Eng.

d8f0dd23-6d60-46f8-b22e-77ba7b12034a 735 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 5 7 decimal

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

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

This SMath example done prgrammatically using "while" loop.

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Looks in the first column of a "table", for a given "value", and returns the value(s) in the same row(s) in the "column" specified. When multiple values are returned, they appear in a vector. (Downloaded from the Web)

Do not erase this MyDirectory DocumentDirectory : E:\All Smath Files in HP\

MyFile MyDirectory Small Dams Data.xlsx concat : E:\All Smath Files in HP\Small Dams Data.xlsx

cusec ft 3^s / :

value table column vlookup k 1 : j 1 : j table rows ≤ j j 1 + : table j 1 el value ≡ result k 1 el table j column el : k k 1 + : 21 line 0 if for result 31 line :

Inflow Hydrograph Inflow 040018002200034000460005470063300724008160091100115001230015200201002550300350400500600700800900232 mat :

Definitions

acft acre ft * :

tank_data2 MyFile Sheet1 A1 B9 importData.XLSX :

Inflow2 MyFile Sheet1 D1 E23 importData.XLSX :

1. BASIC DATA

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 (read from graphs in reference book

412345648933 mat 3 vlookup 6921 mat

tank_data2 3001050 300.3 11003011213 302.1 1449 303.8 1826 305.3 2195 306.2 2418 306.6 2528 306.7 255992 mat

Inflow2 040018002200034000460005470063300724008160091100115001230015200201002550300350400500600700800900232 mat

Extract first column and assign "hr" unit

T Inflow 1 col hr * :

Extract second column and assign "cusec" unit

Inf Inflow 2 col (cusec * :

Spill length

L_spill 25 ft * :

Crest Elevation

E_crest 300.0 ft * :

Bund Top Level

BTL 310 ft * :

(Assumed)

Water level at start

E_start 300.0 ft * :

Full Supply Level

FSL E_crest :

Spill discharge coefficient varies with head over spill crest

Calculation of Cd, using "cases" function h Calc_Cd 0 h 0 ≤ 3.2 h 1 ≤ HH Cd h linterp h 4 ≤ 3.8 cases :

Cd 3.2 3.4 3.6 3.7 41 mat :

HH 123441 mat :

Ex. 0.1 Calc_Cd 3.2

Ex. 4 Calc_Cd 3.7

Ex. 4.001 Calc_Cd 3.8

2. CALCULATIONS

Max inflow

I.max Inf max : cusec 6000

h Q h ft / Calc_Cd L_spill ft / * h ft / (1.5^* cusec * :

2.1 Spill discharge

Overflow equation

Ex 0.5 ft * Q cusec 28.3

2.2 Interpolating Functions

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

300 fit_ST acft 1050

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

ST 1 el acft / FIT_S_E ft 300

<p>Calculations & Main Routing Program</p>

Main Routing Program (SMath)

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I t e_start Rout 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 augment col cusec * :

Max_Outflow Outflow (max : cusec 1637.78

WL Ans1 11 augment col ft * :

Max_WL WL max : ft 306.67

Header S/N T I I_avg St_in_avg St_out_avg ΔSt St_total h augment :

Header Header Q_out_avg Elv Q_out Counter augment :

Ans2 Header Ans1 stack eval :

Find the point of intersection of Inflow and Outflow curves

SMath Result of Routing Program Ans2 S/N T I I_avg St_in_avg St_out_avg ΔSt St_total h Q_out_avg Elv Q_out Counter 1040000001050003000021800600 49.59 0.53 49.06 1099.06 0.29 6.38 300.29 12.77 33220001400 115.7 3.78 111.92 1210.98 0.99 45.71 300.99 78.65 34340003000 247.93 13.85 234.08 1445.06 2.08 167.64 302.08 256.63 45460005000 413.22 38.47 374.76 1819.82 3.77 465.43 303.77 674.23 46547005350 442.15 75.31 366.84 2186.66 5.27 911.26 305.27 1148.28 47633004000 330.58 107.58 223 2409.66 6.17 1301.67 306.17 1455.05 48724002850 235.54 126.24 109.3 2518.96 6.57 1527.51 306.57 1599.97 49816002000 165.29 133.79 31.5 2550.46 6.67 1618.87 306.67 1637.78 410911001350 111.57 134.24 22.67 - 2527.79 6.6 1624.26 306.6 1610.74 41111500800 132.23 253.01 120.78 - 2407.01 6.16 1530.72 306.16 1450.7 51212300400 33.06 115.15 82.1 - 2324.92 5.83 1393.35 305.83 133641315200250 61.98 293.03 231.05 - 2093.87 4.89 1181.88 304.89 1027.76 61420100150 61.98 348.52 286.53 - 1807.34 3.72 843.41 303.72 659.06 715255075 30.99 225.22 194.23 - 1613.11 2.86 545.04 302.86 431.02 71630025 10.33 147.95 137.62 - 1475.48 2.22 358.05 302.22 285.08 61735000 99.77 99.77 - 1375.71 1.77 241.45 301.77 197.82 51840000 70.67 70.67 - 1305.03 1.45 171.03 301.45 144.24 51950000 92.52 92.52 - 1212.52 1 111.95 301 79.65 72060000 51.79 51.79 - 1160.73 0.69 62.66 300.69 45.67 62170000 30.28 30.28 - 1130.45 0.49 36.63 300.49 27.6 62280000 18.87 18.87 - 1111.58 0.37 22.84 300.37 18.08 52390000 12.71 12.71 - 1098.87 0.29 15.38 300.29 12.69 52413 mat

Interpolating Functions

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

Time & Inflow

0.5 myFit_I cusec 500

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

Time & Outflow

0.5 myFit_Q cusec 0.254 -

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

Time & Water Level

0.5 myFit_WL ft 300.097

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

Downloaded from the Web 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 :

nn Outflow max Outflow match1 : 911 mat

Image of MathCAD Result

Time value corresponding 
to max ouflow T nn el hr 8

Find the point of intersection of Inflow and Outflow curves

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

Eqn to solve

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 7.95

Using "solve" function

T_max hr / myFit_I cusec 1637.92

Both shoud be equal at the intersection point

Max_Outflow T_max hr / myFit_Q : cusec 1637.92

HFL T_max hr / myFit_WL : ft 306.67

Afflux HFL max E_crest - : ft 6.67

Max_Inflow Inf max : cusec 6000

Find the volume of temporary detention when outflow reaches maximum

T_max hr 7.95

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

V.in_temp2 x myFit_I x T_max hr / T max hr / int hr * : acft 437.1

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

V.out_temp2 x myFit_Q x T_max hr / T max hr / int hr * : acft 1881.8

Volume in temporary detention  (in rising limb) at max level ΔV.temp V.in_temp V.out_temp - : acft 1505.4

Volume in temporary falling limb ΔV.temp2 V.out_temp2 V.in_temp2 - : acft 1444.7

Define arguments for plotting

nnn Inf max Inf match1 : 511 mat

TI T hr / Inf cusec / augment :

TO T hr / Outflow cusec / augment :

TE T hr / WL ft / augment :

Time value corresponding 
to max inlow T nnn el hr 4

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 / HFL ft / 22 mat : 7.95 306.67 90 306.67 22 mat

Max_Outflow_Line T min hr / Max_Outflow cusec / T_max hr / Max_Outflow cusec / 22 mat : 0 1637.92 7.95 1637.92 22 mat

Max_Iflow_Line T min hr / Max_Inflow cusec / T nnn el hr / Max_Inflow cusec / 22 mat : 060004600022 mat

TI TO TE Tmax_Line HFL_Line Max_Outflow_Line Max_Iflow_Line 7 1 sys

Max_Inflow cusec 6000

HFL ft 306.7

Max_Outflow cusec 1637.9

Assumed BTL ft 310

L_spill ft 25

E_crest ft 300

Max_Inflow cusec 6000

E_start ft 300

HFL ft 306.7

Afflux ft 6.7

Max_Outflow cusec 1637.9