7295efaf-ce4d-443d-ad16-033e88824882 483 4 8 decimal

Inflow Hydrograph flood_50_Yr 0030609012015 84.9 18 141.5 21 212.25 24 311.3 27 424.5 30 495.25 33 424.5 36 353.75 39 297.15 42 240.55 44.5 20045 192.44 48 169.8 51 141.5 54 141.5 57 141.5 60 183.95 60.6 20063 254.7 66 353.75 69 495.25 72 749.95 75 1584.8 78 2122.5 81 1768.75 84 1457.45 87 1245.2 90 1103.7 93 1018.8 96 905.6 99 806.55 102 665.05 105 509.4 108 396.2 111 311.3 114 254.7 117 198.1 120 169.8 123 141.5 126 113.2 129 113.2 132 84.9 135 84.9 138 84.9 1410502 mat :

Elevation / Area Elev_Area 2003015040350505756085070110080142090180082 mat :

cumec m 3^s / :

1. Define units

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MCM 106^m 3^* :

2. Extract 'Elevation' & 'Area' vectors and calculate Cumulative Capacity at each level

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EL Elev_Area 1 col m * :

Ar Elev_Area 2 col ha * :

Calculate Cumulative Capacity j 1 EL rows range j 1 ≡ V j el 0 : CAP j el 0 : 21 line V j el EL j el EL j 1 - el - (0.5 * Ar j el Ar j 1 - el + (* : CAP j el CAP j 1 - el V j el + : 21 line if 11 line for

Elevation EL m 203040506070809081 mat

Area Ar ha 015035057585011001420180081 mat

Vol between elevations V MCM 0 7.5 25 46.25 71.25 97.5 12616181 mat

Reservoir Capacity CAP MCM 0 7.5 32.5 78.75 150 247.5 373.5 534.5 81 mat

Fitting function using 
linear interpolation x ELtoCAP EL m / CAP MCM / x linterp MCM * :

Example 40 ELtoCAP MCM 32.5

3. Extract 'T' & 'I' vectors for plotting Hydrograph and release from bottom outlet

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T flood_50_Yr 1 col hr * :

I flood_50_Yr 2 col cumec * :

I max cumec 2122.5

Fitting function using 
cubic interpolation t F1 T hr / I cumec / t cinterp cumec * :

Const release from 
bottom outlet Q.r 200 cumec * :

Create vector 
for plotting Qr j 1 T rows range Q j el Q.r : eval 11 line for

Deduct Qr from  
flood inflow t F3 t F1 Q.r - (:

This gives all intersection 
points between "Inflow" & "Qr" tt x F3 x T min hr / T max hr / solve : 20.56 44.5 60.6 116.87 41 mat

Check values of "tt"

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tt 1 el F1 cumec 200

tt 2 el F1 cumec 200

tt 3 el F1 cumec 200

tt 4 el F1 cumec 200

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den 
Funktionen f(x) und g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*n vertical lines (hatching) between 
functions f(x) and g(x) in x-range from x1 to x2. (from SNIPPET Manager) 1 f 1 g x.1 x.2 n hatch dx x.2 x.1 - n / : hh x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range hh hh x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for hh 41 line eval :

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den 
Funktionen f(x) und g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*n vertical lines (hatching) between 
functions f(x) and g(x) in x-range from x1 to x2 (from SNIPPET Manager) 1 f 1 g x.1 x.2 n hatch dx x.2 x.1 - n / eval : hh x.1 x.1 f x.1 x.1 g 22 mat eval : x x.1 x.2 dx - x.1 dx + range hh hh x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack eval : for hh 41 line :

To find the index of a value in a matrix: Developed by Andrey Ivashov z x match1 pos 011 mat : j 1 x rows range x j el z ≡ pos pos j 11 mat augment : continue if 11 line for pos 112 pos cols submatrix 31 line :

For Plotting & hatching

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Define x F2 Q.r :

I max cumec 2122.5

MyHatch1 a F2 a F1 tt 3 el tt 4 el 25 hatch :

Z3 tt 3 el 0 tt 3 el Q.r 22 mat :

Z4 tt 4 el 0 tt 4 el Q.r 22 mat :

Z1 T hr / I cumec / augment :

Z2 T hr / Q cumec / augment :

To find the index of maximum Inflow in Inflow vector

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Index of max Inflow nn I max I match1 : 2911 mat

Max_Iflow_Line T min hr / I max cumec / T nn el hr / I max cumec / 22 mat : 0 2122.5 7811 mat 2122.5 22 mat

Time value corresponding 
to max Inflow T nn el hr 7811 mat

2. Find the net flood volume to absorb

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Area between the two plots (shown hatched from tt₃ to tt₄) gives the flood volume to absorb, negecting other minor peaks of the inflow graph.

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Total flood volume 
from tt3 to tt4 V.in t F1 t tt 3 el tt 4 el int hr * : MCM 174.5

tt 3 el 60.6

where

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tt 4 el 116.87

Tot. Vol released from 
the bottom outlet V.out Q.r tt 4 el tt 3 el - (* hr * : MCM 40.5

Volume required to 
absorb the  Net Flood 
Inflow (hatched area) V.absorb V.in V.out - : MCM 134

Settings for X-Y Plot of Hydrograph

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XYPlot.XLimMin 1 el T min hr / : 011 mat

XYPlot.XLimMax 1 el T max hr 10 * / Ceil 10 * : 15011 mat

XYPlot.YLimMin 1 el I min cumec / : 011 mat

XYPlot.YLimMax 1 el I max cumec 100 * / Ceil 100 * : 220011 mat

XYPlot.XTick 1 el 10 :

XYPlot.YTick 1 el 200 :

Z1 Z2 MyHatch1 Z3 Z4 Max_Iflow_Line 6 1 sys

I max cumec 2122.5

I max cumec 2122.5

Net Flood Vol 
to Absorb V.in V.out - MCM 134

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Const bottom release Q.r 200 cumec * :

tt 3 el 60.6

tt 4 el 116.87

Settings for X-Y Plot of Elevation/Area/Capacity Curve

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XYPlot.XLimMin 2 el EL min m / : 02021 mat

XYPlot.XLimMax 2 el EL max m / 10 + : 15010021 mat

XYPlot.YLimMin 2 el CAP min MCM / : 0021 mat

XYPlot.YLimMax 2 el CAP max MCM / 100 + : 2200 634.5 21 mat

XYPlot.XTick 2 el 10 :

XYPlot.YTick 2 el 100 :

To find Elevation for a given Capacity - Method 1

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Let

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CC 150 MCM * :

ΔEL 1 m * :

x ELtoCAP CC - x EL min ΔEL - m / EL max ΔEL + m / solve m * 60 m *

To find Elevation for a given Capacity - Method 2 - Suitable for programming

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x X F4 x ELtoCAP X - :

x X CAPtoEL x X F4 x EL min ΔEL - m / EL max ΔEL + m / solve m * :

Example x CC CAPtoEL 60 m *

Find Reservoir Parameters

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(1) Let dead storage elevation

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Assumed EL.ds EL min 10 m * + : 30 m *

C.ds EL.ds m / ELtoCAP : MCM 7.5

(2) Capacity at dead storage

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(3) Volume to absorb

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Already calculated V.absorb MCM 134

(4) First trial value for the capacity of

the reservoir to absorb flood volume

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C.trial C.ds V.absorb + : MCM 141.5

(5) Elevation corresponding to C_trial

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E.trial x C.trial CAPtoEL : 58.81 m *

(6) Add 3 m to E_trial to get HFL (as a safety factor) & round off to nearest integer

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HFL E.trial m / 3 + Ceil m * : 62 m *

C.hfl HFL m / ELtoCAP : MCM 169.5

(7) Now find capacity at HFL

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(8) Deduct V.absorb

to get min.

operating capacity

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C.mol C.hfl V.absorb - : MCM 35.5

(9) Min. operating level (MOL)

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MOL x C.mol CAPtoEL : 40.65 m *

(10j) Allow 3 m free board (FB)

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FB 3 m * :

(11) Hence, Bund Top Level (BTL)

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BTL HFL FB + : 65 m *

C.btl BTL m / ELtoCAP : MCM 198.75

(12) Capacity at BTL

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Z5 HFL m / 0 HFL m / C.hfl MCM / 22 mat : 62062 169.5 22 mat

Z6 EL m / min C.hfl MCM / HFL m / C.hfl MCM / 22 mat : 20 169.5 62 169.5 22 mat

EL m / CAP MCM / augment EL m / Ar ha / augment Z5 Z6 4 1 sys

C.hfl MCM 169.5

HFL 62 m *

Summary

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Flood Vol absorbed

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V.absorb MCM 134

Const release from bottom outlet

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Q.r cumec 200

Description

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Elevation

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Capacity

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At dead storage

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EL.ds 30 m *

C.ds MCM 7.5

At MOL

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MOL 40.65 m *

C.mol MCM 35.5

At HFL

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HFL 62 m *

C.hfl MCM 169.5

At BTL

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BTL 65 m *

C.btl MCM 198.75

Ratio of Net Flood Volume 
absorbed to Effective 
Capacity at HFL V.absorb C.hfl C.ds - / % 82.7

1 f 1 g a b N hatch2 Δx b a - N 1 - / : x a : ξ a Δx 2 / + : R 0 : 14 mat k 1 N range R 4 k * 3 - 1 el x : R 4 k * 3 - 2 el x f : R 4 k * 2 - 1 el x : R 4 k * 2 - 2 el x g : R 4 k * 1 - 1 el ξ : R 4 k * 1 - 2 el ξ g : R 4 k * 1 el ξ : R 4 k * 2 el ξ f : x x Δx + : ξ ξ Δx + : 52 mat for R b b f b b g 22 mat stack 31 line eval :

G a F2 a F1 tt 3 el tt 4 el 25 hatch2 :

Z1 Z2 G Z3 Z4 Max_Iflow_Line 6 1 sys

I max cumec 2122.5

I max cumec 2122.5

Net Flood Vol 
to Absorb V.in V.out - MCM 134

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Const bottom release Q.r 200 cumec * :

tt 3 el 60.6

tt 4 el 116.87