Eng.

d8f0dd23-6d60-46f8-b22e-77ba7b12034a 1053 Eng. N.D.T.M. Amarasekera MAKITHULA is a proposed medium tank to store and regulate water from diversion under the NWP Canal Project, Sri Lanka. Ministry of Irrigation and Water Resources Management, Sri Lanka MAHAKITHULA, 500 yr Flood Routing 4 8 decimal

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

Original example has been done manually by trial & error method for each time step.

This SMath example is done prgrammatically using a "while" loop.

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cusec ft 3^s / :

Definitions

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acft acre ft * :

Inflow Hydrograph
From TABLE 9-1 & 
Fig 9.2) Inflow 040018002200034000460005470063300724008160091100115001240013400132 mat :

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 * :

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 300.0 ft * :

Full Supply Level

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FSL E_crest :

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 ≤ 3.2 h 1 ≤ HH Cd h linterp h 5 ≤ 3.8 cases :

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 #

Ex. 1 Calc_Cd #

Ex. 2 Calc_Cd #

Ex. 3 Calc_Cd #

Ex. 4 Calc_Cd #

Ex. 5 Calc_Cd #

2. CALCULATIONS

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Max inflow

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I.max Inf max : cusec 6000

This is an emperical formula; 
hence units must be adjusted accordingly h Q h ft / Calc_Cd L_spill ft / * h ft / (1.5^* cusec * :

2.1 Spill discharge

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Overflow equation

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Ex 0.5 ft * Q cusec #

2.2 Interpolating Functions

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

300 fit_ST acft 1050

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

ST 1 el acft / FIT_S_E ft 300

Main Routing Program (SMath)

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I t e_start Rout n 1 el 1 : elv 1 el e_start : elv 1 el E_crest ≤ h 1 el 0 : 11 line h 1 el elv 1 el E_crest - : 11 line if st 1 el elv 1 el ft / fit_ST eval : I_avg 1 el 0 : st_in_avg 1 el 0 : st_out_avg 1 el 0 : Δst 1 el 0 : st_total 1 el st 1 el Δst 1 el + : q_out 1 el h 1 el Q : 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 Q 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 61 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 :

I t e_start Rout2 j 1 I rows range j 1 ≡ n j el j : elv j el e_start : elv j el E_crest ≤ h j el 0 : 11 line h j el elv j el E_crest - : 11 line if st j el elv j el ft / fit_ST eval : I_avg j el 0 : st_in_avg j el 0 : st_out_avg j el 0 : Δst j el 0 : st_total j el st j el Δst j el + : q_out j el h j el Q : q_out_avg j el 0 : counter j el 0 : 121 line 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 Q 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 61 line if 11 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 : 41 line :

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

Outflow Ans1 12 col cusec * :

Max_Outflow Outflow (max : cusec #

WL Ans1 11 col ft * :

Max_WL WL max : ft #

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

Header Header Q_out_avg Elv Q_out Iterations augment :

Results with header Ans2 Header Ans1 stack eval :

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 linterp cusec * :

Time & Inflow

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2 myFit_I cusec 2000

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

Time & Outflow

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2 myFit_Q cusec #

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

Time & Water Level

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2 myFit_WL ft #

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

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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 :

nn Outflow max Outflow match1 : #

pos 112 pos cols submatrix

Time value corresponding 
to max ouflow T nn el hr #

pos 12 pos cols range el

nnn Inf max Inf match1 : 511 mat

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

Eqn to solve

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x F1 x myFit_I x myFit_Q - (:

T_max x F1 x T nn 1 - el hr / T nn 1 + el hr / solve hr * : hr #

Using "solve" function

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T_max hr / myFit_I cusec #

Both shoud be equal at

the intersection point

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Max_Outflow T_max hr / myFit_Q : cusec #

HFL T_max hr / myFit_WL : ft #

Afflux HFL max E_crest - : ft #

Max_Inflow Inf max : cusec 6000

Find the volume of temporary detention when outflow reaches maximum

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T_max hr #

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

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

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

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 : #

HFL_Line T_max hr / HFL ft / T max hr / HFL ft / 22 mat : #

Max_Outflow_Line T min hr / Max_Outflow cusec / T_max hr / Max_Outflow cusec / 22 mat : #

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

X.min T Min hr / : #

X.max T Max hr / : #

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Plotting Paramaters

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Y.min Inf Min cusec / : #

Y.max Inf Max cusec / 1000 + : #

Limited to 24 to 
get a better graph XYPlot.XLimMax 1 el 13 :

XYPlot.XLimMin 1 el X.min :

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X-Y Plot Settings

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XYPlot.YLimMin 1 el 0 :

XYPlot.YLimMax 1 el Y.max :

XYPlot.XTick 1 el 1 :

XYPlot.YTick 1 el 500 :

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 DEVELOPED BY "MKRASKA" FOR SMATH FORUM: 
Use 'myunit' if F(x) & G(x) are not default unit 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 / #

T max hr / 13

T min hr / 0

T_max hr / #

For hatching

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MyHatch1 a myFit_I a myFit_Q T min hr / T_max hr / 40 cusec hatch :

MyHatch2 a myFit_Q a myFit_I T_max hr / T max hr / 25 cusec hatch :

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

TI TO TE Tmax_Line HFL_Line Max_Outflow_Line Max_Iflow_Line MyHatch1 MyHatch2 9 1 sys

Max_Inflow cusec 6000

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S.sur acft #

HFL ft #

Max_Outflow cusec #

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Assumed BTL ft 310

L_spill ft 25

E_crest ft 300

Max_Inflow cusec 6000

E_start ft 300

HFL ft #

Afflux ft #

Max_Outflow cusec #

Free Board FB BTL HFL - : ft #

DATA L_spill 25 ft @ = E_crest 300 ft @ = BTL 310 ft @ = Max_Inflow 6000 cusec @ = 41 line

RESULT HFL 306.7 ft @ = Afflux 6.7 ft @ = Max_Outflow 1636 cusec @ = FB 3.3 ft @ = 41 line

From text book:  Inflow Volume from start to point of max outflow ST.in 50117 + 250 + 417 + 446 + 333 + 238 + 167 + (acft * : acft 2018

From text book:  Outflow Volume from start to point of max outflow ST.out 04 + 14 + 40 + 77 + 110 + 128 + 136 + (acft * : acft 509

Surcharge Volume ST.in ST.out - acft 1509

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From Integration S.sur acft #

From Smath Program

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STT.in Ans2 21055 submatrix sum : #

Ans2 210 range 55 range el sum #

STT.out Ans2 21066 submatrix sum : #

Ans2 210 range 66 range el sum #

STT.in STT.out - #

SMath Result of Routing Program Ans2 #

STT.out STT.in ST.out ST.in FB S.sur x dx hatch XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min X.max X.min ΔV.in V.out_temp V.in_temp Max_Inflow Afflux HFL T_max F1 nnn nn match1 myFit_WL myFit_Q myFit_I Ans2 Header Max_WL Max_Outflow Rout FIT_S_E fit_ST Q I.max Calc_Cd FSL E_start BTL E_crest L_spill cumec acft cusec lastError STT.out STT.in ST.out ST.in FB S.sur x dx hatch XYPlot.YTick XYPlot.XTick XYPlot.YLimMax XYPlot.YLimMin XYPlot.XLimMin XYPlot.XLimMax Y.max Y.min X.max X.min ΔV.in V.out_temp V.in_temp Max_Inflow Afflux HFL T_max F1 nnn nn match1 myFit_WL myFit_Q myFit_I Ans2 Header Max_WL WL Max_Outflow Outflow Ans1 Rout FIT_S_E fit_ST Q I.max HH Cd Calc_Cd FSL E_start BTL E_crest L_spill Inf T ST H cumec acft cusec lastError STT.out STT.in ST.out ST.in FB S.sur x dx Y.max Y.min X.max X.min ΔV.in V.out_temp V.in_temp Max_Inflow Afflux HFL T_max F1 myFit_WL myFit_Q myFit_I Max_WL Max_Outflow FIT_S_E fit_ST Q I.max FSL E_start BTL E_crest L_spill cumec acft cusec

Results in Table Form
Ans2
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