We will first neglect the velocity head of the approach flow in other words,

we will assume that E0 h0. With this assumption, Cv 1.0 from Equation 6.14,and by using Equation 6.17

kd 0:358 0:038 0:200:75

0:368

Then, from Equation 6.16, kw (0.368)(1.0) 0.368. Substituting this intoEquation 6.15,

Q kw2g

pLwh

3=20 0:368

29:81

p1:00:203=2 0:146 m3=s

We will now refine the solution by taking the approach velocity head into account

based on the calculated discharge. The total depth at the approach section is

0.30 0.20 0.50 m, thus, V0 0.146/[(0.50)(1.0)] 0.292 m/s. The correspond-ing velocity head becomes V 20 /(2g) (0.292)2/[2(9.81)] 0.004 m. Thus,E0 0.20 0.004 0.204 m. We can now recalculate Cv and kd, usingEquations 6.14 and 6.17, respectively, as

Cv E0h0

3=2 0:204

0:20

3=2 1:03

and

kd 0:358 0:038E0Lb

0:358 0:038 0:2040:75

0:368

Then, by using Equation 6.16, kw (0.368)(1.03) 0.379. Substituting this intoEquation 6.15, we obtain Q 0.15 m3/s. We can now update the velocity headagain using this discharge, and repeat the calculations. The next set of

calculations results in Q 0.15 m3/s. This is the same as the result of theprevious iteration, and is accepted as the final result.

6.1.3 FLUMES

Flumes are open-channel flow segments built with contracted sidewalls and/or

raised bottoms. Among the various types of flumes available as flow measuring

devices summarized by US Bureau of Reclamation (2001), the Parshall flume is

employed most widely. A schematic of a Parshall flume is shown in Figure 6.8,

with the dimensions given in Table 6.1 for various sizes. Flumes with throat

widths of less than 8 ft have a rounded entrance with a 25% floor slope.

The flow passes through the critical depth at the throat section when the

downstream depth is shallow. This condition is known as free flow. A unique

water surface profile develops within the flume for each discharge under the free

flow conditions, and it is adequate to take one depth measurement, h0, to

determine the discharge. However, high downstream depths cause submerged

6.1 Flow measurement structures 209

flow conditions. In such a case a second depth measurement, hT, is needed to

determine the discharge. The percentage of submergence for Parshall flumes

is defined as 100(hT/h0). For flumes having a throat width of 18 ft, the

submergence should exceed 70% to affect the discharge measurement in the

flume. For flumes with larger throat widths, the threshold submergence is 80%

(Kilpatrick and Schneider, 1983).

LC LT LD

D

N

C

2C/3

h0hT

WCWT WD

K

ab

Q

Q

Q

Q

L

FIGURE 6.8 ParshallFlume (after

Kilpatrick andSchneider, 1983)

TABLE 6.1 Standard Parshall Flume Dimensions (After Kilpatrick and Schneider 1983)

Widths Axial lengths Vertical dimensions Gage points Free flow capacity

WT (ft) WC (ft) WD (ft) LC (ft) LT (ft) LD (ft) D (ft) N (ft) K (ft) C (ft) L (ft) a (ft) b (ft) Min. (cfs) Max. (cfs)

1.0 2.77 2.00 4.41 2.0 3.0 3.0 0.75 0.25 4.50 3.00 0.167 0.25 0.11 16.11.5 3.36 2.50 4.66 2.0 3.0 3.0 0.75 0.25 4.75 3.17 0.167 0.25 0.15 24.62.0 3.96 3.00 4.91 2.0 3.0 3.0 0.75 0.25 5.00 3.33 0.167 0.25 0.42 33.13.0 5.16 4.00 5.40 2.0 3.0 3.0 0.75 0.25 5.50 3.67 0.167 0.25 0.61 50.44.0 6.35 5.00 5.88 2.0 3.0 3.0 0.75 0.25 6.00 4.00 0.167 0.25 1.30 67.95.0 7.55 6.00 6.38 2.0 3.0 3.0 0.75 0.25 6.50 4.33 0.167 0.25 1.60 85.66.0 8.75 7.00 6.86 2.0 3.0 3.0 0.75 0.25 7.00 4.67 0.167 0.25 2.60 103.57.0 9.95 8.00 7.35 2.0 3.0 3.0 0.75 0.25 7.50 5.00 0.167 0.25 3.00 121.48.0 11.15 9.00 7.84 2.0 3.0 3.0 0.75 0.25 8.00 5.33 0.167 0.25 3.50 139.510.0 15.60 12.00 14.00 3.0 6.0 4.0 1.12 0.50 9.00 6.00 6.0 300.012.0 18.40 14.67 16.0 3.0 8.0 5.0 1.12 0.50 10.00 6.67 8.0 520.015.0 25.00 18.33 25.00 4.0 10.0 6.0 1.50 0.75 11.50 7.67 8.0 900.020.0 30.00 24.00 25.00 6.0 12.0 7.0 2.25 1.00 14.00 9.33 10.0 1340.025.0 35.00 29.33 25.00 6.0 13.0 7.0 2.25 1.00 16.50 11.00 15.0 1660.030.0 40.40 34.67 26.00 6.0 14.0 7.0 2.25 1.00 19.00 12.67 15.0 1990.040.0 50.80 45.33 27.00 6.0 16.0 7.0 2.25 1.00 24.00 16.00 20.0 2640.050.0 60.80 56.67 27.00 6.0 20.0 7.0 2.25 1.00 29.00 19.33 25.0 3280.0

210 6 Hydraulic structures

The headdischarge relationship under the free flow conditions can be

approximately expressed as (Davis, 1963):

Y0 Q20

2Y 20 1 0:4X02 1:351Q0:6450 6:18

where

Y0 h0WT

6:19

X0 LWT

6:20

Q0 QfW 5=2T g

1=26:21

and Qf free flow discharge. The solution of this equation requires a trial-and-error method. For flumes with throat widths not exceeding 6 ft, we can replace

Equation 6.18 with a simpler expression (Dodge, 1963):

Q0 Y1:55040

1:3096X0:076606:22

For submerged conditions, the discharge is calculated by using

Qs Qf ksQc 6:23

where Qs submerged flow discharge, ks discharge correction factor, andQc discharge correction unadjusted to flume size (Kilpatrick and Schneider,1983). Figures 6.9 and 6.10 can be used to determine ks and Qc, depending on

the throat size. In these figures, the percentage of submergence is 100 hT/h0.

EXAMPLE 6.4 A standard Parshall flume has a throat width of WT 4.0 ft.Determine the free flow discharge corresponding to h0 2.4 ft.For WT 4.0 ft, from Table 6.1 we obtain L 4.0 ft. Then, by using Equations6.19, 6.20, and 6.22,

Y0 h0WT

2:44:0

0:6

X0 LWT

4:04:0

1:0

Q0 Y1:55040

1:3096X0:07660 0:6

1:5504

1:30961:00:0766 0:3459

Finally, by rearranging Equation 6.21 and evaluating Qf,

Qf Q0W 5=2T g1=2 0:34594:05=232:21=2 62:8 cfs

6.1 Flow measurement structures 211

EXAMPLE 6.5 Suppose the downstream depth is hT 1.82 ft in the Parshallflume considered in Example 6.4. Determine the discharge.

The percentage of submergence is 100(1.82/2.4) 76%. From Figure 6.9, withh0 2.4 ft and WT 4.0 ft, we obtain Qc 1.15 cfs and ks 3.1. Then, by usingEquation 6.23,

Qs Qf ksQc 62:8 3:11:15 59:2 cfs:

6.2 CULVERTS

Culverts are short drainage conduits that convey stormwater through highway

and railway embankments. They are also used as outlet structures for detention

basins. Most culverts are circular, rectangular (box), or elliptical in cross-section.

Other commonly used shapes include arch and pipe-arch culverts. Most culverts

are made of concrete, corrugated aluminum, and corrugated steel. Concrete

culverts may be reinforced. Some are lined with another material, such as

asphalt, to prevent corrosion and reduce flow resistance.

The inlet configuration plays an important role in the hydraulic performance of

culverts. A variety of prefabricated and constructed-in-place inlet installations

are commonly used. These include projecting culvert barrels, concrete headwalls,

end sections, and culvert ends mitered to conform to the fill slope. Figure 6.11

depicts various standard inlet types.

A variety of flow types can occur in a culvert, depending on the upstream and

downstream conditions, the inlet geometry, and the conduit characteristics.

A culvert may flow full, partially full (in subcritical or supercritical flow

h 0 (ft

)

Qc (cfs)0.06

0.3

0.4

0.5

0.6

0.8

1.0

1.5

2.0

2.5

0.14 0.2 0.3 0.4 0.6 0.8 1.0 1.4 2.0 4.0

Size of flume(feet)1.01.52.03.04.06.08.0

1.01.41.82.43.14.35.4

Correctionfactor, ks

6.0 8.0 10.0

70 74 78 82 86 90 94

72 76Percen

tage of s

ubmerge

nce

80 84 88 92 96

FIGURE 6.9 Submerged discharge correction for throat lengths of 18 ft (after Kilpatrick and Schneider, 1983)

212 6 Hydraulic structures