地下水揚水量 井壁が帯水層を貫通している場合,Calculation of Water Volume Flowing in Well. Case:Confined groundwater,Thiem Equation.

Equation
Thiemの式
Q=\frac{2 \pi kb(H-h)}{2.3\log(R/r)}
000181

Scilab
181sci01181sci02181sci03181sci04

 -->clear;
-->funcprot(0); 
-->xset("window",1);clf();
-->deff('[Q]=f(R,r)','Q=2*%pi*k/100*b*(H-h)/(2.3*log10(R/r))');
-->//地下水揚水量:Q(m^3/sec)
-->k=10^-1;//透水係数(cm/sec)
-->H=30;//(m)
-->h=4;//(m)
-->b=1;//(m)
-->R=linspace(5,20);//(m)
-->r=linspace(0.5,3);//(m)
-->xgrid();
-->xtitle('地下水揚水量Q(m^3/sec)','R(m)','r(m)','Q(m^3/s)',boxed=1);
-->fplot3d(R,r,f,flag=[33 , 2 , 4]);
-->xset("window",2);clf();
-->xgrid();
-->xtitle('地下水揚水量Q(m^3/sec)','R(m)','r(m)','Q(m^3/s)',boxed=1);
-->contour(R,r,f,30,flag=[2,2,4]);
-->f(5,3)
 ans  =
 
    0.3201610  
-->f(20,0.5)
 ans  =
 
    0.0443350  
-->clear;
-->funcprot(0); 
-->xset("window",3);clf();
-->deff('[Q]=f(H,h)','Q=2*%pi*k/100*b*(H-h)/(2.3*log10(R/r))');
-->//地下水揚水量:Q(m^3/sec)
-->k=10^-1;//透水係数(cm/sec)
-->R=20;//(m)
-->r=3;//(m)
-->b=1;//(m)
-->H=linspace(8,15);//(m)
-->h=linspace(0,7);//(m)
-->xgrid();
-->xtitle('地下水揚水量Q(m^3/sec)','H(m)','h(m)','Q(m^3/s)',boxed=1);
-->fplot3d(H,h,f,flag=[34 , 2 , 4]);
-->xset("window",4);clf();
-->xgrid();
-->xtitle('地下水揚水量Q(m^3/sec)','H(m)','h(m)','Q(m^3/s)',boxed=1);
-->contour(H,h,f,30,flag=[2,2,4]);
-->f(15,7)
 ans  =
 
    0.0265255  

SciNotes

clear;
funcprot(0); 
xset("window",1);clf();
deff('[Q]=f(R,r)','Q=2*%pi*k/100*b*(H-h)/(2.3*log10(R/r))');
//地下水揚水量:Q(m^3/sec)
k=10^-1;//透水係数(cm/sec)
H=30;//(m)
h=4;//(m)
b=1;//(m)
R=linspace(5,20);//(m)
r=linspace(0.5,3);//(m)
xgrid();
xtitle('地下水揚水量Q(m^3/sec)','R(m)','r(m)','Q(m^3/s)',boxed=1);
fplot3d(R,r,f,flag=[33 , 2 , 4]);
xset("window",2);clf();
xgrid();
xtitle('地下水揚水量Q(m^3/sec)','R(m)','r(m)','Q(m^3/s)',boxed=1);
contour(R,r,f,30,flag=[2,2,4]);
f(5,3)
f(20,0.5)
 
clear;
funcprot(0); 
xset("window",3);clf();
deff('[Q]=f(H,h)','Q=2*%pi*k/100*b*(H-h)/(2.3*log10(R/r))');
//地下水揚水量:Q(m^3/sec)
k=10^-1;//透水係数(cm/sec)
R=20;//(m)
r=3;//(m)
b=1;//(m)
H=linspace(8,15);//(m)
h=linspace(0,7);//(m)
xgrid();
xtitle('地下水揚水量Q(m^3/sec)','H(m)','h(m)','Q(m^3/s)',boxed=1);
fplot3d(H,h,f,flag=[34 , 2 , 4]);
xset("window",4);clf();
xgrid();
xtitle('地下水揚水量Q(m^3/sec)','H(m)','h(m)','Q(m^3/s)',boxed=1);
contour(H,h,f,30,flag=[2,2,4]);
f(15,7)

キーワード
Water Volume Flowing in Well,Impermeable Layer,Groundwater Level,Well Bottom,Sidewall of well,Radius of Well,Hydraulic conductivity,Confined groundwater,pump displacement,Darcy’s law,Inflow only from sidewall of well,Thiem Equation,Aquiclude.

参考文献
川島普、篠原紀、西川泰治(1999).『新訂衛生工学』.明現社.184pp.

アプリケーション
Scilab http://www.scilab.org/