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Flood Routing Example - Ref: Design of Small Dams (USBR) - 3rd Ed. - page 342

Text Book example has been done manually by trial & error method at each time step.

This SMath example does it prgrammatically using a "while" loop to iterate at each time step

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t.0 1 time :

MCM 106^m 3^* :

Definitions

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acft acre ft * :

ham ha m * :

Inflow HydrographFrom TABLE 9-1 & Fig 9.2 Inflow 040018002200034000460005470063300724008160091100115001240013400132 mat :

cusec ft 3^s / :

cumec m 3^s / :

1. BASIC DATA

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Elevation H 300 300.3 301 302.1 303.8 305.3 306.2 306.6 306.7 91 mat ft * :

Storage ST 10501100121314491826219524182528255991 mat acft * :

Elevation & Storage

(Extracted from TABLE 9.1)

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From

Table 9.1

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From

Fig 9.2

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Extract first column

and assign "hr" unit

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T Inflow 1 col hr * :

Extract second column

and assign "cusec" unit

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Inf Inflow 2 col (cusec * :

Spill length

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L_spill 25 ft * :

(For 72.13 ft, u Q = 3000 cusec)

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(For 33.87 ft, u Q = 2000 cusec)

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Crest Elevation

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E_crest 300.0 ft * :

Bund Top Level

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BTL 310 ft * :

(Assumed)

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Water level at start

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E_start 300 ft * :

Full Supply Level

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FSL E_crest :

4 - appVersion 0.99.7799.1257

<content> </content> <content> UTILITIES & Other PROGRAMS </content>

Spill discharge coefficient varies with head over spill crest

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Calculation of Cd, using "cases" function h Calc_Cd 0 h 0 ≤ HH Cd h linterp h 05 ltle 3.8 cases 11 line :

Cd 3.2 3.4 3.6 3.7 3.8 51 mat :

HH 1234551 mat :

From FIG 9.4)

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Ex. 0 Calc_Cd 0

Ex. 1 Calc_Cd 3.2

Ex. 2 Calc_Cd 3.4

Ex. 3 Calc_Cd 3.6

Ex. 4 Calc_Cd 3.7

Ex. 5 Calc_Cd 3.8

2. CALCULATIONS

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Max inflow

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I.max Inf max : cusec 6000

Sanity check HH Calc_Cd vectorize 3.2 3.4 3.6 3.7 3.8 51 mat

2.1 Spill discharge

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Overflow equation

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This is an Emperical formula, with fps units;hence units must be balanced accordingly. h L_sp Q2 h ft / Calc_Cd L_sp ft / * h ft / (1.5^* cusec * :

Example 0.5 ft * L_spill Q2 cusec 27.4

2.2 Interpolating Functions

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x fit_ST H ft / ST acft / x ainterp acft * :

300 fit_ST acft 1050

295 fit_ST acft 77.9

xx 296308297 range : 296297298299300301302303304305306307308131 mat

x FIT_S_E ST acft / H ft / x ainterp ft * :

ST 1 el acft / FIT_S_E ft 300

Main Routing Program (SMath)

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PROGRAM 1 - Main Routing program I t e_start L_sp Rout n 1 el 1 : elv 1 el e_start : (WL at start ≡ elv 1 el E_crest ≤ (check WL at start ≡ h 1 el 0 : (no driving head if WL is below crest ≡ 11 line h 1 el elv 1 el E_crest - : (head above crest ≡ 11 line if st 1 el elv 1 el ft / fit_ST eval : (Storage at start ≡ I_avg 1 el 0 : (no avg inflow at start ≡ st_in_avg 1 el 0 : (no avg in_storage at start ≡ st_out_avg 1 el 0 : (no avg out_storage at start ≡ Δst 1 el 0 : (no change in storage st start ≡ st_total 1 el st 1 el Δst 1 el + : (tot. storage at start ≡ q_out 1 el h 1 el L_sp Q2 : q_out_avg 1 el 0 : counter 1 el 0 : 121 line j 2 I rows range n j el j : I_avg j el 0.5 I j el I j 1 - el + (* : st_in_avg j el I_avg j el t j el t j 1 - el - (* : st_total j el st_total j 1 - el st_in_avg j el + eval : ------------------- ------------------- elv j el st_total j el acft / FIT_S_E eval : elv j el E_crest ≤ st_out_avg j el 0 : h j el 0 : Δst j el st_in_avg j el : q_out j el 0 : q_out_avg j el 0 : counter j el 0 : 61 line h j el elv j el E_crest - : d1 E_crest : Δd 0.001 ft * : d 0.5 d1 * : counter j el 0 : d1 d - abs Δd ≥ d d1 : h j el d1 E_crest - eval : q_out j el h j el L_sp Q2 eval : q_out_avg j el 0.5 q_out j el q_out j 1 - el + (* : st_out_avg j el q_out_avg j el t j el t j 1 - el - (* : Δst j el st_in_avg j el st_out_avg j el - : st_total j el st_total j 1 - el Δst j el + eval : d1 st_total j el acft / FIT_S_E eval : elv j el d1 : counter j el counter j el 1 + : 101 line while 61 line if 81 line for A n t hr / I cusec / I_avg cusec / st_in_avg acft / augment eval : A A st_out_avg acft / Δst acft / st_total acft / h ft / augment eval : A A q_out_avg cusec / elv ft / q_out cusec / counter augment eval : 51 line :

st SS j 1 st rows range cc j el st j el fit_ST acft / : 11 line for cc 21 line :

xx SS xx augment

xx SS 293.24 498.14 692.57 876.52 10501213 1426.88 1643.78 1874.46 2120.81 2368.25 2660.4 3089.4 131 mat

383.33 550 716.67 883.33 10501213 1427.55 1648.59 1875.2 2121.2 2368.44 26522962131 mat

Use routing program  to get the results Ans1 Inf T E_start L_spill Rout :

Outflow Ans1 12 col cusec * :

Max_Outflow Outflow (max : cusec 1637.8

WL Ans1 11 col ft * :

Max_WL WL max : ft 306.6731

Header1 S/N T I I_avg ST_in_avg ST_out_avg ΔST ST Tot h augment :

Header1 Header1 Q_out_avg Elv Q_out Iterations augment :

UT S:' # S:'hr S:'cusec S:'cusec S:'acft S:'acft S:'acft S:'acft S:'ft S:'cusec S:'ft S:'cusec S:' # 131 mat transpose :

Header1 Header1 UT stack :

WL =

E_start ft 300

E_crest ft 300

Results with header Ans2 Header1 Ans1 stack eval :

Ans2 S/N T I I_avg ST_in_avg ST_out_avg ΔST ST Tot h Q_out_avg Elv Q_out Iterations S:' # S:'hr S:'cusec S:'cusec S:'acft S:'acft S:'acft S:'acft S:'ft S:'cusec S:'ft S:'cusec S:' # 1040000001050003000021800600 49.59 0.5 49.08 1099.08 0.29 6.11 300.29 12.21 33220001400 115.7 3.75 111.95 1211.03 0.99 45.42 300.99 78.62 34340003000 247.93 13.85 234.08 1445.11 2.08 167.65 302.08 256.67 45460005000 413.22 38.47 374.75 1819.86 3.77 465.47 303.77 674.28 46547005350 442.15 75.31 366.83 2186.7 5.27 911.31 305.27 1148.33 47633004000 330.58 107.58 223 2409.7 6.17 1301.72 306.17 1455.1 48724002850 235.54 126.24 109.29 2518.99 6.57 1527.55 306.57 160049816002000 165.29 133.79 31.5 2550.49 6.67 1618.91 306.67 1637.81 410911001350 111.57 134.24 22.67 - 2527.82 6.6 1624.29 306.6 1610.77 41111500800 132.23 253.02 120.79 - 2407.03 6.16 1530.75 306.16 1450.73 51212400450 37.19 115.38 78.19 - 2328.84 5.84 1396.09 305.84 1341.46 41313400400 33.06 106.68 73.62 - 2255.22 5.54 1290.86 305.54 1240.27 41513 mat

Find the point of intersection of Inflow and Outflow curves

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Interpolating Functions

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y myFit_I T hr / Inf cusec / y ainterp cusec * :

Time & Inflow

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2 myFit_I cusec 2000

y myFit_Q T hr / Outflow cusec / y ainterp cusec * :

Time & Outflow

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2 myFit_Q cusec 78.6219

y myFit_WL T hr / WL ft / y ainterp ft * :

Time & Water Level

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2 myFit_WL ft 300.9894

We have to find the index of max outflow in Outflow vector

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Outflow (max 46.3776 m 3^s / *

PROGRAM 2 - To locate position of a value in an Array (Downloaded from FORUM) 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 12 pos cols range el 31 line :

WL at spill level

S/N T I I_avg ST_in_avg ST_out_avg ΔST ST Tot h Q_out_avg Elv Q_out Iterations S:' # S:'hr S:'cusec S:'cusec S:'acft S:'acft S:'acft S:'acft S:'ft S:'cusec S:'ft S:'cusec S:' # 1040000001050003000021800600 49.59 0.53 49.06 1099.06 0.29 6.38 300.29 12.76 33220001400 115.7 3.77 111.93 1210.99 0.99 45.65 300.99 78.54 34340003000 247.93 13.86 234.08 1445.06 2.08 167.68 302.08 256.82 45460005000 413.22 38.46 374.76 1819.83 3.77 465.36 303.77 673.89 46547005350 442.15 75.3 366.85 2186.68 5.27 911.11 305.27 1148.33 47633004000 330.58 107.59 222.99 2409.67 6.17 1301.87 306.17 1455.41 48724002850 235.54 126.25 109.28 2518.95 6.57 1527.65 306.57 1599.9 49816002000 165.29 133.79 31.5 2550.45 6.67 1618.84 306.67 1637.78 410911001350 111.57 134.24 22.67 - 2527.79 6.6 1624.26 306.6 1610.74 41111500800 132.23 253.05 120.82 - 2406.97 6.16 1530.94 306.16 1451.15 51212400450 37.19 115.45 78.26 - 2328.71 5.85 1396.96 305.85 1342.78 41313400400 33.06 106.75 73.69 - 2255.02 5.55 1291.64 305.54 1240.51 41513 mat

Outflow 2 round vectorize 0 0.35 m 3^s / * 2.23 m 3^s / * 7.27 m 3^s / * 19.09 m 3^s / * 32.52 m 3^s / * 41.2 m 3^s / * 45.31 m 3^s / * 46.38 m 3^s / * 45.61 m 3^s / * 101 mat

nnn Inf max Inf match1 : 511 mat

Time value corresponding to max inflow T nnn el hr 411 mat

nn Outflow max Outflow match1 : 911 mat

Time value corresponding to max ouflow T nn el hr 811 mat

Eqn to solve

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x F1 x myFit_I x myFit_Q - (:

ε 1012 -^:

Alternatively

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ZZ T Outflow 2 round vectorize augment :

ZZ 2 col max 2 round 46.38 m 3^s / *

T_max x F1 x T nn el 2.0 hr * - hr / T nn el 2.0 hr * + hr / solve hr * : hr 7.95

Using "solve" function

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XX ZZ 2 col max : cusec 1638

ZZ 003600 s * 0.35 m 3^s / * 7200 s * 2.23 m 3^s / * 10800 s * 7.27 m 3^s / * 14400 s * 19.09 m 3^s / * 18000 s * 32.52 m 3^s / * 21600 s * 41.2 m 3^s / * 25200 s * 45.31 m 3^s / * 28800 s * 46.38 m 3^s / * 32400 s * 45.61 m 3^s / * 102 mat

Guess value T nn el 1 el hr 8

T_max x hr / F1 T nn el 1 el FindRoot :

Easier than  "match1(),but tricky " TT ZZ XX 2 findrows 1 el : hr 8

ZZ XX 2 findrows 28800 s * 46.38 m 3^s / * 12 mat

Alternatively x hr / F1 T nn el 1 el FindRoot hr 7.95

XX Clear 1

T_max hr / myFit_I cusec 1637.95

Both shoud be equal at

the intersection point

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Max_Outflow T_max hr / myFit_Q : cusec 1637.95

HFL T_max hr / myFit_WL : ft 306.67

Afflux HFL E_crest - : ft 6.67

Free Board FB BTL HFL - : ft 3.33

Max_Inflow Inf max : cusec 6000

Find the volume of temporary detention when outflow reaches maximum

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T_max hr 7.9464

V.in_temp x myFit_I x T min hr / T_max hr / int hr * : acft 1997.7

EL_Star L_Spill T_max Outflow HFL V_surcharge 3002581636 306.7 1500.6 30050 6.9 2486.4 305.6 1211.4 300 73.7 6.3 3000 304.9 1047.5 29825 8.4 1385.2 306 1648.8 56 mat

V.out_temp x myFit_Q x T min hr / T_max hr / int hr * : acft 492.2

HFL 93.47 m *

Vol in temporary detention  (in rising limb at max level ΔV.in V.in_temp V.out_temp - : acft 1505

Define arguments for plotting

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TI T hr / Inf cusec / augment :

TO T hr / Outflow cusec / augment :

TE T hr / WL ft / augment :

Tmax_Line T_max hr / 0 T_max hr / HFL ft / 22 mat : 7.946 0 7.946 306.673 22 mat

HFL_Line T_max hr / HFL ft / T max hr / 2 + HFL ft / 22 mat : 7.9464 306.6735 15 306.6735 22 mat

HFL_Line 12 range el 7.95 306.67 21 mat

Max_Outflow_Line T min hr / Max_Outflow cusec / T_max hr / Max_Outflow cusec / 22 mat : 0 1637.9486 7.9464 1637.9486 22 mat

HFL_Line 1 el 7.95

Max_Iflow_Line T min hr / Max_Inflow cusec / T nnn el hr / Max_Inflow cusec / 22 mat : 06000411 mat 600022 mat

BTL_Line T_max hr / BTL ft / T Max hr / 2 + BTL ft / 22 mat : 7.9464 3101531022 mat

HFL_Line 1 el 7.95

X.min T Min hr / : 0

X.max T Max hr / 2 + : 15

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Plotting Paramaters

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Y.min Inf Min cusec / : 400

Y.max Inf Max cusec / 1000 + : 7000

Limited to 24 to get a better graph XYPlot.XLimMax 1 el 15 :

XYPlot.XLimMin 1 el X.min : 011 mat

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X-Y Plot Settings

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XYPlot.YLimMin 1 el 0 :

XYPlot.YLimMax 1 el Y.max : 700011 mat

XYPlot.XTick 1 el 1 :

XYPlot.YTick 1 el 500 :

PROGRAM 3: Generates a matrix for 2*n vertical lines (hatching) between functions f(x) and g(x) in x-range from x1 to x2 DEVELOPED BY "MKRASKA" FOR SMATH FORUM: Use 'myunit' if F(x) & G(x) are not default unit 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. x f x g x.1 x.2 n myunit hatch x f x f myunit / : x g x g myunit / : 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 61 line eval :

T_max hr / 7.9464

T max hr / 13

T min hr / 0

T_max hr / 7.9464

Δs 60 :

Δx1 T_max hr / T min hr / - : 7.9464

Δx2 T max hr / T_max hr / - : 5.0536

ΔX2 Δs ΔX1 - : 21

ΔX1 Δx1 Δx1 Δx2 + / Δs * Ceil : 37

ΔX2 Δx2 Δx1 Δx2 + / Δs * Ceil : 24

For hatching

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MyHatch1 a myFit_I a myFit_Q T min hr / T_max hr / ΔX1 cusec hatch :

MyHatch2 a myFit_Q a myFit_I T_max hr / T max hr / ΔX2 cusec hatch :

Surcharge storage S.sur x myFit_I x myFit_Q - (x T min hr / T_max hr / int (hr * : acft 1505

Pt1 T_max hr / Max_Outflow cusec / 12 mat : 7.9464 1637.9486 12 mat

Pt2 T_max hr / HFL ft / 12 mat : 7.9464 306.6735 12 mat

mytext Max OUTFLOW = Max_Outflow cusec / 0 var2str Cusec concat : Max OUTFLOW = 1638 Cusec

Pt3 0.2 Max_Outflow cusec / XYPlot.YTick 1 el 0.6 * + mytext 10 red 15 mat : 0.2 1937.9486 Max OUTFLOW = 1638 Cusec 10 red 15 mat

mytext SPILL Length = L_spill ft / 1 var2str ft concat : SPILL Length = 25.0 ft

L_spill ft / 1 var2str

Pt33 0.2 Max_Outflow cusec / 50 - mytext 10 red 15 mat : 0.2 1587.9486 SPILL Length = 25.0 ft 10 red 15 mat

mytext HFL = HFL ft / 2 var2str ft concat : HFL = 306.67 ft

XYPlot.XLimMax 1 el

Pt41 XYPlot.XLimMax 1 el 0.75 * HFL ft / 0.6 + mytext 10 red 15 mat : 11.25 307.2735 HFL = 306.67 ft 10 red 15 mat

T_max hr / 1.0 +

mytext Max Inflow = Inf Max cusec / 0 var2str Cusec concat : Max Inflow = 6000 Cusec

Pt5 0.6 Max_Inflow cusec / 350 + mytext 10 black 15 mat : 0.6 6350 Max Inflow = 6000 Cusec 10 black 15 mat

mytext BTL = BTL ft / 0 var2str ft (assumed) concat : BTL = 310 ft (assumed)

XYPlot.XLimMax 1 el 15

2 myFit_I 56.6337 m 3^s / *

Pt6 XYPlot.XLimMax 1 el 0.7 * BTL ft / 0.6 + mytext 10 brown 15 mat : 10.5 310.6 BTL = 310 ft (assumed) 10 brown 15 mat

T_max hr / 1.0 +

With Both Arrow Heads; Arrow(Starting point x coordinate, Starting point y coordinate,Length of the vector, Angle of the vector): Revision to Jean's program SP.x SP.y L.v H.L H.W α Arrow_Both.LA 00 H.L H.W 2 / - H.L H.W 2 / 00 L.v 0 L.v H.L - H.W 2 / L.v H.L - H.W 2 / - L.v 082 mat α cos α sin α sin - α cos 22 mat * (SP.x SP.y SP.x SP.y SP.x SP.y SP.x SP.y SP.x SP.y SP.x SP.y SP.x SP.y SP.x SP.y 82 mat + :

T_max 2 hr * / 3.97

Arrow(Starting point x coordinate, Starting point y coordinate,Length of the vector, Angle of the vector): By JEAN SP.x SP.y L.v H.L H.W α Arrow.LA 00 L.v 0 L.v H.L - H.W 2 / L.v H.L - H.W 2 / - L.v 052 mat α cos α sin α sin - α cos 22 mat * (SP.x SP.y SP.x SP.y SP.x SP.y SP.x SP.y SP.x SP.y 52 mat + :

Ar1 T_max hr / HFL ft / BTL ft / HFL ft / - (0.75 0.20 90 ° * Arrow.LA : 7.95 306.67 7.95 310 7.85 309.25 8.05 309.25 7.95 31052 mat

Ar2 T_max hr / HFL ft / BTL ft / HFL ft / - (0.75 0.20 90 ° * Arrow_Both.LA : 7.95 306.67 8.05 307.42 7.85 307.42 7.95 306.67 7.95 310 7.85 309.25 8.05 309.25 7.95 31082 mat

Arrow_New 1010 0.75 0.25 0 Arrow.LA 205 0.75 0.25 30 ° * Arrow.LA 005 0.75 0.25 45 ° * Arrow.LA 31 sys :

Ar2 10.5 HFL ft / BTL ft / HFL ft / - (0.75 0.20 90 ° * Arrow_Both.LA : 10.5 302.38 10.6 303.13 10.4 303.13 10.5 302.38 10.5 310 10.4 309.25 10.6 309.25 10.5 31082 mat

T_max hr / 7.95

mytext FB = FB ft / 2 var2str ft concat : FB = 3.33 ft

Pt7 T_max hr / 1.5 + HFL ft / BTL HFL - 2 ft * / 0.25 + (+ mytext 10 black 15 mat : 9.45 308.59 FB = 3.33 ft 10 black 15 mat

Max_Inflow Max_Outflow - cusec / 4362.05

Pt8 T_max hr / BTL ft / 12 mat : 7.95 31012 mat

T.max_inflow Inflow Inflow max 2 findrows 1 el : 4

Arrow_New

Y Max_Outflow cusec / Max_Inflow Max_Outflow - cusec / 0.5 * + : 3818.97

X 0.2 :

Since X & Y scales are not same,arrow angle is set to 0 deg.Any rotation will distort the arrow beyond recognition. Ar3 X Y T.max_inflow 0.75 1250 ° * Arrow.LA : 0.2 3818.97 4.2 3818.97 3.45 3881.47 3.45 3756.47 4.2 3818.97 52 mat

mytext Max Surcharge = S.sur acft / 0 var2str Acft concat : Max Surcharge = 1505 Acft

Pt9 X Y 350 + mytext 10 black 15 mat : 0.2 4168.97 Max Surcharge = 1505 Acft 10 black 15 mat

x y angle m Arrow ar 0 0.736 0.68 0.8 0.68 0.736 00 0.016 0.016 0.08 0 0.08 - 0.016 - 0.016 - 0.016 28 mat transpose : Ro ar rows 1 matrix x + ar rows 1 matrix y + augment : Ro m ar * angle cos angle sin angle sin - angle cos 22 mat * + 31 line :

0 0 π 10 / - 1 Arrow 0.5 0.2 π 6 / 1.5 Arrow 0.5 0.2 π - 1.5 Arrow 3 1 sys

HFL_Line 1 el 7.9464

HFL_Line 2 el 306.6735

Not shown in the Plot Ar4 HFL_Line 1 el HFL_Line 2 el 120 deg * 3 Arrow :

Creating Units for each color. This list come from mkraska's interactive handbook
The color units are defined as color.colorname

XYPlot.YTick 1 el 500

XYPlot.YTick 1 el 0.6 * 300

Pt_T_max T_max hr / XYPlot.YTick 1 el 0.7 * 12 mat : 7.9464 35012 mat

mytext T_Max = T_max hr / 2 var2str hr concat : T_Max = 7.95 hr

Pt10 Pt_T_max 1 el Pt_T_max 2 el mytext 10 black 15 mat : 7.9464 350 T_Max = 7.95 hr 10 black 15 mat

M aliceblue antiquewhite aqua aquamarine azure beige bisque blanchedalmond black blue blueviolet brown burlywood cadetblue chartreuse chocolate coral cornflowerblue cornsilk crimson cyan darkblue darkcyan darkgoldenrod darkgray darkgreen darkkhaki darkmagenta darkolivegreen darkorange darkorchid darkred darksalmon darkseagreen darkslateblue darkslategray darkturquoise darkviolet deeppink deepskyblue dimgray dodgerblue firebrick floralwhite forestgreen fuchsia gainsboro ghostwhite gold goldenrod gray green greenyellow honeydew hotpink indianred indigo ivory khaki lavender lavenderblush lawngreen lemonchiffon lightblue lightcoral lightcyan lightgoldenrodyellow lightgray lightgreen lightpink lightsalmon lightseagreen lightskyblue lightslategray lightsteelblue lightyellow lime limegreen linen magenta maroon mediumaquamarine mediumblue mediumorchid mediumpurple mediumseagreen mediumslateblue mediumspringgreen mediumturquoise mediumvioletred midnightblue mintcream mistyrose moccasin navajowhite navy oldlace olive olivedrab orange orangered orchid palegoldenrod palegreen paleturquoise palevioletred papayawhip peachpuff peru pink plum powderblue purple red rosybrown royalblue saddlebrown salmon sandybrown seagreen seashell sienna silver skyblue slateblue slategray snow springgreen steelblue tan teal thistle tomato turquoise violet wheat white whitesmoke yellow yellowgreen 354 mat :

Plotting parameters Plot1 TI TO TE Tmax_Line HFL_Line Max_Outflow_Line Max_Iflow_Line MyHatch1 MyHatch2 Pt1 Pt2 Pt3 Pt41 Pt5 Pt6 BTL_Line Ar2 Pt7 Pt8 Ar3 Pt9 Pt33 Pt10 231 sys :

Plotting parameters Plot2 TI TO TE Tmax_Line HFL_Line Max_Outflow_Line Max_Iflow_Line MyHatch1 MyHatch2 Pt1 Pt2 111 sys :

Result BTL HFL Afflux FB E_crest E_start L_spill Max_Inflow Max_Outflow T_max S.sur 111 mat transpose :

myHeader BTL HFL Afflux FB Cresst Elev Start Elev Spill Length Max Inflow Max Outflow T_Max Max Surcharge 111 mat transpose :

Unit_Type S:'ft S:'ft S:'ft S:'ft S:'ft S:'ft S:'ft S:'cusec S:'cusec S:'hr S:'acft 111 mat transpose :

Unit summary input to new TABLE un ft ft ft ft ft ft ft cusec cusec hr acft 111 mat transpose :

myHeader myHeader Unit_Type stack :

XYPlot.Title.Text Flood Routing Example setprop 1

XYPlot.Title.TitleFont Callibri,16pt,style=Bold setprop 1

XYPlot.Title.TitleFontColor Black setprop 1

XYPlot.ChartStyle.PlotBackColor lavenderblush setprop 1

Plot1

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Q = 3000 cusec / Spil Length = 72.13 ft : Curve C

Q = 1636 cusec / Spil Length = 25 ft : Curve B

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T_max hr 7.95

Assumed BTL ft 310

L_spill ft 25

E_crest ft 300

Max_Inflow cusec 6000

E_start ft 300

HFL ft 306.6735

Afflux ft 6.7

Max_Outflow cusec 1637.9

Method (A). Matrices without units in TABLES

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Ans2 S/N T I I_avg ST_in_avg ST_out_avg ΔST ST Tot h Q_out_avg Elv Q_out Iterations S:' # S:'hr S:'cusec S:'cusec S:'acft S:'acft S:'acft S:'acft S:'ft S:'cusec S:'ft S:'cusec S:' # 1040000001050003000021800600 49.59 0.5 49.08 1099.08 0.29 6.11 300.29 12.21 33220001400 115.7 3.75 111.95 1211.03 0.99 45.42 300.99 78.62 34340003000 247.93 13.85 234.08 1445.11 2.08 167.65 302.08 256.67 45460005000 413.22 38.47 374.75 1819.86 3.77 465.47 303.77 674.28 46547005350 442.15 75.31 366.83 2186.7 5.27 911.31 305.27 1148.33 47633004000 330.58 107.58 223 2409.7 6.17 1301.72 306.17 1455.1 48724002850 235.54 126.24 109.29 2518.99 6.57 1527.55 306.57 160049816002000 165.29 133.79 31.5 2550.49 6.67 1618.91 306.67 1637.81 410911001350 111.57 134.24 22.67 - 2527.82 6.6 1624.29 306.6 1610.77 41111500800 132.23 253.02 120.79 - 2407.03 6.16 1530.75 306.16 1450.73 51212400450 37.19 115.38 78.19 - 2328.84 5.84 1396.09 305.84 1341.46 41313400400 33.06 106.68 73.62 - 2255.22 5.54 1290.86 305.54 1240.27 41513 mat

un Unit_Type Result Pt10 Pt_T_max Arrow Pt9 X Y Pt8 Pt7 Arrow.LA Arrow_Both.LA Pt6 Pt5 Pt41 Pt33 Pt3 Pt2 Pt1 S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min TE TO TI ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ZZ ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I UT Max_WL WL Max_Outflow Outflow Ans1 SS Rout FIT_S_E xx fit_ST Q2 I.max Calc_Cd FSL E_start BTL E_crest L_spill Inf T cumec cusec Inflow ham acft MCM t.0 Plot2 Plot1 Arrow X Y Arrow_New Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I Ans2 UT Header1 Max_WL WL Max_Outflow Outflow Ans1 SS Rout FIT_S_E xx fit_ST Q2 I.max HH Cd Calc_Cd FSL E_start BTL E_crest L_spill Inf T ST H cumec cusec ham acft MCM t.0 X Y Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 dx g f Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 myFit_WL myFit_Q myFit_I Max_WL WL Max_Outflow Outflow FIT_S_E xx fit_ST Q2 I.max FSL E_start BTL E_crest L_spill Inf T cumec cusec ham acft MCM t.0

Routing Results in Table Form
Ans1
1	0	400	0	0	0	0	1050	0	0	300	0	0
2	1	800	600	49.6	0.5	49.1	1099.1	0.3	6.1	300.3	12.2	3
3	2	2000	1400	115.7	3.8	111.9	1211	1	45.4	301	78.6	3
4	3	4000	3000	247.9	13.9	234.1	1445.1	2.1	167.6	302.1	256.7	4
5	4	6000	5000	413.2	38.5	374.8	1819.9	3.8	465.5	303.8	674.3	4
6	5	4700	5350	442.1	75.3	366.8	2186.7	5.3	911.3	305.3	1148.3	4
7	6	3300	4000	330.6	107.6	223	2409.7	6.2	1301.7	306.2	1455.1	4
8	7	2400	2850	235.5	126.2	109.3	2519	6.6	1527.6	306.6	1600	4
9	8	1600	2000	165.3	133.8	31.5	2550.5	6.7	1618.9	306.7	1637.8	4
10	9	1100	1350	111.6	134.2	-22.7	2527.8	6.6	1624.3	306.6	1610.8	4
11	11	500	800	132.2	253	-120.8	2407	6.2	1530.8	306.2	1450.7	5
12	12	400	450	37.2	115.4	-78.2	2328.8	5.8	1396.1	305.8	1341.5	4
13	13	400	400	33.1	106.7	-73.6	2255.2	5.5	1290.9	305.5	1240.3	4
#
S/N	T	I	I_avg	ST_in_avg	ST_out_avg	ΔST	ST Tot	h	Q_out_avg	Elv	Q_out	Iterations
S:' #	S:'hr	S:'cusec	S:'cusec	S:'acft	S:'acft	S:'acft	S:'acft	S:'ft	S:'cusec	S:'ft	S:'cusec	S:' #
#
#
#

Ans1 1040000001050003000021800600 49.5868 0.5047 49.082 1099.082 0.2944 6.1074 300.2944 12.2148 33220001400 115.7025 3.7536 111.9489 1211.0309 0.9889 45.4183 300.9894 78.6219 34340003000 247.9339 13.855 234.0789 1445.1098 2.0824 167.6453 302.0824 256.6688 45460005000 413.2231 38.4689 374.7543 1819.8641 3.7748 465.4735 303.7745 674.2782 46547005350 442.1488 75.3146 366.8342 2186.6983 5.267 911.3065 305.2664 1148.3347 47633004000 330.5785 107.5799 222.9986 2409.6969 6.1675 1301.7166 306.1667 1455.0985 48724002850 235.5372 126.2439 109.2933 2518.9902 6.5705 1527.5507 306.5699 1600.0029 49816002000 165.2893 133.7939 31.4954 2550.4856 6.6736 1618.906 306.6731 1637.8091 410911001350 111.5702 134.2389 22.6687 - 2527.8169 6.5999 1624.2911 306.5994 1610.773 41111500800 132.2314 253.0167 120.7853 - 2407.0316 6.1552 1530.7513 306.156 1450.7295 51212400450 37.1901 115.3797 78.1896 - 2328.842 5.8421 1396.094 305.8413 1341.4584 41313400400 33.0579 106.6828 73.625 - 2255.217 5.5445 1290.8623 305.5438 1240.2662 41313 mat

un Unit_Type Result Pt10 Pt_T_max Arrow Pt9 X Y Pt8 Pt7 Arrow.LA Arrow_Both.LA Pt6 Pt5 Pt41 Pt33 Pt3 Pt2 Pt1 S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I UT Max_WL Max_Outflow SS Rout FIT_S_E fit_ST Q2 I.max Calc_Cd FSL E_start BTL E_crest L_spill cumec cusec ham acft MCM t.0 un Unit_Type myHeader Result Plot2 Plot1 Arrow X Y Arrow_New Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I Max_WL WL Max_Outflow Outflow SS Rout FIT_S_E xx fit_ST Q2 I.max HH Cd Calc_Cd FSL E_start BTL E_crest L_spill Inf T ST H cumec cusec ham acft MCM t.0 un Result X Y Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 nn nnn myFit_WL myFit_Q myFit_I Max_WL Max_Outflow FIT_S_E fit_ST Q2 I.max FSL E_start BTL E_crest L_spill cumec cusec ham acft MCM t.0

Result
310	306.67	6.67	3.33	300	300	25	6000	1637.95	7.95	1505.46
0.3 m	0.3 m	0.3 m	0.3 m	0.3 m	0.3 m	0.3 m	0.03 (m^3)/s	0.03 (m^3)/s	3600 s	1233.48 m^3
BTL	HFL	Afflux	FB	Cresst Elev	Start Elev	Spill Length	Max Inflow	Max Outflow	T_Max	Max Surcharge
S:'ft	S:'ft	S:'ft	S:'ft	S:'ft	S:'ft	S:'ft	S:'cusec	S:'cusec	S:'hr	S:'acft
#
#
#

PROGRAM 1.1 - Main Routing program: Results with units I t e_start L_sp Rout_With_Units n 1 el 1 : elv 1 el e_start : (WL at start ≡ elv 1 el E_crest ≤ (check WL at start ≡ h 1 el 0 : (no driving head if WL is below crest ≡ 11 line h 1 el elv 1 el E_crest - : (head above crest ≡ 11 line if st 1 el elv 1 el ft / fit_ST eval : (Storage at start ≡ I_avg 1 el 0 : (no avg inflow at start ≡ st_in_avg 1 el 0 : (no avg in_storage at start ≡ st_out_avg 1 el 0 : (no avg out_storage at start ≡ Δst 1 el 0 : (no change in storage st start ≡ st_total 1 el st 1 el Δst 1 el + : (tot. storage at start ≡ q_out 1 el h 1 el L_sp Q2 : q_out_avg 1 el 0 : counter 1 el 0 : 121 line j 2 I rows range n j el j : I_avg j el 0.5 I j el I j 1 - el + (* : st_in_avg j el I_avg j el t j el t j 1 - el - (* : st_total j el st_total j 1 - el st_in_avg j el + eval : ------------------- ------------------- elv j el st_total j el acft / FIT_S_E eval : elv j el E_crest ≤ st_out_avg j el 0 : h j el 0 : Δst j el st_in_avg j el : q_out j el 0 : q_out_avg j el 0 : counter j el 0 : 61 line h j el elv j el E_crest - : d1 E_crest : Δd 0.001 ft * : d 0.5 d1 * : counter j el 0 : d1 d - abs Δd ≥ d d1 : h j el d1 E_crest - eval : q_out j el h j el L_sp Q2 eval : q_out_avg j el 0.5 q_out j el q_out j 1 - el + (* : st_out_avg j el q_out_avg j el t j el t j 1 - el - (* : Δst j el st_in_avg j el st_out_avg j el - : st_total j el st_total j 1 - el Δst j el + eval : d1 st_total j el acft / FIT_S_E eval : elv j el d1 : counter j el counter j el 1 + : 101 line while 61 line if 81 line for A n t I I_avg st_in_avg augment eval : A A st_out_avg Δst st_total h augment eval : A A q_out_avg elv q_out counter augment eval : 51 line :

Use routing program  to get the results AWU Inf T E_start L_spill Rout_With_Units :

Results AWU 10 11.3 m 3^s / * 0000 1.3 106^* m 3^* 00 91.4 m * 0023600 s * 22.7 m 3^s / * 17 m 3^s / * 61164.4 m 3^* 622.6 m 3^* 60541.8 m 3^* 1.4 106^* m 3^* 0.1 m * 0.2 m 3^s / * 91.5 m * 0.3 m 3^s / * 337200 s * 56.6 m 3^s / * 39.6 m 3^s / * 1.4 105^* m 3^* 4630 m 3^* 1.4 105^* m 3^* 1.5 106^* m 3^* 0.3 m * 1.3 m 3^s / * 91.7 m * 2.2 m 3^s / * 3410800 s * 113.3 m 3^s / * 85 m 3^s / * 3.1 105^* m 3^* 17089.9 m 3^* 2.9 105^* m 3^* 1.8 106^* m 3^* 0.6 m * 4.7 m 3^s / * 92.1 m * 7.3 m 3^s / * 4514400 s * 169.9 m 3^s / * 141.6 m 3^s / * 5.1 105^* m 3^* 47450.7 m 3^* 4.6 105^* m 3^* 2.2 106^* m 3^* 1.2 m * 13.2 m 3^s / * 92.6 m * 19.1 m 3^s / * 4618000 s * 133.1 m 3^s / * 151.5 m 3^s / * 5.5 105^* m 3^* 92899.2 m 3^* 4.5 105^* m 3^* 2.7 106^* m 3^* 1.6 m * 25.8 m 3^s / * 93 m * 32.5 m 3^s / * 4721600 s * 93.4 m 3^s / * 113.3 m 3^s / * 4.1 105^* m 3^* 1.3 105^* m 3^* 2.8 105^* m 3^* 3106^* m 3^* 1.9 m * 36.9 m 3^s / * 93.3 m * 41.2 m 3^s / * 4825200 s * 68 m 3^s / * 80.7 m 3^s / * 2.9 105^* m 3^* 1.6 105^* m 3^* 1.3 105^* m 3^* 3.1 106^* m 3^* 2 m * 43.3 m 3^s / * 93.4 m * 45.3 m 3^s / * 4928800 s * 45.3 m 3^s / * 56.6 m 3^s / * 2105^* m 3^* 1.7 105^* m 3^* 38849 m 3^* 3.1 106^* m 3^* 2 m * 45.8 m 3^s / * 93.5 m * 46.4 m 3^s / * 41032400 s * 31.1 m 3^s / * 38.2 m 3^s / * 1.4 105^* m 3^* 1.7 105^* m 3^* 27961.4 m 3^* - 3.1 106^* m 3^* 2 m * 46 m 3^s / * 93.5 m * 45.6 m 3^s / * 41139600 s * 14.2 m 3^s / * 22.7 m 3^s / * 1.6 105^* m 3^* 3.1 105^* m 3^* 1.5 105^* m 3^* - 3106^* m 3^* 1.9 m * 43.3 m 3^s / * 93.3 m * 41.1 m 3^s / * 51243200 s * 11.3 m 3^s / * 12.7 m 3^s / * 45873.3 m 3^* 1.4 105^* m 3^* 96445.4 m 3^* - 2.9 106^* m 3^* 1.8 m * 39.5 m 3^s / * 93.2 m * 38 m 3^s / * 41346800 s * 11.3 m 3^s / * 11.3 m 3^s / * 40776.3 m 3^* 1.3 105^* m 3^* 90815.1 m 3^* - 2.8 106^* m 3^* 1.7 m * 36.6 m 3^s / * 93.1 m * 35.1 m 3^s / * 41313 mat

un2 1 hr cusec cusec acft acft acft acft ft cusec ft cusec 1131 mat transpose :

Header1 transpose S/N S:' # T S:'hr I S:'cusec I_avg S:'cusec ST_in_avg S:'acft ST_out_avg S:'acft ΔST S:'acft ST Tot S:'acft h S:'ft Q_out_avg S:'cusec Elv S:'ft Q_out S:'cusec Iterations S:' # 132 mat

T_max hr 7.95

T_max hr / myFit_I cusec 1637.9

T_max hr / myFit_Q cusec 1637.9

T_max hr 7.9464

un4 1 hr cumec cumec ham ham ham ham m cumec m cumec 1131 mat transpose :

Header4 S/N S:' # T S:'hr I S:'cumec I_avg S:'cumec ST_in_avg S:'ham ST_out_avg S:'ham ΔST S:'ham ST Tot S:'ham h S:'m Q_out_avg S:'cumec Elv S:'m Q_out S:'cumec Iterations S:' # 132 mat transpose :

un5 1 hr cumec cumec MCM MCM MCM MCM m cumec m cumec 1131 mat transpose :

Header5 S/N S:' # T S:'hr I S:'cumec I_avg S:'cumec ST_in_avg S:'MCM ST_out_avg S:'MCM ΔST S:'MCM ST Tot S:'MCM h S:'m Q_out_avg S:'cumec Elv S:'m Q_out S:'cumec Iterations S:' # 132 mat transpose :

Method (B). Matrices with units (other than default units: Volume in acft) in TABLES

]]> un5 un4 un2 AWU Rout_With_Units un Unit_Type Result Pt10 Pt_T_max Arrow Pt9 X Y Pt8 Pt7 Arrow.LA Arrow_Both.LA Pt6 Pt5 Pt41 Pt33 Pt3 Pt2 Pt1 S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min TE TO TI ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ZZ ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I UT Max_WL WL Max_Outflow Outflow Ans1 SS Rout FIT_S_E xx fit_ST Q2 I.max Calc_Cd FSL E_start BTL E_crest L_spill Inf T cumec cusec Inflow ham acft MCM t.0 Header5 un5 Header4 un4 un2 AWU Rout_With_Units Plot2 Plot1 Arrow X Y Arrow_New Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I Ans2 UT Header1 Max_WL WL Max_Outflow Outflow Ans1 SS Rout FIT_S_E xx fit_ST Q2 I.max HH Cd Calc_Cd FSL E_start BTL E_crest L_spill Inf T ST H cumec cusec ham acft MCM t.0 un5 un4 un2 X Y Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 dx g f Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 myFit_WL myFit_Q myFit_I Max_WL WL Max_Outflow Outflow FIT_S_E xx fit_ST Q2 I.max FSL E_start BTL E_crest L_spill Inf T cumec cusec ham acft MCM t.0

AWU
1	0	400	0	0	0	0	1050	0	0	300	0	0
2	1	800	600	49.6	0.5	49.1	1099.1	0.3	6.1	300.3	12.2	3
3	2	2000	1400	115.7	3.8	111.9	1211	1	45.4	301	78.6	3
4	3	4000	3000	247.9	13.9	234.1	1445.1	2.1	167.6	302.1	256.7	4
5	4	6000	5000	413.2	38.5	374.8	1819.9	3.8	465.5	303.8	674.3	4
6	5	4700	5350	442.1	75.3	366.8	2186.7	5.3	911.3	305.3	1148.3	4
7	6	3300	4000	330.6	107.6	223	2409.7	6.2	1301.7	306.2	1455.1	4
8	7	2400	2850	235.5	126.2	109.3	2519	6.6	1527.6	306.6	1600	4
9	8	1600	2000	165.3	133.8	31.5	2550.5	6.7	1618.9	306.7	1637.8	4
10	9	1100	1350	111.6	134.2	-22.7	2527.8	6.6	1624.3	306.6	1610.8	4
11	11	500	800	132.2	253	-120.8	2407	6.2	1530.8	306.2	1450.7	5
12	12	400	450	37.2	115.4	-78.2	2328.8	5.8	1396.1	305.8	1341.5	4
13	13	400	400	33.1	106.7	-73.6	2255.2	5.5	1290.9	305.5	1240.3	4
1	3600 s	0.03 (m^3)/s	0.03 (m^3)/s	1233.48 m^3	1233.48 m^3	1233.48 m^3	1233.48 m^3	0.3 m	0.03 (m^3)/s	0.3 m	0.03 (m^3)/s	1
S/N	T	I	I_avg	ST_in_avg	ST_out_avg	ΔST	ST Tot	h	Q_out_avg	Elv	Q_out	Iterations
S:' #	S:'hr	S:'cusec	S:'cusec	S:'acft	S:'acft	S:'acft	S:'acft	S:'ft	S:'cusec	S:'ft	S:'cusec	S:' #
#
#
#

Already defined: This is an Emperical formula, with fps units;hence units must be balanced accordingly. h L_sp Q2 h ft / Calc_Cd L_sp ft / * h ft / (1.5^* cusec * ≡

h Afflux : ft 6.67

h L_spill Q2 cusec 1637.8

Max_Outflow cusec 1637.9

Cdd 0.598 0.635 0.673 0.692 0.71 51 mat :

FPS g.e ft s 2^/ / 32.17

SI g.e m s 2^/ / 9.8066

Method (C). Matrices with units (metric units: Volume in ham) in TABLES

]]> h un5 un4 un2 AWU Rout_With_Units un Unit_Type Result Pt10 Pt_T_max Arrow Pt9 X Y Pt8 Pt7 Arrow.LA Arrow_Both.LA Pt6 Pt5 Pt41 Pt33 Pt3 Pt2 Pt1 S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min TE TO TI ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ZZ ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I UT Max_WL WL Max_Outflow Outflow Ans1 SS Rout FIT_S_E xx fit_ST Q2 I.max Calc_Cd FSL E_start BTL E_crest L_spill Inf T cumec cusec Inflow ham acft MCM t.0 Cdd h Header5 un5 Header4 un4 un2 AWU Rout_With_Units Plot2 Plot1 Arrow X Y Arrow_New Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I Ans2 UT Header1 Max_WL WL Max_Outflow Outflow Ans1 SS Rout FIT_S_E xx fit_ST Q2 I.max HH Cd Calc_Cd FSL E_start BTL E_crest L_spill Inf T ST H cumec cusec ham acft MCM t.0 h un5 un4 un2 X Y Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 dx g f Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 myFit_WL myFit_Q myFit_I Max_WL WL Max_Outflow Outflow FIT_S_E xx fit_ST Q2 I.max FSL E_start BTL E_crest L_spill Inf T cumec cusec ham acft MCM t.0

AWU
1	0	11.3	0	0	0	0	129.5	0	0	91.4	0	0
2	1	22.7	17	6.1	0.1	6.1	135.6	0.1	0.2	91.5	0.3	3
3	2	56.6	39.6	14.3	0.5	13.8	149.4	0.3	1.3	91.7	2.2	3
4	3	113.3	85	30.6	1.7	28.9	178.3	0.6	4.7	92.1	7.3	4
5	4	169.9	141.6	51	4.7	46.2	224.5	1.2	13.2	92.6	19.1	4
6	5	133.1	151.5	54.5	9.3	45.2	269.7	1.6	25.8	93	32.5	4
7	6	93.4	113.3	40.8	13.3	27.5	297.2	1.9	36.9	93.3	41.2	4
8	7	68	80.7	29.1	15.6	13.5	310.7	2	43.3	93.4	45.3	4
9	8	45.3	56.6	20.4	16.5	3.9	314.6	2	45.8	93.5	46.4	4
10	9	31.1	38.2	13.8	16.6	-2.8	311.8	2	46	93.5	45.6	4
11	11	14.2	22.7	16.3	31.2	-14.9	296.9	1.9	43.3	93.3	41.1	5
12	12	11.3	12.7	4.6	14.2	-9.6	287.3	1.8	39.5	93.2	38	4
13	13	11.3	11.3	4.1	13.2	-9.1	278.2	1.7	36.6	93.1	35.1	4
1	3600 s	1 (m^3)/s	1 (m^3)/s	10000 m^3	10000 m^3	10000 m^3	10000 m^3	1 m	1 (m^3)/s	1 m	1 (m^3)/s	1
S/N	T	I	I_avg	ST_in_avg	ST_out_avg	ΔST	ST Tot	h	Q_out_avg	Elv	Q_out	Iterations
S:' #	S:'hr	S:'cumec	S:'cumec	S:'ham	S:'ham	S:'ham	S:'ham	S:'m	S:'cumec	S:'m	S:'cumec	S:' #
#
#
#

"C" in FPS C1 23 / Cdd * 2 g.e ft s 2^/ / * sqrt * : 3.2 3.4 3.6 3.7 3.8 51 mat

"C" in SI C2 23 / Cdd * 2 g.e m s 2^/ / * sqrt * : 1.77 1.87 1.99 2.04 2.1 51 mat

Method (D). Matrices with units (metric units: Volume in MCM) in TABLES

]]> h un5 un4 un2 AWU Rout_With_Units un Unit_Type Result Pt10 Pt_T_max Arrow Pt9 X Y Pt8 Pt7 Arrow.LA Arrow_Both.LA Pt6 Pt5 Pt41 Pt33 Pt3 Pt2 Pt1 S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min TE TO TI ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ZZ ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I UT Max_WL WL Max_Outflow Outflow Ans1 SS Rout FIT_S_E xx fit_ST Q2 I.max Calc_Cd FSL E_start BTL E_crest L_spill Inf T cumec cusec Inflow ham acft MCM t.0 C2 C1 Cdd h Header5 un5 Header4 un4 un2 AWU Rout_With_Units Plot2 Plot1 Arrow X Y Arrow_New Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I Ans2 UT Header1 Max_WL WL Max_Outflow Outflow Ans1 SS Rout FIT_S_E xx fit_ST Q2 I.max HH Cd Calc_Cd FSL E_start BTL E_crest L_spill Inf T ST H cumec cusec ham acft MCM t.0 h un5 un4 un2 X Y Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 dx g f Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 myFit_WL myFit_Q myFit_I Max_WL WL Max_Outflow Outflow FIT_S_E xx fit_ST Q2 I.max FSL E_start BTL E_crest L_spill Inf T cumec cusec ham acft MCM t.0

AWU
1	0	11.33	0	0	0	0	1.3	0	0	91.44	0	0
2	1	22.65	16.99	0.06	0	0.06	1.36	0.09	0.17	91.53	0.35	3
3	2	56.63	39.64	0.14	0	0.14	1.49	0.3	1.29	91.74	2.23	3
4	3	113.27	84.95	0.31	0.02	0.29	1.78	0.63	4.75	92.07	7.27	4
5	4	169.9	141.58	0.51	0.05	0.46	2.24	1.15	13.18	92.59	19.09	4
6	5	133.09	151.5	0.55	0.09	0.45	2.7	1.61	25.81	93.05	32.52	4
7	6	93.45	113.27	0.41	0.13	0.28	2.97	1.88	36.86	93.32	41.2	4
8	7	67.96	80.7	0.29	0.16	0.13	3.11	2	43.26	93.44	45.31	4
9	8	45.31	56.63	0.2	0.17	0.04	3.15	2.03	45.84	93.47	46.38	4
10	9	31.15	38.23	0.14	0.17	-0.03	3.12	2.01	45.99	93.45	45.61	4
11	11	14.16	22.65	0.16	0.31	-0.15	2.97	1.88	43.35	93.32	41.08	5
12	12	11.33	12.74	0.05	0.14	-0.1	2.87	1.78	39.53	93.22	37.99	4
13	13	11.33	11.33	0.04	0.13	-0.09	2.78	1.69	36.55	93.13	35.12	4
1	3600 s	1 (m^3)/s	1 (m^3)/s	1000000 m^3	1000000 m^3	1000000 m^3	1000000 m^3	1 m	1 (m^3)/s	1 m	1 (m^3)/s	1
S/N	T	I	I_avg	ST_in_avg	ST_out_avg	ΔST	ST Tot	h	Q_out_avg	Elv	Q_out	Iterations
S:' #	S:'hr	S:'cumec	S:'cumec	S:'MCM	S:'MCM	S:'MCM	S:'MCM	S:'m	S:'cumec	S:'m	S:'cumec	S:' #
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Unit summary input to new TABLE un6 m m m m m m m cumec cumec hr ham 111 mat transpose :

myHeader2 BTL HFL Afflux FB Cresst Elev Start Elev Spill Length Max Inflow Max Outflow T_Max Max Surcharge 111 mat transpose :

Unit_Type2 S:'m S:'m S:'m S:'m S:'m S:'m S:'m S:'cumec S:'cumec S:'hr S:'ham 111 mat transpose :

myHeader2 myHeader2 Unit_Type2 stack :

Unit_Type2 un6 h un5 un4 un2 Rout_With_Units un Unit_Type Result Pt10 Pt_T_max Arrow Pt9 X Y Pt8 Pt7 Arrow.LA Arrow_Both.LA Pt6 Pt5 Pt41 Pt33 Pt3 Pt2 Pt1 S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I UT Max_WL Max_Outflow SS Rout FIT_S_E fit_ST Q2 I.max Calc_Cd FSL E_start BTL E_crest L_spill cumec cusec ham acft MCM t.0 Unit_Type2 myHeader2 un6 C2 C1 Cdd h Rout_With_Units un Unit_Type myHeader Result Plot2 Plot1 Arrow X Y Arrow_New Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 hatch dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 nn nnn match1 myFit_WL myFit_Q myFit_I Max_WL WL Max_Outflow Outflow SS Rout FIT_S_E xx fit_ST Q2 I.max HH Cd Calc_Cd FSL E_start BTL E_crest L_spill Inf T ST H cumec cusec ham acft MCM t.0 un6 h un Result X Y Arrow.LA Arrow_Both.LA S.sur x Δx2 Δx1 dx g f XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min ΔV.in V.out_temp V.in_temp Max_Inflow FB Afflux HFL TT T_max ε F1 nn nnn myFit_WL myFit_Q myFit_I Max_WL Max_Outflow FIT_S_E fit_ST Q2 I.max FSL E_start BTL E_crest L_spill cumec cusec ham acft MCM t.0

Result
94.49	93.47	2.03	1.01	91.44	91.44	7.62	169.9	46.38	7.95	185.7
1 m	1 m	1 m	1 m	1 m	1 m	1 m	1 (m^3)/s	1 (m^3)/s	3600 s	10000 m^3
BTL	HFL	Afflux	FB	Cresst Elev	Start Elev	Spill Length	Max Inflow	Max Outflow	T_Max	Max Surcharge
S:'m	S:'m	S:'m	S:'m	S:'m	S:'m	S:'m	S:'cumec	S:'cumec	S:'hr	S:'ham
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Result
310	306.67	6.67	3.33	300	300	25	6000	1637.95	7.95	1505.46
0.3 m	0.3 m	0.3 m	0.3 m	0.3 m	0.3 m	0.3 m	0.03 (m^3)/s	0.03 (m^3)/s	3600 s	1233.48 m^3
BTL	HFL	Afflux	FB	Cresst Elev	Start Elev	Spill Length	Max Inflow	Max Outflow	T_Max	Max Surcharge
S:'ft	S:'ft	S:'ft	S:'ft	S:'ft	S:'ft	S:'ft	S:'cusec	S:'cusec	S:'hr	S:'acft
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1 time t.0 - 0.9 s *