_jh_B_1_37a.wxmx
--> kill(all);

\[\]\[\tag{%o0} \ensuremath{\mathrm{done}}\]

--> P:'integrate(ro·g·(H−h)·a,h,0,b);

\[\]\[\tag{%o1} a g \int_{}^{}H\mathop{-}h{\, dh} \ensuremath{\mathrm{ro}}\]

--> ro:1000;g:9.81;H:3;a:1;b:2;

\[\]\[\tag{%o2} 1000\]

\[\]\[\tag{%o3} 9.81\]

\[\]\[\tag{%o4} 3\]

\[\]\[\tag{%o5} 1\]

\[\]\[\tag{%o6} 2\]

--> P:'integrate(ro·g·(H−h)·a,h,0,b);

\[\]\[\tag{%o7} 9810.0 \int_{}^{}3\mathop{-}h{\, dh}\]

--> P:integrate(ro·g·(H−h)·a,h,0,b);

\[\]\[\tag{%o8} 39240.0\]

--> mP:integrate(ro·g·(H−h)·a·h,h,0,b);

\[\]\[\tag{%o9} 32700.0\]

--> h_D:mP/P;

\[\]\[\tag{%o10} 0.8333333333333334\]

Standart
--> h_C:H−b/2;

\[\]\[\tag{%o11} 2\]

--> p_c:ro·g·h_C;

\[\]\[\tag{%o12} 19620.0\]

--> w:b·a;

\[\]\[\tag{%o13} 2\]

--> P_:p_c·w;

\[\]\[\tag{%o14} 39240.0\]

--> I_0:(a·b··3)/12,numer;

\[\]\[\tag{%o16} 0.6666666666666666\]

Up
--> h_D_:h_C+(I_0/(h_C·w));

\[\]\[\tag{%o17} 2.1666666666666665\]

Down
--> H−h_D_;

\[\]\[\tag{%o18} 0.8333333333333335\]

Created with wxMaxima.

The source of this Maxima session can be downloaded here.