The hyetograph of a storm event of duration $140$ minutes is shown in the figure:

The infiltration capacity at the start of this event $(t=0)$ is $17 \: mm/hour$, which linearly decreases to $10 \: mm/hour$ after $40$ minutes duration. As the event progresses, the infiltration rate further drops down linearly to attain a value of $4 \: mm/ hour$ at $t=100$ minutes and remains constant thereafter till the end of the storm event. The value of the infiltration index, $\phi$ (in $mm/hour$ round off to $2$ decimal places), is _____________