Parshall flume, the

Cutthroat flume, and the Long-Throated flume. In the Cutthroat and Long-throated flumes the bed

is horizontal, and as such these flumes are easier to make. In the Parshall flume, the bed drops and

then rises again at the control section. The Cutthroat flume has a zero throat width compared to the

Parshall and the Long-Throated flumes. Flumes are placed parallel to the direction of flow in an


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open channel; that is, they are "in-line" structures. Therefore, flumes cannot be used for discharge

regulation; they can be used only for discharge measurement. Since weirs and orifices are placed

normal to the flow direction, they can be used both for discharge measurement and regulation.

4.3 Broad-Crested Weirs

Classified under the term broad-crested weirs are those structures over which the streamlines are

straight and parallel to each other, at least for a short distance. As such, hydrostatic pressure

distribution may be assumed at the control section. To obtain this condition, the crest length in the

flow direction, L, is defined in relation to the upstream energy head over the crest h1.

4.3 a. Round-Nosed Broad-Crested Weir

Description

The weir comprises a truly level and horizontal crest between vertical abutments. The upstream

corner is rounded to avoid flow separation. Downstream of the horizontal crest there may be a

vertical face, a downward slope or a rounded corner, depending on the submergence ratio underwhich the weir should operate at modular flow. The weir structure should be at right angles to the

flow direction. The dimensions of the weir and its abutments should comply with the requirements

indicated in Figure 4.1. The minimum radius of the upstream rounded nose (r) is 0.11 h1, although

for economic design of field structures a value r = 0.2 h1is recommended. The length of the

horizontal portion of the weir crest should not be less than 1.75 h1to obtain a favorable discharge

coefficient Cd. The head measurement section should be located a distance of between two to three

times h1upstream of the weir block.

Figure 4.1: Round-nosed Broad-crested Weir.

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Measurement of discharge

The depth-discharge relationship for a broad-crested weir can be derived from fundamental

hydraulic principles. This is possible because of the streamline flow that exists at the crest which

enables us to assume hydrostatic pressure distribution at the crest (Figure 4.2)

Broad-Crested Weir

Section 2

Section 1

Figure 4.2: Streamline Flow at the Crest of Broad-crested Weir

Applying energy equation between upstream (section 1) and the control section (section 2) with crest

as the datum and assuming no energy loss, we get

g

vy

g

vh

22

2

22

2

11 +=+ or

g

vyH

2

2

221 +=

which gives velocity at the crest,

)(2 212 yHgv =

and discharge Q as

)(2 21 yHgAQ =

For rectangular crest section of width b,

)(2 212 yHgbyQ =

At the crest section, flow is critical and therefore,

123

2

3

2HEyy CC ===

The discharge equation can therefore be written as

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)3

2(2

3

2111 HHgHbQ = or 2

3

13

2

3

2bHgQ= (4.3)

In practice, we can measure h1which is the flow depth over the weir crest. If we replace energy

head H1with flow depth h1, we must use a coefficient of velocity Cvto account for the approach

velocity head. Equation (4.3) can then be written as

2

3

13

2

3

2bhgCQ v= (4.4)

Another coefficient to be introduced is the coefficient of discharge Cdto account for the streamline

convergence at the entrance to the crest.

2

3

13

2

3

2bhgCCQ vd= (4.5)

Equation (4.5) gives the depth-discharge relationship for broad-crested weirs with rectangular

control section. Similar relationships can be developed for other common shapes of the control

section such as the triangular and trapezoidal. Since these shapes are more commonly used in

flumes, we will present them in the section on flumes.

The discharge coefficient Cd corrects for the energy loss between the gauging and control sections

and for the streamline curvature. These phenomena are closely related to the value of the ratio H1.

Figure 4.3 gives the value of Cdas a function of the ratioH1. The range of application is

0.11.0 1 L

H (4.6)

ForL

H1 < 0.1, minor changes in the boundary roughness of the weir crest cause large variation in

the Cd value. For values ofL

H1 > 1.0, pressure distribution at the control section is no longer

hydrostatic, because of the large streamline curvature.

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Figures 4.3: Cdas a function of ratio H1/L

The approach velocity coefficient Cv corrects for the use of flow depth (h1) instead of total energy

head (H1) and thus neglectingg

v

2

2

1 . In general, Cv therefore equals

=

1

1

h

HCv (4.7)

where equals the power of h1in the head-discharge equation; that is for rectangular control

section, = 1.5. Because the discharge is determined by the area of flow at the control section and

approach velocity is mainly determined by the area of flow at the gauging station, Cv can be

correlated to the area ratio1

*

A

A(Figure 4.4). In the area ratio, the value A* equals the imaginary

flow area at the control section if the water depth would equal h1, and A1is the area of flow at the

gauging station.

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Modular limit

The flow over a weir is modular when it is independent of variations in the upstream water level.

The weir height above the bottom of the channel, p2, in relation to upstream energy head, H1,

determines the modular limit. The modular limit can be read from Figure 4.5 as a function of2

1

pH

and the back face slope of the weir. The design value of p2is established by trial and error.

Limits of application

The practical lower limit of

height of water surface over

the crest, h1, is related to the

magnitude of the influence

of fluid properties, to the

boundary roughness, and to

the accuracy with which h1

can be determined. The

recommended lower limit is

0.06 m or 0.05 L, whichever

is greater.

Figure 4.4: Cvas a Function of the Area Ratio

The limitations on pH1 arise from difficulties experienced when the

Froude number in the approach channel exceeds 0.5. The

recommended upper limit is pH1 = 1.5, where p should be greater

than or equal to 0.15 m.

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The limitation on LH1 arise from the necessity of ensuring a

hydrostatic pressure distribution at the critical section of the crest, and

of preventing the formation of undulations above the weir crest.

Values of the ratio LH1 should therefore range between 0.05 and

0.50. The width b of the weir crest should not be less than 0.30 m, nor

less than maximum upstream energy head, H1.

Figure 4.5: Modular Limit as a Function of H1/p2.


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4.3 b. Broad-Crested Weir with Upstream Ramp

Description

In recent applied research by Bos, M.G., Replogle, J.A. Clemmens, A.J. and Tony Wahl, a slopingapproach ramp has been added to the horizontal broad crest (Figure 4.6). The upstream approach

channel with the ramp is necessary for the development of parallel streamline flow and stable water

surface at the crest. The streamline flow, in which water enters the control section without flow

separation, is most important. It enables the application of available hydraulic theory to accurately

predict the hydraulic performance of the control structure. Also, the smooth transition results in low

head loss for passing a given discharge under modular flow conditions.

Figure 4.6: Broad-crested Weir with Ramp in Lined Canal.

The modified broad-crested weirs can be used both in concrete-lined canals and in earthen canals.

In concrete-lined canals, a simple upstream ramp is required with no additional provisions in the

upstream approach. Also, no downstream ramp is necessary for protection against bed erosion

(Figure 4.6). For the weirs in earthen channels, a upstream approach section and a downstream

ramp are added. The broad-crested weirs for earthen channels will be described in the next section.

Measurement of Discharge

The hydraulic control relationship for the weir is the same as given in Equation 4.5. Based on this

relationship, rating tables have been prepared for a number of standard weirs with different crest

widths. The standard weirs with necessary design information are given in Tables 4.1 and 4.2. The

discharge rating tables for these standard weirs are given in Tables 4.3 and 4.4.

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Design and Selection

Estimate or determine the tail-water depth y2for the maximum discharge. The depth y2

is the normal flow depth in the canal at the design discharge. Know the existing canal shape and dimensions. Using Table 4.1 or Table 4.2, locate the canal shape that best fits the existing canal. Select a weir such that the design discharge Q falls within the range of discharge that can

be measured by the weir.

Determine the sill-referenced head (h1) from the rating tables for the weir (Tables 4.3 and4.4).

Determine the required headloss H for maintaining modular flow at the weir. Check whether h1+ p > y2 + H . If not, go back and choose another weir. Check the canal depth d. See if d 1.2 h 1max + p1(this will provide a free board = 0.2

h1).

Determine appropriate dimensions as follows:L = length of crest 1.5 H1maxLa = approach length 1.0 H 1maxLb= horizontal length of ramp = 2 to 3 times p1Ramp slope = 3 Horizontal :1 Vertical

The USBR Hydraulics Lab staff in Denver have developed a computer program WinFlume, which

allows the user to conveniently design a flume for required conditions. It also provides the control

equation and/or rating tables for the designed flume. The web address for downloading the software

is: www.usbr.gov/pmts/hydraulics_lab

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http://www.usbr.gov/pmts/hydraulics_labhttp://www.usbr.gov/pmts/hydraulics_lab


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Table 4.1: Choices of Weir Sizes and Rating Tables for Lined Canals in Metric Units

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Table 4.2: Choices of Weir Sizes and Rating Tables for Lined Canals in English Units

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Table 4.3: Rating Table for Weirs in Trapezoidal Lined Canals in Metric Units

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Table 4.3 continued: Rating Table for Weirs in Trapezoidal Lined Canals in Metric Units

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Table 4.4: Rating Tables for Weirs in Trapezoidal Canals in EnglishUnits

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Table 4.4 continued: Rating Tables for Weirs in Trapezoidal Canals in EnglishUnits

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Table 4.4 continued: Rating Tables for Weirs in Trapezoidal Canals in EnglishUnits

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Design Example

Given a existing canal with bottom width b1= 0.3 m, side slope 1:1 and a total canal depth d = 0.55

m. For a design discharge of 150 L/s, normal flow depth y2= 0.43 m.

Required: Select a broad-crested weir

Solution: From Table 4.1, weir types that can be suitable are Bmthrough Em1.

Trial 1. Choose Bmsince it has minimum sill height, p1 = 0.15 m. Using Table 4.3, for weir Bm to

pass Q = 150 L/s, required upstream head h1= 0.219 m. Using Table 4.1, find H (required headloss) = 0.017 m. Also, H = 0.1 h1, = 0.022 m. Use H = 0.022 m

Check: h1+ p1> y2+ H .219 + .15 > .43 + .022

.369 m is not greater than .452 m. Try next weir type.

Trial 2. Try weir Dm1

h1 = .197 m, p1= 0.25 (Table 4.1)

H = 0.1 h1= .02 so use H = .025 mh1+ p1 = .447 m

y2 + H = .455 mSince h1+ p1not greater than y2+ H , try again

Trial 3. Try weir Em1

p1 = 0.3 m, h1= 0.187, H = 0.029m

h1 + p1= .487 m and y2+ H = .459 m

Since H1+ p1> y2+ H , the weir is desirable. The flow will be modular for the range of discharges0.12 m

3/s to 0.52 m

3/s. The weir sill will be 0.3 m above the upstream bed level. Other design

dimensions are calculated as follows.

La = Length of the gauge to the end of the ramp = 1.0 H1.

Therefore, La = 0.2 m.

Lb= Upstream ramp = 3p1= 3.0*3 = 0.9 m.

L = Sill Length = 1.5 h1= 1.5 * 0.187 = 0.27 = 0.3 m.

However, from Table 4.3, sill length for Em1 weir must be between 0.38 m to 0.56 m. So, choose L =

0.38 m.

Crest width bc = 0.9 m.

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4.3.c Broad-Crested Weirs for Earthen Canals

Components and dimensions

Weirs for earthen canals require the following basic parts: approach channel, converging section,

throat, diverging section and downstream protection in the form of a stilling basin and riprap (Figure4.7). The structure is longer and, therefore, more expensive for earthen canals as compared to one in

lined canals. In lined canals, the approach channel and structure sides are already available and no

downstream protection is needed. Approach channel provides a known flow and velocity of

approach. Rating tables assume rectangular approach section of same width as throat.

Figure 4.7: Broad-crested Weir in Earthen Canal

The structure shown in Figure 4.7 can be shortened by deleting the downstream diverging section

as illustrated in Figure 4.8.

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Figure 4.8: Shortened Weir in Earthen Canal

In constructing the weirs and flumes shown above, the designer may select any locally available

construction materials. For example, wings and sidewalls can be brickwork containing a

mortar-plastered sill; or the entire structure can be made of reinforced concrete.

Discharge Rating Tables

Tables 4.5 and 4.6 give rating tables for rectangular broad-crested weirs in earthen canals.

Discharges in these tables are limited to keep the approach channel Froude Number below 0.45.

Total discharge Q = qbc where q is the discharge per unit width from Tables 4.5 and 4.6, and bcis

the weir crest width.

Design Procedure

Obtain data on the flow conditions in the existing channel. Estimate head required to maintain modular flow for a design discharge and still not

overtop the channel. Enter Tables 4.5 and 4.6 with value of head h1. Read one of the columns and select unitdischarge q.

Determine required head loss. Select a sill height such that flow is modular and the canal is not overtopped.

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Table 4.5: Rating Table for Rectangular Weirs with Discharge per Meter Width

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Table 4.5 (continued): Rating Table for Rectangular Weirs

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Table 4.6: Rating Table for Rectangular Weirs in English Units

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Table 4.6 (continued): Rating Table for Rectangular Weirs in English Units

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4.4 Sharp-crested weirs

The sharp-crested weirs are overflow structures whose crest length in flow direction is equal to or

less than two millimeters. The crest surface and the sides of the notch have plane surfaces which

make sharp 90-degree intersections with the upstream weir face. The downstream edge of the notchshould be beveled if the weir plate is thicker than two millimeters. The beveled surfaces should

make an angle of not less than 45 degrees with the surface of a rectangular notch, and an angle of not

less than 60 degrees if the throat section is non rectangular (Figure 4.9).

In general, sharp-crested weirs are used where accurate discharge measurements are required, for

example in hydraulic laboratories, industry, and irrigation pilot schemes. To obtain this high

accuracy the downstream water level should be low to ensure ventilation of the air pocket beneath

the overflow jet. Consequently the sharp-crested weirs require a substantial head loss to obtain

modular flow, which is a major disadvantage of sharp-crested weirs.

4.4 a. Rectangular sharp-crested weirs

A rectangular notch, symmetrically located in a vertical thin metal plate, placed perpendicular to the

flow direction is defined as a rectangular sharp-crested weir (Figure 4.10). Rectangular

sharp-crested weirs are classified in following three types.

Figure 4.9: Cross-section Over a Sharp-crested Weir.

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Figure 4.10: Rectangular Sharp-crested Weir.

Contracted weirshave an approach channel whose bed and walls are sufficiently remote from the

weir crest and sides, so that the channel boundaries have no significant influence on the contraction

of the overflow jet.

Width or suppressedweirs extend across the full width of the rectangular approach channel. As a

result, the channel boundaries significantly affect the contraction pattern.

Partially contracted weirs, where contractions are not fully developed due to the proximity of the

walls and/or the bottom of the approach channel.

In general, all three types of rectangular weirs should be located in a rectangular approach channel.

If the approach channel is sufficiently large to render the approach velocity negligible, and the weir

is fully contracted, the shape of the approach channel is unimportant. Consequently, the fully

contracted weir may be used with non-rectangular approach channels. The fully contracted weir

may be described by limitations on various dimensions as shown in Table 4.7.

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Table 4.7: Limitation on Dimensions of a Rectangular Sharp-crested Contracted Weir.


The basic head-discharge equation for a sharp-crested weir is

5.1

123

2bhgCQ d= (4.8)

To apply this equation to fully contracted and partially contracted weirs, it is modified as

5.12

3

2eed hbgCQ= (4.9)

where the effective width beequals b + Kb and the effective head, he, equals h1+ Kh. The quantities

Kband Kh represent the combined effects of viscosity and surface tension. Empirically defined

values for Kbas a function of the ratio b/B are given in Figure 4.11 and a constant positive value forKh = 0.001 m is recommended for all values of the ratios b/B and h1/p.

Ceis an effective discharge coefficient which is a function of the ratios b/B and h1/p and can be

determined from Figure 4.12. For a rectangular sharp-crested weir which has been constructed with

reasonable care and skill, the error in the effective discharge coefficient is expected to be less than 1

percent.


The lower limit of h1is related to the magnitude of the influence of fluid properties and the accuracy

with which h1can be determined. The recommended lower limit is 0.03 m. Critical depth will

occur in the approach channel upstream of the weir if ratio h1/p exceeds about 5. Alternatively the

weir is not a control section for values of h1/p greater than 5. Further limitations on h1/p arise from

observational difficulties and measurement errors. For precise discharge measurement, the

recommended upper limit for h1/p is 2.0 and p should be at least 0.10 m. The width of the weir crest

should not be less than 0.15 m; and to facilitate aeration of the nappe, the downstream water level

should remain at least 0.05 m below crest level.

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Figure 4.11: Values of Kbas a Function of b/B

Figure 4.12: Coefficient Ce as a Function of Ratios b/B and h1/p

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4.4 b. V-Notch Sharp-Crested Weirs

A V-shaped notch in a vertical thin plate placed perpendicular to the sides and bottom of a straight

channel is defined as a V-notch sharp-crested weir (Figure 4.13). The line which bisects the angle of

the notch should be vertical and equal distance from

both sides of the channel. The V-notchsharp-crested weir is a very precise discharge

measuring device suitable for a wide range of flow.

In international literature, the V-notch

sharp-crested weir is also referred to as the

Thomson weir.

The flow regime encountered in V-notch

sharp-crested weirs may be partially or fully

contracted. A partially contracted weir does not

have fully developed end contractions due to

proximity of walls and/or bed of the approachchannel. A fully contracted weir has an approach

channel whose bed and sides are quite remote from

the edges of the V-notch. This allows for a

sufficiently large approach velocity component

parallel to the weir face so that the end contraction

is fully developed.

The two types of flow regimes in V-notch

sharp-crested weirs may be classified by the

limitations on various dimensions shown in Table

4.8. From Table 4.8, it appears that a weir may befully contracted at low head, but with increasing

head it becomes partially contracted.

Figure 4.13: V-notch Sharp-crested Weir

Table 4.8: Limitations on Dimensions of V-notch Sharp-crested Weirs

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The basic head-discharge equation for a V-notch sharp-crested weir is

5.2

12tan2

15

8hgCQ

e

= (4.10)

To apply this equation to both fully and partially contracted sharp- crested weirs, it is modified to a

form

5.2

2tan2

15

8ee hgCQ

= (4.11)

where is the notch angle and heis the effective head which equals h1+ Kh. The quantity Kh

represents the combined effect of fluid properties such as viscosity and surface tension. Empirically

defined values for Khas a function of the notch angle are presented in Figure 4.14.

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Figure 4.14: Value of Khas a Function of the Notch Angle.

For water at ordinary temperature, that is 5oC to 30

oC (40

oF to 85

oF), the effective coefficient of

discharge, Ce, is a function of three variables.

= ,,

1

1

B

p

p

hfCe

If the ratio h1/p < 0.4 and p/B1< 0.2, the V-notch weir is fully contracted and Cebecomes a function

of only the notch angle , as illustrated in Figure 4.15. If the contraction of the nappe is not fully

developed, the effective discharge coefficient can be read from Figure 4.16 for a 90-degree V-notch

only. Insufficient experimental data are available to recommend Cevalues for non 90-degree

partially contracted V-notch weirs.


The limits of application of Equation (4.10) for V-notch sharp- crested weirs are:

Ratio h1/p should be equal to or less than 1.2 Ratio h1/B should be equal to or less than 0.4, Head over the vertex, h1, should not be less than 0.05 m nor more than 0.60

m,

Height of the notch vertex above the approach channel bed, p, should not beless than 0.10 m

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Figure 4.15: Coefficient of Discharge Ceas a Function of Notch Angle

for Fully Contracted V-notch weirs.

31

Figure 4.16: Ce as a Function

of h1/p and p/B for 90-degree

V-notch Sharp-crested Weir.

Commonly used sizes of

V-notches for fully contracted

sharp-crested weirs are

90-degree,2

190-degree and

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90-degree notches as shown in Figure 4.17. The dimensions across the top are twice, equal to and

half the vertical depth respectively. A rating table for discharge of these three V-notch weirs is

given as Table 4.9. Downstream water level should remain below the vertex of the notch. Notch

angle of a fully contracted weir may range from 25 to 100 degrees. Partially contracted weirs have a

90-degree notch only.

Figure 4.17. V-Notch Weir Sizes

Table 4.9: Rating Table for V-Notch Weirs


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Table 4.9 continued: Rating Table for V-Notch Weirs

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The limits of application of the Cipoletti fully contracted weir are given below.

The height of the weir crest above the approach channel bottom should be atleast twice the head over the crest with a minimum of 0.30.

The distance between sides of the trapezoidal control section and theapproach channel should be at least twice the head over the crest with a

minimum of 0.30 m.

The upstream head over the weir crest h1should not be less than 0.06 m andnot more than 0.60 m.

The ratio h1/b should be equal to or less than 0.50. To enable aeration of the nappe, the tailwater level should be at least 0.05 m

below crest level.

Table 4.10: Rating Table for Standard Cipoletti Weir


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4.5 Flumes

A flume is a geometrically specified horizontal constriction in an open channel to obtain critical flow

conditions. The channel constriction may be formed by side contractions only, by a bottom

contraction, or by both side and bottom contractions. A flume, therefore, has an entrance transition

to converge the flow, a throat section where the flow is critical, and a downstream expansion to

smoothly diverge the flow to its initial flow conditions. Flumes are "in-line" structures; that is, their

flow axis is parallel to the channel flow axis. Therefore flumes cannot be used as dual purpose

regulating and measurement structures; they are used for discharge measurement only.

4.5 a. Long-Throated Flumes

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Long-throated flumes have a throat section in which streamlines are parallel to each other, at least

for a short distance (Figure 4.19). Because of this parallel streamline flow, hydrostatic pressure

distribution can be assumed at the throat control section. At the throat section the bottom is truly

horizontal in the direction of flow. The most common throat sections are rectangular, V-shaped and

trapezoidal. The entrance transition should be

of sufficient length to avoid flow separationeither at the bottom or at the sides of the

transition. The floor of the transition should be

flat and level and at no point higher than the

throat invert. The head measurement station

should be located upstream of the flume at a

distance equal to 2 or 3 times the maximum

head to be measured.

Figure 4.19: Long-throated Flume Dimensions

Discharge measurement

The hydraulic behavior of a long-throated flume is essentially the same as that of a broad-crested

weir because of the parallel streamline flow at control section. Consequently, the depth-discharge

equation for these flumes are derived in the same way as for broad-crested weirs (Section 4.3). Thebasic depth discharge equation for a rectangular long-throated flume is the same as Equation (4.5),

that is,

2

3

13/23

2bhgCCQ vd= (4.13)

For a triangular (V-shaped) control section,

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2

5

12

tan5/225

16hgCCQ vd

= (4.14)

and for a trapezoidal control section,

Q = Cd(b yC+ z yC2) [2g(H1- yC)]

1/2 (4.15)

where h1= depth of flow at the head measurement station,

H1 = total upstream energy head with respect to throat bed as datum =g

Vh

2

2

1+

yC= critical depth of flow in the throat section. For trapezoidal sections, Table 4.11 is used

to find yC Cd = discharge coefficient which is a function of the ratio H1/L and its value is presented in

Figure 4.20, and

Cv= approach velocity coefficient and its value may be obtained from Figure 4.4 as a

function of the dimensionless ratio1

*

A

ACd

Table 4.11: Values of the Ratio yC/H1 as a Function of Side Slope and H1/b

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Figure 4.20: Discharge Coefficients for Long-throated Flumes

The error in the product CdCvof a well maintained long-throated flume which has been constructed

with reasonable care and skill may be deduced from the equation

xc= + 2 (21 - 20 Cd) percent

It is recommended that the divergences of each plane surface be not more abrupt than 1:4. If in

some circumstances it is desirable to construct a short downstream expansion, it is better to truncate

the transition rather than to enlarge the angle of divergence. If no velocity head needs to be

recovered, the downstream transition can be fully truncated. When almost all velocity head needs to

be recovered, a transition with a very gradual expansion of sides and bed is required.


The limits of application of a long-throated flume for reasonable accurate flow measurements are as

follows.

The practical lower limit of h1is related to the magnitude of the influence of fluid properties,

boundary roughness, and the accuracy with which h1can be measured. The recommended

lower limit is 0.06 m or 0.1 L, whichever is greater.

To prevent water surface instability in the approach channel the Froude number Fr =

v1/(gA1/B)1/2

should not exceed 0.5.

The lower limitation on the ratio H1/L arises from the necessity to prevent undulations in the

flume throat. Values of the ratio H1/L should range between 0.1 and 1.0.

The water surface width in the throat at maximum stage should not be less than 0.30 m, nor

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less than H1max, nor less then L/5.

The width of the water surface in a triangular throat at minimum stage should not be less

than 0.20 m.

4.5 b. Cutthroat Flumes

Description

The geometry of the throatless flume with broken plane transition was first developed in 1912 in the

Punjab (Pakistan and India). Since 1967 Skogerboe et al. (1973, 1972) have extended the original

studies in rating a group of Cutthroat flumes which have the same geometric shape. In the Cutthroat

flume, the flume discharge and modular limit are related to the piezometric heads at two points -- in

the converging section (ha) and in the downstream expansion (hb). Cutthroat flumes have been

tested with a flat bottom only. A definition sketch of this structure is shown in Figure 4.22.

In the original Cutthroat flume design, various discharge capacities were obtained by simply

changing the throat width b. Flumes with a throat width of 4, 8, 12, 24 and 36 inches were tested

and rating tables have been prepared. The rating tables are given in the Colorado State UniversityExperiment Station Bulletin Number 120, (Skogerboe, G. 1973). The Cutthroat flume operates

satisfactorily under both free flow and submerged flow conditions. The free flow equation for

cutthroat flumes is

(4.17)nf

aff hCQ =

where Qfis the free flow rate in ft3/s, Cfis the free flow coefficient and nf is the free flow exponent.

The value of the exponent nf was found to be a function only of the flume length (Figure 4.23). The

value of the free flow coefficient, Cf, is a function of both flume length and throat width,

Cf = KfW1.025

(4.18)

where Kfis the flume length coefficient (Figure 4.23), and W is the throat width in feet. For

accurate discharge measurements, the recommended ratio of upstream flow depth to flume length

(ha/L) should be equal to or less than 0.33. Higher values of this ratio result in inaccuracies because

of higher approach velocities and a rapidly changing water surface at the upstream measuring

section.

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Figure 4.22: Definition Sketch for a Cutthroat Flume

Figure 4.23: Coefficients for Cutthroat Flumes

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The submerged flow in cutthroat flumes is represented by the equation

( )

( )nst

nf

bas

sS

hhCQ

log

= (4.19)

The value of ns depends only on the flume length (Figure 4.23). The submerged coefficient (Ks) and

the transition submergence (St) are also plotted in Figure 4.23. These are used to compute the

submerged flow coefficient, Cs, as follows,

Cs= KsW1.025

(4.20)

4.5 c. Parshall flumes

Parshall flumes were developed by R. Parshall (1922) at Colorado State University after whom the

device was named. The flume consists of a converging section with a level floor, a throat section

with a downward sloping floor, and a diverging section with an upward sloping floor (Figure 4.24).

Because of the throat, the flume operates satisfactorily with a headloss much less than that required

for a sharp-crested weir. The primary disadvantage of the Parshall flume compared to the Cutthroat

flume is its longer length. In deviation from the general rule for long-throated flumes where the

upstream head must be measured in the approach channel, Parshall flumes are calibrated to measure

piezometric head, ha, at a prescribed location in the converging section. The downstream

piezometric head, hb, is measured in the throat.

Parshall flumes were developed in various sizes, the dimensions of which are given in Table 4.12.

The flumes must be constructed exactly in accordance with the structural dimensions given for each

of the 22 flumes, because the flumes are not hydraulic scale models of each other. Since throat

length and throat bottom slope remain constant for a series of flumes while other dimensions arevaried, each of the 22 flumes is an entirely different device. For example, it cannot be assumed that

a dimension in the 12-ft flume will be three times the corresponding dimension in the 4-ft flume.

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Figure 4.24: Definition Sketch for Parshall Flume

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Table 4.12: Dimensions for Parshall Flumes

Parshall flumes are arbitarily classified into three groups, on the basis of throat width, for selecting

sizes and discharge determination. These groups are "very small" for 1, 2, and 3 inch flumes;"small" for 6 in. through 8 ft. flumes; and "large" for 10 ft. up to 50 ft. flumes.

Very small flumes(1", 2", and 3")

The discharge capacity of very small flumes ranges from 0.09 L/s to 32 L/s. The capacity of each

flume overlaps that of the next size by about one-half the discharge range (Table 4.13). The

relatively deep and narrow throat section causes turbulence and makes the hbgauge difficult to read

in very small flumes. Consequently, hcgauge, located near the downstream end of the diverging

section is added. Under submerged flow conditions, this gauge may be read instead of the hbgauge.

The hcreadings are converted to hbreadings by using a graph, as will be explained later under the

section of submerged flow.

Small flumes(6", 9", 1', 1'6", 2' up to 8')

46

The discharge capacity of small flumes ranges from 0.0015 m3/s to 3.95 m

3/s. The piezometer tap

for the upstream head, ha, is located in one of the converging walls a distance of a = 2/3 A upstream

from the end of the horizontal crest, where A is length of the converging section side wall. The

location of the piezometer tap for the downstream head, hb, is the same in all small flumes, being 51

mm upstream from the low point in the sloping throat floor and 76 mm above it.


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Table 4.13: Discharge Characteristics of Parshall Flumes

Large flumes(10' up to 50')

The discharge capacity of the large flumes ranges from 0.16 m3/s to 93.04 m3/s. The axial length ofthe converging section is considerably longer than it is in small flumes to obtain an adequately

smooth flow pattern in the upstream part of the structure. The measuring station for the upstream

head, ha, is at a = b/3 + 0.813 m upstream from the end of the horizontal crest. The location of the

piezometer tap for the downstream head, hb, is the same in all large flumes, being 305 mm upstream

from the floor at the downstream edge of the throat and 229 mm above it.

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The upstream head-discharge relationship for Parshall flumes, as calibrated empirically, is

represented by an equation of the form

(4.21)

aKhQ=

where K denotes a dimensional factor which is a function of the throat width. The power varies

between 1.522 and 1.60. Values of K and for each flumes size are given in Table 4.13. In the

listed equation, Q is the modular discharge in m3/s, and hais the upstream gauge reading in meters.

Submerged flow

When the ratio of gauge readings hb/ha exceeds the limits of 0.60 for 3, 6, and 9 inch flumes, 0.70 for

1 to 8 ft flumes and 0.80 for 10 to 50 ft flumes, the modular flume discharge is reduced due to

submergence. The submerged flow discharge of Parshall flumes equals

( )

( )nst

nf

bas

sS

hhCQ

log

= (4.22)

where Qs= submerged flow discharge, Cs = submerged flow coefficient (Table 4.14 )

ha = upstream head and hb= downstream head

nfand ns= free flow and submerged flow exponents (Table 4.14).

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Table 4.14: Coefficients and Exponents for Parshall Flume.

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4.6. Orifices

A well defined opening in a plate or bulkhead, the top of which is placed well below the upstream

water level, is classified as an orifice. The upstream water level must always be well above the top

of the opening to avoid vortex flow and obtain true orifice flow. If the upstream water level drops

below the top of the opening, it no longer performs as an orifice but as a weir. The orifice can be setto discharge freely into the atmosphere, resulting in a considerable head loss. To avoid this

excessive head loss, the orifice is arranged with the tailwater above the top of the opening. This

submerged orifice conserves head and can be used where there is insufficient fall for a sharp-crested

weir, or where the head difference is too small to produce modular flow with a broad-crested weir or

flume. A general disadvantage of submerged orifices is that debris, weeds and sediment can

accumulate upstream of the orifice; and may prevent accurate measurements.

4.6 a. Circular Sharp-Edged Orifice

A circular sharp-edged orifice is a well-defined circular opening in a plate which is placed

perpendicular to the sides and bottom of a straight approach channel. Circular orifices have theadvantage that during installation no leveling is required. In practice, circular sharp-edged orifices

are fully contracted by having the channel bed and sides and the free water surface sufficiently

remote from the control section. The fully contracted circular orifice may be placed in a

non-rectangular approach channel.The basic head-discharge equation for submerged orifice flow is

HgACCQvd = 2 (4.23)

In this equation, H equals the head differential across the orifice and A is the cross-sectional areaof the orifice. Orifices should be installed and maintained so that the approach velocity is small, thus

ensuring that velocity coefficient Cvapproaches unity. Calibration studies by various researchers

give the average Cdvalues shown in Table 4.16. The error in the discharge coefficient for a well

maintained circular sharp-crested orifice, constructed with reasonable care and skill, is about 2

percent.

Table 4.16: Average Discharge Coefficients for Circular Orifices

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To ensure full contraction and accurate flow measurements, thelimits of application of the circular

orifice are: The edge of the orifice should be sharp and smooth. The upstream face of the orifice plate

should be vertical and smooth.

The distance from the orifice edge to the bed and side slopes of the approach and tailwater

channels should not be less than the radius of the orifice. To prevent air entrainment, the

upstream water level should be at a height above the orifice top which is at least equal to the

orifice diameter.

To make the approach velocity negligible, the wetted cross-sectional area at the upstream

head measurement station should be at least 10 times the orifice area.

The practical lower limit of the differential head across the orifice is related to fluid

properties, and to the accuracy with which gauge readings can be made. The recommended

lower limit is 0.03 m.

4.6 b. Rectangular Sharp-Edged Orifice

A rectangular sharp-edged orifice, used as a discharge measuring device, is a well-defined

rectangular opening in a thin plate or bulkhead, which is placed perpendicular to the bounding

surfaces of the approach channel. The top and bottom edges should be horizontal and the sides

vertical. Most submerged rectangular orifices have a height, w, which is considerably less than the

width, b. This is necessary because the ratio of depth to width of irrigation canals is generally small,

and because changes in flow depth should not influence the discharge coefficient too

rapidly. The principal type of rectangular orifice for which the discharge coefficient has been

carefully determined in laboratory tests is the submerged, fully contracted, sharp-edged orifice.Since the discharge coefficient is not so well defined where the contraction is partially suppressed, it

is advisable to use a fully contracted orifice wherever conditions permit. To regulate discharge, it is

possible to suppress both bottom and side contractions so that the orifice becomes an opening below

a sluice gate.

A submerged rectangular orifice structure is shown in Figure 4.28. A box is provided downstream

from the orifice to protect unlined canals from erosion. The box sides and the floor should be set

away from the orifice a distance of at least two times the orifice height. The top of the orifice wall is

set lower than the maximum design water level in the canal, so that the wall may act as an overflow

spillway if the orifice should become blocked. Suitable submerged orifice-box dimensions for a

concrete, masonry, or wooden structure as shown in Figure 4.28 are listed in Table 4.17.


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Figure 4.28: Rectangular Orifice Dimensions

Table 4.17: Recommended Dimensions for a Rectangular Orifice


Equation (4.23) is the basic head-discharge equation for submerged orifice flow, and for rectangularorifice it can be written as

)(2 21 hhgwbCCQ vd = (4.24)

where h1- h2equals the head differential across the orifice. In general, submerged orifices should be

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designed and maintained so that the approach velocity is negligible and the coefficient Cv

approaches unity. For a fully contracted, submerged, rectangular orifice, the discharge coefficient

Cd= 0.61. If the contraction is suppressed along part of the orifice perimeter, then following

approximate discharge coefficient may be used.

Cd= 0.61 (1 + 0.15 r) (4.25)

where r equals the ratio of the suppressed portion of the orifice perimeter to the total perimeter.

If water discharges freely through an orifice with both bottom and side contractions suppressed, the

flow pattern equals that of free outflow below a vertical sluice gate as shown in Figure 4.29. The

free discharge below a sluice gate is a function of upstream water depth and the gate opening,

expressed as follows.

)(2 21 yygwbCCQ vd = (4.26)

Figure 4.29: Flow through a Sluice Gate

chapter 4 flow measurement

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