• 21 Sep 2022
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Article Summary

The Flow-Head Control imposes a specified flow discharge relationship at a channel control point such as a flume or weir.

## Data

Field in Data Entry Form

Description

Name in Datafile

Upstream Node

Upstream node label

Label1

Downstream Node

Downstream node label

Label2

Elevation of Weir

Elevation of weir crest (m above datum)

Zc

Modular Limit

modular limit (eg 0.9, range 0.999 to 0)

m

Interpolation Method

SPLINE if a cubic spline is to be fitted to the data, or LINEAR to use linear interpolation. (If the field is blank then linear interpolation is used.)

smooth

n/a

Number of ensuing flow and water level data pairs

n1

Discharge

Flow corresponding to water level yi (in m3/s)

Qi

Stage

Water level (in metres above datum)

yi

## Theory and Guidance

The Flow-Head Control imposes a specified flow discharge relationship at a channel control point such as a flume or weir.

It is not always possible to describe all channel controls such as weirs, sluices, flumes or even bridges in terms of simple equations for free and drowned flows. The Flow-Head Control lets you define points on a rating curve corresponding to estimated or measured flow and head values at a channel control.

### Equations

#### Mode 1 - Free Flow (positive or negative)

Condition

h2/ h1 < m

Equation

 Q = f(y1) (1)

where

f is the specified function (values are interpolated from the user entered table of Q:y).

For negative flows y2 is substituted for y1.

#### Mode 2 - Drowned Flow (positive or negative)

Condition

h2 / h1 ≥ m

Equation

 Q = f(y1) drownf (2)

where or

drownf = (1 - (y2 - zc) / (y1 - zc)) / (0.3 * (1 - m))

if the first formula gives drownf < 0.3

h1 = upstream depth of water above crest = y1 - zc

h2 = downstream depth of water above crest = y2 - zc

zc = crest elevation

m = modular limit

For negative flows switch h2 and h1

### General

If a SPLINE is specified, then a cubic spline is fitted to the data. This will help smooth data where the curvature is high. However, if the data are 'noisy' or if there are sudden changes in gradient, splines may lead to oscillations and may not be suitable.

In free flow (mode 1) the flows and levels at the Flow-Head Control will comply with the user input table. However in drowned flow (mode 2) the table of values is altered by the drowned flow reduction factor (drownf). To encourage free flow you can set the modular limit to a high value (eg 0.999).

The second form of the drownf equation is an approximation used to avoid an infinite derivative as the downstream and upstream levels equalise. It is a linearisation of the drowning function between drownf = 0.3 and drownf = 0.0.

The maximum number of q-h data pairs allowed in the unit is 500.

## Datafile Format

Line 1 - Keyword 'QH CONTROL' [comment]

Line 2 - Label1, Label2

Line 3 - zc , m, [smooth]

Line 4 - n1

Line 5 to Line 4+n 1 - Q, yi

### Example

``````QH CONTROL
UNIT027     UNIT028
1.000     0.900SPLINE
3
1.000     0.000
2.000     1.000
3.000     2.000``````