For the closed beam section subjected to a vertical shear force $S_y=5kN$ acting through the shear center as shown in Fig. $1($a$),$ determine:

$($i$)$ the shear flow distribution in terms of $s_1,s_2$ and $s_3$ as shown in Fig. $1($b$)$ and the shear flow at points $1_{,}{2}_{,}{3}_{?}$ and $4_{?}(1_{?}$ and $4_{?}$ are at the mid height of the two vertical spar panel$)$; and $($ii$)$ the position of the shear center $S_{cx}.$

$($hint: make a cut at point $1$ in Fig. $1($b$)$ and introduce an unknown shear flow $q_{s0}$; and assume positive shear flow in clockwise direction$)$

Fig. $1($b$)$