地下水揚水量 井底が不透水層にまで達する場合,CALCULATION OF WATER VOLUME FLOWING IN WELL. CASE:UNCONFINED GROUNDWATER,INFLOW ONLY FROM SIDEWALL OF WELL.

Equation
Q=\frac{\pi k(H^{2}-t^{2})}{2.3\log(R/r)}

Scilab
000180180sci01180sci02

 -->clear;
-->funcprot(0); 
-->xset("window",1);clf();
-->deff('[Q]=f(R,r)','Q=%pi*k/100*(H^2-t^2)/(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)
-->t=4;//(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]);contour(R,r,f,20,flag=[0,2,4]);
-->f(5,3)
 ans  =
 
    5.4427366  
-->f(20,0.5)
 ans  =
 
    0.7536948  
-->clear;
-->funcprot(0); 
-->xset("window",2);clf();
-->deff('[Q]=f(H,t)','Q=%pi*k/100*(H^2-t^2)/(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)
-->H=linspace(8,15);//(m)
-->t=linspace(0,7);//(m)
-->xgrid();
-->xtitle('地下水揚水量Q(m^3/sec)','H(m)','t(m)','Q(m^3/s)',boxed=1);
-->fplot3d(H,t,f,flag=[33,2,4]);contour(H,t,f,20,flag=[0,2,4]);
-->f(15,7)
 ans  =
 
    0.2917800  

※SciNotes

clear;
funcprot(0); 
xset("window",1);clf();
deff('[Q]=f(R,r)','Q=%pi*k/100*(H^2-t^2)/(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)
t=4;//(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]);contour(R,r,f,20,flag=[0,2,4]);
f(5,3)
f(20,0.5)

clear;
funcprot(0); 
xset("window",2);clf();
deff('[Q]=f(H,t)','Q=%pi*k/100*(H^2-t^2)/(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)
H=linspace(8,15);//(m)
t=linspace(0,7);//(m)
xgrid();
xtitle('地下水揚水量Q(m^3/sec)','H(m)','t(m)','Q(m^3/s)',boxed=1);
fplot3d(H,t,f,flag=[33,2,4]);contour(H,t,f,20,flag=[0,2,4]);
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,Free groundwater,Unconfined groundwater,pump displacement,Darcy’s law,Inflow only from sidewall of well.

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/