04 With general structure

User structure rating equation

Background

If the discharge relation required for stage-discharge transformation of a structure is not covered by one of the measuring structures presented in the next section, then the user can provide a stage-discharge relation of the following power type:

where:

• h_ct = corrected water level: 0 £f_c £1
• a_i , b_i , c_i , = parameters applicable to the water level interval i, h_1,i to h_1,i+1 , with i £3
• h_1t = observed upstream water level at time t relative to the crest of the structure sill
• f_c = velocity head correction factor
• f_s = correction factor for submergence:
  (logarithmic)
  (polynomial)
  (power)
  
• H₁ , H₂ = energy head upstream respectively downstream of the structure
  Notes
• The discharge relations can be computed for a maximum of 3 interval levels. The upper boundary of the n'th level is taken equal to the lower boundary of the (n-1)'th interval.
• fs can be computed for a maximum of 3 intervals of SH . For each interval of SH the lower boundary and the parameters have to be entered. The lowest boundary will be treated as modular limit.
• The observed water levels upstream and downstream of the structure h ₁ and h ₂ may not represent the actual water levels depending on the hydraulic characteristics of the mouth of the intake pipe of the measuring well. In some cases it may be necessary to add to the observations a part of the velocity head to get the proper value.
• To compute the velocity head and the submergence ratio H2/H1 , the cross-sectional profiles of the channel at the water level measuring locations upstream and downstream of the structure have to be known. These profiles can be entered through option <cross-sectional profiles> under <Entry & editing>.
  

  Structure Functions

  There are four possible options for calculating the discharge over a structure depending on the correction applied. It is possible to correct the water level by a velocity head correction factor and/or to correct for submergence. The four available options will be described in more detail.
  

  Power Type

  For the Power Type Equation an upstream water level series and a gate level series is required. Besides these time series a processing period and some coefficients must be entered. The following equations are used:
  Without overflow height: Q = C*(h - gate) ^B
  With overflow height: Q = C*(h - gate) ^B for h-gate < Overflow height
  Q = C*(h - gate +A)) ^B for h-gate >= Overflow height
  where:
  h = observed upstream water level series
  gate = observed structure gate level series
  A, B, C = rating parameters entered by the user
  

  Power type with submergence correction

  For the Power Type Equation with Submergence Correction an upstream water level series as well as a downstream water level series is required. If available a gate level series may also be entered. When no gate level series is entered the gate level will be equal to the lower boundary of the first equation. Besides these time series a processing period and some coefficients must be entered.
  The following equation is used to calculate the discharges:
  
  where:
  h = observed upstream water level series
  gate = observed structure gate level series, or lower boundary of the rating
  equation of the first interval.
  A, B, C = rating parameters entered by the user
  f _s = correction factor for submergence
  Q = computed discharges
  For the submergence correction the ratio of the measured downstream and upstream water levels is computed:
  S _h = 100 h ₂ /h ₁
  where:
  h ₁ = upstream water level minus the gate level.
  h ₂ = downstream water level minus the gate level.
  Selection of the appropriate submergence interval equation is done by using the following rules:
  S <L₁ then f_s = 1
  L₁ < S < L₂ then f_s computed with coefficients of first interval
  L₂ < S < L₃ then f_s computed with coefficients of second interval
  S > L₃ then f_s computed with coefficients of third interval
  where
  L_1,2,3 = Lower boundary for respectively interval 1, 2 and 3.
  f_s = correction factor for submergence.
  The following rules appear for the computation of the discharges:
  
• if upstream water level < gate level then q=0
• if upstream water level < downstream water level then q = missing
  

  Power type with velocity head correction

  For the Power Type Equation with Velocity Head Correction an upstream water level series is required. If available a gate level series may also be selected. When no gate level series is selected the gate level will be equal to the lower boundary of the first equation. Besides these time series a processing period and some coefficients must be entered. For the correction of the velocity head also an upstream cross-section profile is required, this cross-section is the cross-section of the upstream water level series.
  The following equation is used to calculate the discharges:
  
  where:
  h = observed upstream water level series
  gate = observed structure gate level series
  A, B, C = rating parameters entered by the user
  f_c = velocity head correction factor (0 £f_c £1)
  v = computed upstream velocity by using cross-section profile
  g = 9.81
  Q = computed discharges
  

  Power type with velocity head and submergence correction

  For the Power Type Equation with Velocity Head and Submergence Correction an upstream water level series as well as a downstream water level series is required. If available a gate level series may also be selected. When no gate level series is selected the gate level will be equal to the lower boundary of the first equation. Besides these time series a processing period and some coefficients must be entered. For the correction of the velocity head also an upstream and a downstream cross-section profile is required. These cross-section profiles are the cross-sections of the upstream and downstream water level series.
  The following equation is used to calculate the discharges:
  
  where:
  h = observed upstream water level series
  gate = observed structure gate level series
  A, B, C = rating parameters entered by the user
  f_c = velocity head correction factor (0 £f_c £1)
  v = computed upstream velocity by using cross-section profile
  g = 9.81
  Q = computed discharges
  The submergence correction is computed on the same way as for the Power Type Equation with Submergence Correction.
  

  Application

  Select the function <Q-H-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, if available, 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 equation option from the function listbox. HYMOSwill now present all input fields for the selected equation type. Remember that for relations with velocity corrections also cross-sections must be selected from the cross-sections list boxes.
  

  Transformation period

  By double-clicking the date textboxes you can change the validity time period of the transformation equation. It is also possible to change the dates manually by typing the start and end dates in the textboxes.
  

  Add Relation

  If all coefficients of the relation is entered you can save the relation to the database by pressing the <Add Relation> button. It is however not possible to have overlapping relations for a discharge series. HYMOSwill warn the user when the new relation overlaps exiting relations, the user has the choice to remove the old relations and save the newly made relation, or cancel the save job.
  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>.
  

  Example of computation procedure

  As an example of the computation procedure the option "Power Type with submergence correction" will be explained in more detail. The computation will be done as follows:
  1. No velocity head correction is used therefore the corrected water levels are equal to the measured water levels: h_ct = upper water level
  2. Compute H₁ en H₂ :
• H₁ = upper water level - gate level_{}
• H₂ = lower water level - gate level_{}
  3. If H₁ < 0 then the discharge is 0, Q=0
  4. Assume there is no submergence, correction factor f_s = 1
  5. Compute the discharge Q with the given equation and correction factor f_s .
  6. If H₂ <= 0 there is no submergence, computation is finished.
  7. If H₂ > 0 then the submergence correction ration is computed, SH = H2/H1. Select the correct submergence function:
• If SH < Submergence boundary 1 then f_s = 1
  
• If boundary 1 < SH < boundary 2; compute submergence factor with first level coefficients
• etc...
• If SH > Upper boundary then use upper level coefficients.
  8. If the submergence factor f_s > 1, then set factor f_s = 1.
  9. Compute the discharge as in point 5
  Note :
  The boundaries for submergence must be entered as percentage ratio SH=100*H2/H1.
  The boundaries for the computation of the discharge Q are entered according to the water levels.