OPEN-CHANNEL HYDRAULICS:  LECTURE 042 - CONTROL OF FLOW

1. CONTROL OF FLOW

1.01
Control of flow means the establishment of a unique relation between stage and discharge, that is, a unique rating curve.
1.02
Critical flow and uniform flow are flow controls.
1.03
Gradually varied flow and unsteady flow are not flow controls.
1.04
Flow control can be of two types: (1) section control, and (2) channel control.
1.05
Critical flow can provide section and channel control.
1.06
Uniform flow can provide only channel control.
1.07
The most practical form of flow control is critical section control, that is, critical flow at a given control section.
1.08
Stage-discharge measurements at the control section enable the establishment of a suitable rating curve.
1.09
A measuring flume forces critical flow within the flume to establish flow control and allow the direct conversion of stage to discharge.
1.10
The Parshall flume is a commonly used measuring flume.

Fig. 01

Parshall flume, Cucuchucho constructed wetland, Michoacan, Mexico.

1.11
The flume can operate under both free-flow and partially submerged conditions.
1.12
Under free-flow conditions, only one stage measurement is required to determine the discharge.

2. WEIR DISCHARGE

2.01
Section control is usually provided by a weir, where the flow changes from subcritical upstream to supercritical downstream.
2.02
The control section is located in the vicinity of the weir crest.
2.03
For a broad-crested weir, the theoretical control discharge is:


 q = vc yc 

Eq. 1

2.04
in which q = unit-width discharge, v = flow velocity, and y = flow depth.
2.05
The critical velocity is:


 vc = (gyc)1/2 

Eq. 2

2.06
Therefore:


 q = g1/2 yc3/2 

Eq. 3

2.07
The critical depth in terms of the specific energy at the critical section He is:


 yc = (2/3) He 

Eq. 4

2.08
Therefore, the discharge is:


 q = (2/3)3/2 g1/2 He3/2 

Eq. 5


 q = Cd He3/2 

Eq. 6

2.09
The discharge coefficient is:


 Cd = (2/3)3/2 g1/2 

Eq. 7

2.10
In SI units, the discharge coefficient is 1.7; in U.S. Customary units, it is 3.09.

2.11
These are theoretical values, since the location of the critical section is uncertain.

2.12
In practice, the weir equation is expressed as:


 q = C H3/2 

Eq. 8

2.13
where H is the elevation of the water surface above the weir crest.

2.14
This assumes that the approach velocity, at a section sufficiently far from the weir, is zero.

2.15
The discharge coefficient C depends on the shape of the broad-crested weir and the local hydraulic conditions. It is typically less than the theoretical value.

2.16
For example, a discharge coefficient equal to 1.46, in lieu of the theoretical 1.7, has been reported for the spillway weir at the Boeraserie Conservancy, Guyana.

Fig. 02

Spillway weir, Boeraserie Conservancy, Guyana.

Fig. 03

Spillway weir at Valle Grande Dam, Cuajone, Moquegua, Peru.

Fig. 01

Parshall flume, Cucuchucho constructed wetland, Michoacan, Mexico.

Fig. 02

Spillway weir, Boeraserie Conservancy, Guyana.

Fig. 03

Spillway weir at Valle Grande Dam, Cuajone, Moquegua, Peru.

Narrator: Victor M. Ponce

Music: Fernando Oñate

Editor: Flor Pérez

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