Eng.

d8f0dd23-6d60-46f8-b22e-77ba7b12034a 740 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 2 5 decimal

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

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 : C:\Documents and Settings\Owner\My Documents\Downloads\

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 :

Low High step x fnct inc U Low High step range : i 1 U rows range f i el U i el fnct : for U f augment 31 line :

MyFile MyDirectory Small Dams Data.xlsx concat : C:\Documents and Settings\Owner\My Documents\Downloads\Small Dams Data.xlsx

cusec ft 3^s / :

Inflow Hydrograph Inflow 040018002200034000460005470063300724008160091100115001230015200201002550300350400500600700800900232 mat :

Definitions

acft acre ft * :

tank_data2 MyFile Sheet1 A1 B9 importData.XLSX :

412345648933 mat 3 vlookup 6921 mat

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

tank_data2 #

Inflow2 #

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 #

Ex. 4 Calc_Cd #

Ex. 4.001 Calc_Cd #

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 #

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>

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 #

WL Ans1 11 augment col ft * :

Max_WL WL max : ft #

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 #

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 #

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

Time & Water Level

0.5 myFit_WL ft #

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 : #

Image of MathCAD Result

Time value corresponding 
to max ouflow T nn el hr #

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 #

Using "solve" function

T_max hr / myFit_I cusec #

Both shoud be equal at the intersection point

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

T_max hr #

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

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

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

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

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

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

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 : #

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 : 060004600022 mat

TI TO TE Tmax_Line HFL_Line Max_Outflow_Line Max_Iflow_Line 7 1 sys

Max_Inflow cusec 6000

HFL ft #

Max_Outflow cusec #

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 #

Inflow Hydrograph Inflow 040018002200034000460005470063300724008160091100115001230015200201002550300350400500600700800900232 mat :

a 300 300.3 301 302.1 303.8 305.3 306.2 306.6 306.7 91 mat :

b 10501100121314491826219524182528255991 mat :

Storage a b augment :

InfX Inflow 1 col :

InfY Inflow 2 col :

StoX Storage 1 col :

StoY Storage 2 col :

Inf InfX InfY . 10 red plotG :

Stor StoX StoY . 10 red plotG :

Inflow Inf 2 1 sys Storage Stor 2 1 sys

Data 1 3.2 2 3.4 3 3.6 4 3.7 42 mat :

X Data 1 col :

Prepare the Poly model

Y Data 2 col :

x φ 1 x x 2^x 3^41 mat :

1 x x 2^x 3^41 mat

1 x x 1.75^x 2.5^41 mat

n X length :

n 4

PolyOrder 3 :

degree PolyOrder 1 + :

x i^(i 0 PolyOrder sum 1 x 1 x + x 2^+ (* +

j 0 degree range :

i 1 n range :

j 1 degree range i 1 n range M i j el X i el φ j el : for for

M 111112481392714166444 mat

Φ M transpose M * :

d M transpose Y * :

b Φ 1 -^eval d * :

b 3.1 0.01667 0.1 0.01667 - 41 mat

x fit b x φ * :

<= recast the scalar model

x Myfit 3.1 0.01667 x * + 0.1 x 2^* + 0.01667 x 3^* - :

<= same as fit(x)

Setup the plot

Poly 14 1.01 x fit inc :

data X Y . 14 red plotG :

Coefficient of discharge [Cd] vs Height [H] ... units as per Data ?

Poly data 2 1 sys