Get Help

Share

Flow Characteristics

Parshall Flume Free-Flow Discharge Equations

 

9-Inch Parshall Flume for Open Channel Flow MeasurementThe general free-flow discharge equation for Parshall flumes may be expressed as:

 

Equation

Throat Width

C (Imperial)

C (SI)

n

1”

0.338

0.0479

1.55

2”

0.676

0.0959

1.55

3”

0.992

0.141

1.55

6”

2.06

0.264

1.58

9”

3.07

0.393

1.53

1’

4

0.624

1.522

1’-6”

6

0.887

1.538

2’

8

1.135

1.55

3’

12

1.612

1.566

4’

16

2.062

1.578

5’

20

2.5

1.587

6’

24

2.919

1.595

7’

28

3.337

1.601

8’

32

3.736

1.607

10’

39.38

4.709

1.6

12’

46.75

5.590

1.6

19’

57.81

6.912

1.6

20’

76.25

9.117

1.6

25’

94.69

11.32

1.6

30’

113.13

13.53

1.6

40’

150

17.94

1.6

50’

186.88

22.35

1.6


Submergence Transition in Parshall Flumes

Submerged flow in a flume occurs when downstream resistance to flow controls the flow upstream.  Submergence results in lower flow velocities and higher water surface levels than would otherwise occur for a given flow rate under free-flow conditions.  Submerged flumes discharge less flow than would otherwise be indicated were the standard free-flow ratings tables used.

The submergence ratio is a ratio of the downstream depth (Hb) to the upstream depth at the point of measurement (Ha).  The submergence ratio (Hb/Ha) is expressed as a percentage.

The point at which the downstream water level becomes sufficiently high to reduce the velocity (where the effects of submergence are not negligible) is termed the transition submergence, st.  Transition submergence ratios for Parshall flumes range from 50% to 80%, and increase as the flume length increases.

 

Parshall Flume Submergence Transition (St)

Flume Size

St

1” – 3”

50%

6”-9”

60%

1’-8’

70%

10’-50’

80%


When measuring submerged flow in a Parshall flume two head measurements are made:  one at the point of measurement (Ha) and the other in the throat of the flume (Hb).  Note that the zero elevation for Hb is the same as for Ha, although the intake for Hb is lower than the floor of the flume where Ha is measured.

Keep in mind, though, that since the flow in the throat is quite turbulent, causing the water level to fluctuate considerably, it is difficult to accurately measure Hb with a staff gauge.  Consequently, a stilling well is typically required for an accurate measurement of Hb.  The addition of a secondary stilling well creates its own problems, though, as silting and clogging (and the associated maintenance) become issues on solids / debris laden flows.

Due to the added instrumentation costs and operational complexity of operating under submerged flow conditions, Openchannelflow recommends operating flumes under free-flow conditions whenever possible.

Parshall Flume Submergd Flow Discharge Equations

For submerged flow in Parshall flumes two options exist: determine the indicated flow and submergence ratio and then correct the flow by utilizing the submergence – discharge tables, or utilize the equations below. Wahl – 1’ to 8’ Parshall:

Equation

Size of Flume

Multiplying Factor, M

1’

1.0

1.5’

1.4

2’

1.8

3’

2.4

4’

3.1

5’

3.7

6’

4.3

7’

4.9

8’

5.4


Where ISO 9826:1992(E):

Equation

Accuracy of the Parshall Flume

Under laboratory conditions Parshall flumes can be expected to operate accurately to better and 2%.  Unless maintenance is meticulous, growth of vegetation in the channel, accumulations of trash and silt near the flume, and deterioration of the flume from corrosion or growths of algae on the surface make accuracies of better than 5% doubtful.  These conditions, however, generally apply to all flumes in experiencing similar conditions and should not be taken solely as a reflection on the nature of the Parshall flume.

Flow Velocity Approaching a Parshall Flume

As a general rule for flumes, the approach velocity should be no greater than:

Equation

Sources:

ASTM D 1941-91 (Reapproved 2007) Standard Test method for Open Channel Flow Measurement of Water with the Parshall Flume.

Water Measurement Manual, 3rd Edition, U.S. Department of the Interior, Bureau of Reclamation, 1997.

ISO 9826:1992 Measurement of Liquid in Open Channels – Parshall and SANIIRI Flumes.

Wahl, T., Equations for Computing Submerged Flow in Parshall Flumes.

Replogle, J., Flow Meters for Water Resource Management, Water Resources Bulletin, Vol. 6, No. 3, 1970.