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

Equation
Kozenyの式
Q=\frac{2\pi kb{c}'(H-h)}{2.3\log(R/r)}(1+7\sqrt{\frac{r}{2b{c}'}}\cos\frac{\pi {c}'}{2})
{c}'=c/b
000182

Scilab
000182sci01000182sci02000182sci03000182sci04000182sci05000182sci06

 -->clear;
-->funcprot(0); 
-->deff('[Q]=f(R,r)','Q=2*%pi*k/100*b*c/b*(H-h)/(2.3*log10(R/r))*(1+7*sqrt(r/(2*b*c/b))*cos(%pi*c/b/2))');//地下水揚水量:Q(m^3/sec)
-->k=10^-1;//透水係数(cm/sec)
-->H=30;//(m)
-->h=15;//(m)
-->b=5;//(m)
-->c=1;//(m)
-->R=linspace(5,20);//(m)
-->r=linspace(0.5,3);//(m)
-->xset("window",1);
-->clf();
-->xgrid();
-->condition='k='+string(k)+',H='+string(H)+',h='+string(h)+',b='+string(b)+',c='+string(c);
-->graphtitle='地下水揚水量Q(m^3/sec).' + condition;
-->xtitle(graphtitle,'R(m)','r(m)','Q(m^3/s)',boxed=1);
-->color(240,255,240);
-->idcolor=color(240,255,240);
-->fplot3d(R,r,f,flag=[idcolor , 2 , 4]);
-->xset("window",2);
-->clf();
-->xgrid();
-->xtitle(graphtitle,'R(m)','r(m)','Q(m^3/s)',boxed=1);
-->contour(R,r,f,30,flag=[2,2,4]);
-->f(5,3)
 ans  =
 
    1.6907475  
-->f(20,0.5)
 ans  =
 
    0.1107189  
-->clear;
-->funcprot(0); 
-->deff('[Q]=f(H,h)','Q=2*%pi*k/100*b*c/b*(H-h)/(2.3*log10(R/r))*(1+7*sqrt(r/(2*b*c/b))*cos(%pi*c/b/2))');//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=5;//(m)
-->c=1;//(m)
-->H=linspace(8,15);//(m)
-->h=linspace(0,7);//(m)
-->xset("window",3);
-->clf();
-->xgrid();
-->condition='k='+string(k)+',R='+string(R)+',r='+string(r)+',b='+string(b)+',c='+string(c);
-->graphtitle='地下水揚水量Q(m^3/sec).' + condition;
-->xtitle(graphtitle,'H(m)','h(m)','Q(m^3/s)',boxed=1);
-->color(255,239,219);
-->idcolor=color(255,239,219);
-->fplot3d(H,h,f,flag=[idcolor , 2 , 4]);
-->xset("window",4);
-->clf();
-->xgrid();
-->xtitle(graphtitle,'H(m)','h(m)','Q(m^3/s)',boxed=1);
-->contour(H,h,f,30,flag=[2,2,4]);
-->f(15,7)
 ans  =
 
    0.2428037  
-->clear;
-->funcprot(0); 
-->deff('[Q]=f(c,b)','Q=2*%pi*k/100*b*c/b*(H-h)/(2.3*log10(R/r))*(1+7*sqrt(r/(2*b*c/b))*cos(%pi*c/b/2))');//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)
-->H=20;//(m)
-->h=15;//(m)
-->c=linspace(1,5);//(m)
-->b=linspace(5,10);//(m)
-->xset("window",5);
-->clf();
-->xgrid();
-->condition='k='+string(k)+',R='+string(R)+',r='+string(r)+',H='+string(H)+',h='+string(h);
-->graphtitle='地下水揚水量Q(m^3/sec).' + condition;
-->xtitle(graphtitle,'c(m)','b(m)','Q(m^3/s)',boxed=1);
-->color(233,150,122);
-->idcolor=color(233,150,122);
-->fplot3d(c,b,f,flag=[idcolor , 2 , 4]);
-->xset("window",6);
-->clf();
-->xgrid();
-->xtitle(graphtitle,'c(m)','b(m)','Q(m^3/s)',boxed=1);
-->contour(c,b,f,30,flag=[2,2,4]);
-->f(2,7)
 ans  =
 
    0.2142539  

SciNotes

clear;
funcprot(0); 
deff('[Q]=f(R,r)','Q=2*%pi*k/100*b*c/b*(H-h)/(2.3*log10(R/r))*(1+7*sqrt(r/(2*b*c/b))*cos(%pi*c/b/2))');//地下水揚水量:Q(m^3/sec)
k=10^-1;//透水係数(cm/sec)
H=30;//(m)
h=15;//(m)
b=5;//(m)
c=1;//(m)
R=linspace(5,20);//(m)
r=linspace(0.5,3);//(m)

xset("window",1);
clf();
xgrid();
condition='k='+string(k)+',H='+string(H)+',h='+string(h)+',b='+string(b)+',c='+string(c);
graphtitle='地下水揚水量Q(m^3/sec).' + condition;
xtitle(graphtitle,'R(m)','r(m)','Q(m^3/s)',boxed=1);
color(240,255,240);
idcolor=color(240,255,240);
fplot3d(R,r,f,flag=[idcolor , 2 , 4]);

xset("window",2);
clf();
xgrid();
xtitle(graphtitle,'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); 
deff('[Q]=f(H,h)','Q=2*%pi*k/100*b*c/b*(H-h)/(2.3*log10(R/r))*(1+7*sqrt(r/(2*b*c/b))*cos(%pi*c/b/2))');//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=5;//(m)
c=1;//(m)
H=linspace(8,15);//(m)
h=linspace(0,7);//(m)

xset("window",3);
clf();
xgrid();
condition='k='+string(k)+',R='+string(R)+',r='+string(r)+',b='+string(b)+',c='+string(c);
graphtitle='地下水揚水量Q(m^3/sec).' + condition;
xtitle(graphtitle,'H(m)','h(m)','Q(m^3/s)',boxed=1);
color(255,239,219);
idcolor=color(255,239,219);
fplot3d(H,h,f,flag=[idcolor , 2 , 4]);

xset("window",4);
clf();
xgrid();
xtitle(graphtitle,'H(m)','h(m)','Q(m^3/s)',boxed=1);
contour(H,h,f,30,flag=[2,2,4]);

f(15,7)

clear;
funcprot(0); 
deff('[Q]=f(c,b)','Q=2*%pi*k/100*b*c/b*(H-h)/(2.3*log10(R/r))*(1+7*sqrt(r/(2*b*c/b))*cos(%pi*c/b/2))');//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)
H=20;//(m)
h=15;//(m)
c=linspace(1,5);//(m)
b=linspace(5,10);//(m)

xset("window",5);
clf();
xgrid();
condition='k='+string(k)+',R='+string(R)+',r='+string(r)+',H='+string(H)+',h='+string(h);
graphtitle='地下水揚水量Q(m^3/sec).' + condition;
xtitle(graphtitle,'c(m)','b(m)','Q(m^3/s)',boxed=1);
color(233,150,122);
idcolor=color(233,150,122);
fplot3d(c,b,f,flag=[idcolor , 2 , 4]);

xset("window",6);
clf();
xgrid();
xtitle(graphtitle,'c(m)','b(m)','Q(m^3/s)',boxed=1);
contour(c,b,f,30,flag=[2,2,4]);

f(2,7)

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,Kozeny Equation,Aquiclude,Influence Radius,Penetration length,Partial Penetration.

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/