Equations


h3. Total Flow Rate Through Weir

{latex} $$ Q = cC_o [h + {2 \over 3} s] $$ {latex}

 $$ C_o = C_d W \sqrt{2 g s} = {Q_{max} \over H_{dmax}}$$ 

 c :
{latex} $$ c = W k {s^{1 \over 2}} $$ {latex}
The variable k :
{latex} $$ k = 2 C_d \sqrt{2g} $$ {latex}
*Combined and substitued* :
{latex} $$ Q = W 2 C_d \sqrt{2g} {s^{1 \over 2}} [h + {2 \over 3} s] $$ {latex}

h3. Flow Through Rectangular Base of Weir

{latex} $$ q_w = {42 \over 3} W C_d \sqrt{2g} [{{(h + s)}^{23 \over 32}} - {h^{2 \over 3}}] $$ 

 $$ W = Q_max \over {C_d {H_dmax^{3 \over 2}} \sqrt{3 g Pi_Sutro}} $$ 

{latex}

h3. Rectangular Base Height

{latex} $$ s = {3 \over 2} \Pi_{sutro}H_{dmax} $$ 

 $$ Pi_{sutro} = {Q_min \over Q_max} =  {{2 \over 3}s} \over {H_dmax} $$ 

{latex}


h3. Profile of Curved Portion

{latex} $$ y = {W \over 2} [1 - {s \over \Pi} tan^{-1} \sqrt{x \over s} ]$$ {latex}