$8\mathrm{.}68$ A newly designed dam is to be modeled in the laboratory. The prime objective of the general model study is to determine the adequacy of the spillway design and to observe the water ve$-(0)$ locities, elevations, and pressures ate critical points of the structure. The reach of the river to be modeled is $1200m$ long, the width of the dam $($also the maximum width of the reservoir upstream$)$ is to be $300m,$ and the maximum flood discharge to be modeled is $5000\frac{m^3}{s}.$ The maximum laboratory discharge is limited to $0\mathrm{.}90\frac{m^3}{s},$ and the floor space available for the model construction is $50m$ long and $20m$ wide. Determine the largest feasible scale ratio $($model $/$ prototype$)$ for such a study.