There is no energy loss so
E1 = E2
$\begin{array}{l}{\mathrm y}_1+\frac{\mathrm v_1^2}{2\mathrm g}={\mathrm y}_2+\frac{\mathrm v_2^2}{2\mathrm g}\\1+\frac{\mathrm Q^2}{2\mathrm{gA}_1^2}=0.2+\frac{\mathrm Q^2}{2\mathrm{gA}_2^2}\\\frac{\mathrm Q^2}{2\mathrm g}\left[\frac1{\mathrm A_2^2}-\frac1{\mathrm A_2^1}\right]=1-0.2\\\frac{\mathrm Q^2}{2\times10}\left[\frac1{0.2^2}-\frac1{1^2}\right]=0.8\\\mathrm Q^2=\frac{16}{24}\\\mathrm Q^2=\frac23\\\mathrm Q=0.82\;\mathrm m^3/\mathrm s\end{array}$
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