_jh_fp3.wxmx
(%i1) kill ( all ) ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

(%i6) ro : 1000 ; g : 9 . 81 ; H1 : 3 ; p_a : 101325 ; B : 2 ; H2 : 1 . 5 ;

\[\operatorname{ }1000\]

\[\operatorname{ }9.81\]

\[\operatorname{ }3\]

\[\operatorname{ }101325\]

\[\operatorname{ }2\]

\[\operatorname{ }1.5\]

Plate Left
(%i7) h_c1 : H1 / 2 , numer ;

\[\operatorname{ }1.5\]

(%i8) p_c1 : ro · g · h_c1 ;

\[\operatorname{ }14715.0\]

(%i9) w1 : H1 · B ;

\[\operatorname{ }6\]

(%i10) P_x1 : p_c1 · w1 ;

\[\operatorname{ }88290.0\]

(%i11) I_01 : ( B · ( H1 · · 3 ) ) / ( 12 ) , numer ;

\[\operatorname{ }4.5\]

(%i12) h_d1 : h_c1 + ( I_01 / ( h_c1 · w1 ) ) ;

\[\operatorname{ }2.0\]

Plate Righr
(%i13) h_c2 : H2 / 2 , numer ;

\[\operatorname{ }0.75\]

(%i14) p_c2 : ro · g · h_c2 ;

\[\operatorname{ }7357.5\]

(%i15) w2 : H2 · B ;

\[\operatorname{ }3.0\]

(%i16) P_x2 : p_c2 · w2 ;

\[\operatorname{ }22072.5\]

(%i17) I_02 : ( B · ( H2 · · 3 ) ) / ( 12 ) , numer ;

\[\operatorname{ }0.5625\]

(%i18) h_d2 : h_c2 + ( I_02 / ( h_c2 · w2 ) ) ;

\[\operatorname{ }1.0\]

(%i19) h_d1_1 : H1 h_d1 ;

\[\operatorname{ }1.0\]

(%i20) h_d2_1 : H2 h_d2 ;

\[\operatorname{ }0.5\]

(%i21) P : P_x1 P_x2 ;

\[\operatorname{ }66217.5\]

(%i22) mP : h_d1_1 · P_x1 h_d2_1 · P_x2 ;

\[\operatorname{ }77253.75\]

(%i23) h_D : mP / P ;

\[\operatorname{ }1.1666666666666667\]

Figure 1:D:\_jknuba_25_26_autem\_jg_Lections\_j_knuba_hydraulics\_jh_fp3_v1.jpg
Diagram

K123 two plates

(%i24) P1 : integrate ( ro · g · ( H1 h ) · B , h , 0 , H1 ) ;

\[\operatorname{ }88290.0\]

(%i25) ' integrate ( ro · g · ( H1 h ) · B , h , 0 , H1 ) ;

\[\operatorname{ }19620.0 \int_{0}^{3}{\left. 3\operatorname{-}hdh\right.}\]

(%i26) mP1 : integrate ( ro · g · ( H1 h ) · B · h , h , 0 , H1 ) ;

\[\operatorname{ }88290.0\]

(%i30) ' integrate ( ro · g · ( H1 h ) · B · h , h , 0 , H1 ) ;

\[\operatorname{ }19620.0 \int_{0}^{3}{\left. \left( 3\operatorname{-}h\right) hdh\right.}\]

(%i27) P2 : integrate ( ro · g · ( H2 h ) · B , h , 0 , H2 ) ;

\[\]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 3.0 by 3/1 = 3.0 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.125 by 9/8 = 1.125\]

\[\operatorname{ }22072.5\]

(%i28) mP2 : integrate ( ro · g · ( H2 h ) · B · h , h , 0 , H2 ) ;

\[\]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 0.5625 by 9/16 = 0.5625\]

\[\operatorname{ }11036.25\]

(%i29) h_D_k123 : ( mP1 mP2 ) / ( P1 P2 ) ;

\[\operatorname{ }1.1666666666666667\]

(%i38) ' h_D_k123 = ( ' mP1 ' mP2 ) / ( ' P1 ' P2 ) ;

\[\operatorname{ }\ensuremath{\mathrm{h\_ D\_ k123}}\operatorname{=}\frac{\ensuremath{\mathrm{mP1}}\operatorname{-}\ensuremath{\mathrm{mP2}}}{\ensuremath{\mathrm{P1}}\operatorname{-}\ensuremath{\mathrm{P2}}}\]


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