...
- h~r~ = reference level
- L = length of flume
- b = width of flume throat
- m~l~ = modular limit
- h~1~ = upstream water level
- H~1~ = upstream energy level
Q = C~g~ . C~d~ . b .
03 - Stage discharge^image148.gif!
C~d~ =
The modular limit is input, (generally in the order of 0.85 - 0.95). If the modular limit is exceeded a missing value is entered for the discharge.
!h3. Trapezoidal throated flume (Herschy, 1985)
03 - Stage discharge^image187.jpg!
Parameters: - L = length of flume
- b = width of throat bottom
- m = side slope
- m~l~ = modular limit
- h~1~ = upstream water level
- H~1~ = upstream energy level
Q = C~g~ . C~d~ . C~s~ . b .
C~d~ =
where:
x = 0.972 - 0.878 m + 0.366 m^2^ - 0.0543 m^3^ for m £2
x = 0.438 - 0.127 m + 0.015 m^2^ - 0.5976 m^3^ for m > 2
C~s~ = 1.002 + 0.678 y + 0.0327 y^2^ - 0.065 y^3^ for y £3
C~s~ = 0.088 + 1.144 y - 0.0488 y^2^ - 0.0016 y^3^ for y > 3
with:
y = m h~1~ /b
The modular limit is input, (generally in the order of 0.85 - 0.95). If the modular limit is exceeded a missing value is entered for the discharge.Rectangular/triangular/trapezoidal flume (Bos, 1978)
03 - Stage discharge^image191.jpg!
Parameters: - h~r~ = reference level
- L = length of flume
- b = width of throat bottom
- m = side slope
- m~l~ = modular limit
- H~1~ = upstream energy level
C~d~ = 0.845 + 0.726!03 - Stage discharge^image077.gif! - 1.563!03 - Stage discharge^image079.gif! + 1.156!03 - Stage discharge^image081.gif! for!03 - Stage discharge^image097.gif! £0.5
C~d~ = 0.957 - 0.017!03 - Stage discharge^image077.gif! + 0.046!03 - Stage discharge^image079.gif! + 0.017!03 - Stage discharge^image081.gif! for!03 - Stage discharge^image097.gif! > 0.5
y~c~ =for m = 0
y~c~ =
Following profiles can be covered:
b > 0 and m = 0 rectangular flume
b = 0 and m > 0 triangular flume
b > 0 and m > 0 trapezoidal flume
The modular limit is input, (generally in the order of 0.85 - 0.95). If the modular limit is exceeded a missing value is entered for the discharge.Truncated triangular flume (Bos, 1978)
Parameters: - h~r~ = reference level
- L = length of flume
- b = width of flume
- h~tr~ = height of triangle
- m~l~ = modular limit
- H~1~ = upstream energy level
C~d~ is given by the rectangular flume equations
m = b/2h~tr~
C~d~ is given by the rectangular flume equations
The modular limit is input. If the modular limit is exceeded a missing value is entered for the discharge.Parabolic flume (Bos, 1978)
03 - Stage discharge^image215.jpg!
Parameters: - h~r~ = reference level
- L = length of flume
- f = shape parameter
- m~l~ = modular limit
- H~1~ = upstream energy level
Q = C~g~ C~d~ Öf!03 - Stage discharge^image217.gif!
03 - Stage discharge^image219.gif!
C~d~ is given by the rectangular flume equations
The modular limit is input. If the modular limit is exceeded a missing value is entered for the discharge.Circular flume (Bos, 1978)
03 - Stage discharge^image221.jpg!
Parameters:
1. h~r~ = reference level
2. L = length of flume
3. d = diameter of flume
4. m~l~ = modular limit
5. H~1~ = upstream energy level
03 - Stage discharge^image223.gif!
03 - Stage discharge^image195.gif!
C~d~ is given by the rectangular flume equations
y~c~ = H~1~ {0.75183 - 0.04410!03 - Stage discharge^image226.gif! + 0.02578!03 - Stage discharge^image228.gif! - 0.04568!03 - Stage discharge^image230.gif! } for!03 - Stage discharge^image232.gif! £1
y~c~ = H~1~ {0.52496 + 0.53698!03 - Stage discharge^image226.gif! - 0.46709!03 - Stage discharge^image228.gif! - 0.09393!03 - Stage discharge^image230.gif! } for 1 <
y~c~ = H~1~ {1.0505 - 0.34016!03 - Stage discharge^image226.gif! + 0.01743!03 - Stage discharge^image228.gif! - 0.005307!03 - Stage discharge^image230.gif! } for!03 - Stage discharge^image232.gif! > 1.8
a= 2. arccos (1 - 2 y~c~ /d)
The modular limit is input. If the modular limit is exceeded a missing value is entered for the discharge.U-throated flume (Bos, 1978)
Parameters: - h~r~ = reference level
- L = length of flume
- d=b = width of flume
- m~l~ = modular limit
- H~1~ = upstream energy level
For H~1~ < 0.7 d the formulae of the circular flume apply.
For H~1~ ³0.7 d the discharge is computed by:
03 - Stage discharge^image246.gif!
03 - Stage discharge^image248.gif!
C~d~ is given by the rectangular flume equations
The modular limit is input. If the modular limit is exceeded a missing value is entered for the discharge.Parshall flumes
Parameters: - h~r~ = reference level
- n~pf~ = throat width number (see below)
- h~1~ = upstream water level
- h~2~ = downstream water level
The general discharge equation is of the form:
K and u follow from the underneath Table.
Table Parameters of the discharge equation of Parshall flumes
width n~pf~ K u m~l~ p a b c m~f~
1" 1 0.0604 1.55 0.50 1.64 -4.5837 11.118 -4.8464 1.0*10^-3^
2" 2 0.1207 1.55 0.50 1.48 -5.2025 12.141 -5.1189 1.0*10^-3^
3" 3 0.1771 1.55 0.50 1.65 -5.3387 12.834 -5.3693 1.0*10^-3^
6" 4 0.3812 1.58 0.60 1.57 -1.6117 5.3856 -1.3952 1.0*10^-3^
9" 5 0.5354 1.53 0.60 1.50 -4.2328 10.747 -4.0566 1.0*10^-3^
1' 6 0.6909 1.522 0.70 1.54 -5.0446 5.5661 -0.80775 1.0*10^-3^
1'6" 7 1.506 1.538 0.70 1.54 -5.0446 5.5661 -0.80775 1.4*10^-3^
2' 8 1.428 1.550 0.70 1.54 -5.0446 5.5661 -0.80775 1.8*10^-3^
3' 9 2.184 1.566 0.70 1.54 -5.0446 5.5661 -0.80775 2.4*10^-3^
4' 10 2.953 1.578 0.70 1.54 -5.0446 5.5661 -0.80775 3.1*10^-3^
5' 11 3.732 1.587 0.70 1.54 -5.0446 5.5661 -0.80775 3.7*10^-3^
6' 12 4.519 1.595 0.70 1.54 -5.0446 5.5661 -0.80775 4.3*10^-3^
7' 13 5.312 1.601 0.70 1.54 -5.0446 5.5661 -0.80775 4.9*10^-3^
8' 14 6.112 1.607 0.70 1.54 -5.0446 5.5661 -0.80775 5.4*10^-3^
10 ' 15 7.463 1.60 0.80 2.00 -26.086 49.689 -23.103 1.0
12' 16 8.859 1.60 0.80 2.00 -26.086 49.689 -23.103 1.2
15' 17 10.96 1.60 0.80 2.00 -26.086 49.689 -23.103 1.5
20' 18 14.45 1.60 0.80 2.00 -26.086 49.689 -23.103 2.0
25' 19 17.94 1.60 0.80 2.00 -26.086 49.689 -23.103 2.5
30' 20 21.44 1.60 0.80 2.00 -26.086 49.689 -23.103 3.0
40' 21 28.43 1.60 0.80 2.00 -26.086 49.689 -23.103 4.0
50' 22 35.41 1.60 0.80 2.00 -26.086 49.689 -23.103 5.0
The modular limit m~l~ varies from 0.5 to 0.8. In case this limit is exceeded the discharge is reduced with the quantity Q~e~ , where:
q =
The parameters m~l~ , m~f~ , a, b and c are presented in the Table. The corrected discharge then follows from:
Q~c~ = Q - Q~e~H-flumes
Parameters: - h~r~ = reference level
- n~H~ = flume depth number (see below)
- h~1~ = upstream water level
- h~2~ = downstream water level
The parameters a, b and c follow from the underneath table.
Table Parameters of the discharge equation of H-flumes
Type Depth n~H~ a b c m~l~
HS 0.4' 1 -0.4361 2.5151 0.1379 0.25
HS 0.6' 2 -0.4430 2.4908 0.1657 0.25
HS 0.8' 3 -0.4410 2.4571 0.1762 0.25
HS 1.0' 4 -0.4382 2.4193 0.1790 0.25
H 0.5' 5 0.0372 2.6629 0.1954 0.25
H 0.75' 6 0.0351 2.6434 0.2243 0.25
H 1.0' 7 0.0206 2.5902 0.2281 0.25
H 1.5' 8 0.0238 2.5473 0.2540 0.25
H 2.0' 9 0.0237 2.4918 0.2605 0.25
H 2.5' 10 0.0268 2.4402 0.2600 0.25
H 3.0' 11 0.0329 2.3977 0.2588 0.25
H 4.5' 12 0.0588 2.3032 0.2547 0.25
HL 3.5' 13 0.3081 2.3935 0.2911 0.30
HL 4.0' 14 0.3160 2.3466 0.2794 0.30
The modular limit is presented in the last column of the table. If this limit is exceeded, a missing value is entered for the discharge.Application
Select the function <Measurement-Structure> from the Flow Measurements functions map. The required entries to run this function comprise:Series Codes
Select a Discharge series by highlighting the series in the series list and pressing <Select> next to the discharge series textbox. HYMOSwill extract all relations for this series from the database and place them in the relations list box on the form.
You can now add a new relation or use an existing relation. If you want to use an existing relation, choose the relation from the relation list box.Structure equation
Select a structure equation by selecting the appropriate tab of the measurement structures spreadsheet and select the row with the type of structure. HYMOSwill now present all input fields for the selected equation type.Transformation period
By double-clicking the date textboxes you can change the validity time period of the transformation equation.Add Relation
If all coefficients of the relation is entered you can save the relation to the database by pressing the <Add Relation> button.
After you made your selections press <Execute> and analyse the results as a graph, table and report. To show the graph on screen select <Graph> from the functions tab. To analyse the report press <Report> from the functions tab.
You can also Save the generated series by pressing the <Save> button or exporting the series by selecting <Export>.Calculation of Discharges
When the form is loaded a discharge series must be selected from the series list box. HYMOSwill look in the database if a relation for the selected discharge series exists. If so it will show all relations in the relations list box. Structures have relations which are valid for a defined period, for each period a relation can be made. A period is defined by a start and end date of a rating equation. When a discharge series is selected a new relation can be made for a structure or an existing relation can be selected from the relations list box. When a new relation is made the user must also select an upstream water level and a downstream water level. The downstream water level is necessary for checking if there is submerged flow or free flow. When the user does not want a check on submerged flow, a downstream water level in not required.
For correction of the velocity head, a water level series must contain a cross-sectional profile. This profile is necessary to calculate energy levels from the measured water levels. Most measurement structure equations make discharge calculations based on energy levels. The cross-sectional profiles are measured profiles which can be entered in the Entry and Edit functions. These profiles are saved in the HYMOSdatabase with a link to the water level series.
For calculating discharges over a structure, including check on submergence and velocity head correction, HYMOSthus requires two water level series with for each water level series a cross-sectional profile. If cross-sectional profiles are not available in the database, HYMOSwill give a warning when pressing EXECUTE and stop the discharge calculation.
There is one structure, the 'General Weir' which requires also a gate level series for the calculation. This gate level series must be selected from the series list box.
While calculating the discharges it is possible that HYMOSwill return missing values. Missing values are returned in the following situations: - The upstream or downstream water levels are missing.
- If the date of the calculated discharge is outside the validity period of the relation.
- The upstream water level is above the structure height.
- The upstream water level is above the highest point of the upstream cross sectional profile.
- If the modular limit is exceeded.
- The downstream water level is above the highest point of the downstream cross sectional profile.
A zero discharge is returned when: - The upstream water level is below the Sill height of the structure.
- The upstream water level is below the lowest point of the upstream cross sectional profile.
- The downstream water level is below the lowest point of the downstream cross sectional profile.
General computation procedure
The general equation used for measurement structures is:
where:
H = total head
g = acceleration due to gravity
b = width
C~d~ = coefficient of discharge
As mentioned earlier the total head H cannot be measured in practice. Therefore an iterative procedure is included to compute the discharge from the measured head h . This iterative procedure is as follows:
1. The area of cross section flow A is computed from the cross-section profile data for the measured head h .
2. The discharge is computed with the discharge equation, using the measured head h instead of the total head H .
3. The total head H is computed from equations:
4. If the difference between the total head H and the measured head h is larger than 0.001 then the computed total head H is used and the computation is restarted in 1.
Sometimes this iterative procedure is not used to compute the discharge. Instead a dimensionless velocity coefficient C~v~ is used in the equation to correct for the velocity of approach. This coefficient C~v~ can be obtained from a table from the cross-sectional area and C~d~ bh.