55d11d8c-8bbc-4447-81d4-6a7c4e2c8334 291 5 5 decimal

1. Basic Data

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cumec m 3^s / :

MCM 106^m 3^* :

GWHr GW hr * :

Units definition

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Assume 30% probability 
for  average flow P.s 30 :

Head available h 45 m * :

Assumed Plant 
efficiency η 80 % * :

Density of water σ.w 1000 kg m 3^/ * :

2. Import Flow Data (from EXCEL file)

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MyDirectory DocumentDirectory : E:\All Smath Files in ASUS\1. Malwala Operation Study\

MyFile MyDirectory DailyQ_Malwala-R1.xlsx concat :

Read daily flow data file. Define correct

cell range (in this case B5:AF301)

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Q MyFile DailyQ B5 AF301 importData.XLSX :

Q rows 297

Q cols 31

Q length 9207

Q sum 283176.43

3. Calculations

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Convert matrix "Q" to a vector for further analysis vector_Q Q mat2sys sys2mat eval :

vector_Q max 940

vector_Q rows 9207

vector_Q cols 1

Define period (days) for operation study n_day 7 :

4. Process Flow Data for further analysis by removing any -ve values and strings

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NOTE: Digital rainfall data, provided by the Meteorology Department, sometimes contain string values (.0T) to indicate a trace of rain. We have to make it equal to zero initially by suitably ammending the program below. However, it is not necessary in the case of stream flows.

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Program to remove any -ve & string values from Q) v_Q Process_Q Remove - ve values & strings from the vector, if any Resulting vector is 'B' count 0 : j 1 v_Q rows range A1 v_Q j el eval : A1 0 < A1 IsString | (continue count count 1 + : B count el A1 eval : 21 line if 21 line for B eval 51 line :

Q.p vector_Q Process_Q eval :

Q.p rows 9039

vector_Q rows 9207

5. Find 'p' day average flows

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Program to find the 'p' day avgerage of daily flow  
matrix 'v_Q' (after removing any -ve & string values) A p Find_n_day_avg Find 'p' day mean of processed vector r 1 A rows p / trunc range C r el A 1 r 1 - (p * + r p * 11 submatrix eval sum p / : for C 31 line :

Program to find the 'p' day avgerage of daily flow  
matrix 'v_Q' (after removing any -ve & string values) A p Find_n_day_avg Find 'p' day mean of processed vector r 1 A rows p / trunc range C r el A 1 r 1 - (p * + r p * 11 submatrix eval sum p / : for C 31 line :

This is a long vector, 
and a part is shown n_day_avg Q.p n_day Find_n_day_avg :

Very slow A 1 r 1 - (p * + r p * 11 submatrix Mean eval

Fast A 1 r 1 - (p * + r p * 11 submatrix eval Mean

n_day_avg rows 1291

-ve value removed from 'Q' n_day_avg sum 40506.63

'Q' has -ve values,and hence,
the summation gets reduced. Q sum 283176.43

n_day_avg 17 55.43 123.57 91 39.29 15.86 19.14 29.57 13.43 21.86 50.43 10.86 42.71 37.57 20.86 11.86 10.14 6.86 17.14 30.29 201 mat

METHOD 1. Slightly faster than METHOD 2. A 1 r 1 - (p * + r p * 11 submatrix eval sum p /

6. Probability analysis of 'p' day mean flows

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METHOD 2 A 1 r 1 - (p * + r p * 11 submatrix p / eval sum

Arrange data in ascending order II n_day_avg sort reverse :

n_day 7

n_day_avg max 416.86

II Mean 31.38

Q.p Mean 31.38

n_day_avg min 1.86

METHOD 3. This is very slow. A 1 r 1 - (p * + r p * 11 submatrix sum p / eval

Create probability vector j 1 II length range Pr j el 100 j * II rows / eval : for

nda.mean n_day_avg Mean :

7. Fitting function and Flow Duration Curve (FDC)

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Fitting function for data x Fit Pr II x linterp :

Example 30 Fit 34.119

Mean Flow (at 30% probability) Q.s P.s Fit : 34.12

Minimum flow Q.min II min : 1.85714

Function to plot PP30 P.s 0 P.s II max 22 mat : 30030 416.857143 22 mat

Function to plot QQ30 0 Q.s Pr max Q.s 22 mat : 0 34.119 100 34.119 22 mat

Function to plot QQ.min 0 Q.min Pr max Q.min 22 mat : 0 1.85714 100 1.85714 22 mat

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 :

Define x Fit2 0 :

Define x Fit4 Q.s :

MyHatch1 x Fit4 x Fit2 0 P.s 15 hatch :

MyHatch2 x Fit x Fit2 P.s 10030 hatch :

XYPlot.XLimMin 1 el 0 :

XYPlot.XLimMax 1 el Pr max Ceil : 10011 mat

XYPlot.YLimMin 1 el 0 :

XYPlot.YLimMax 1 el II max 100 / Ceil 100 * : 50011 mat

Settings for X-Y Plot

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XYPlot.XTick 1 el 10 :

XYPlot.YTick 1 el 50 :

8. Plant Capacity and Annual Energy (assuming Turbine operates at rated flow Q_s )

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Study period in days n_day 7

Plant Capacity PW1 Q.s cumec * h * g.e * σ.w * η * : MW 12.05

where Q.s 34.12

h 45 m *

Area (A1) of Rectangle 
from 0 to Ps (30%) A1 P.s Q.s * cumec * : cumec 1023.58

Area (A2) from 
30% to the end A2 x Fit x P.s Pr max int cumec * : cumec 1165.97

Total shaded area At A1 A2 + : cumec 2189.56

Annual Energy is given by total shaded area E1 At 100 / 365 * day * h * g.e * σ.w * η * : GWHr 67.71

x Fit QQ30 MyHatch1 MyHatch2 PP30 QQ.min 6 1 sys

Assumed Probability 
for mean flow P.s 30

Flow period in days n_day 7

nda.mean 31.38

Mean Flow 
(at assumed probability) Q.s 34.119

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 :

G1 x Fit4 x Fit2 0 P.s 15 hatch :

G2 x Fit x Fit2 P.s 10030 hatch :

x Fit QQ30 G1 G2 PP30 QQ.min 6 1 sys

Assumed Probability 
for mean flow P.s 30

Flow period in days n_day 7

nda.mean 31.38

Mean Flow 
(at assumed probability) Q.s 34.119