A sluice gate used to control the flow in a horizontal channel of unit width is shown in the figure.
It is observed that the depth of flow is $1.0$ m upstream of the gate, while the depth is $0.2$ m downstream of the gate. Assuming a smooth flow transition across the sluice gate, i.e., without any energy loss, and the acceleration due to gravity $10 \: m/s^2$, the discharge (in $m^3/s$, up to two decimal places) passing under the sluice gate is ___________