In a $5$ m wide rectangular channel, the velocity $u$ distribution in the vertical direction $y$ is given by $u=1.25 y^{\frac{1}{6}}$. The distance $y$ is measured from the channel bed. If the flow depth is $2$ m, the discharge per unit width of the channel is

1. $2.40 \: m^3/s/m$
2. $2.80 \: m^3/s/m$
3. $3.27 \: m^3/s/m$
4. $12.02 \: m^3/s/m$