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The flow rate per unit width $q$ under a sluice gate depends upon the upstream head $d_u,$ the gate opening height $h$ and the acceleration due to gravity $g.$

The Figure below illustrates the sluice gate situation.

The Table below lists physical modelling results of a series of laboratory experiments in dimensional form. Based upon these physical modelling results estimate the sluice gate opening $h($in metres$)$ for a prototype sluice gate with $d_u=8\mathrm{.}0m$ and $q=4\mathrm{.}7\frac{m^2}{s}.$ Provide your answer with $2$ decimal places. $($Hint: linear interpolation is required$)$

Table $1.$ Physical modelling results of laboratory experiments