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Table 2 Model scale set based on the Froude criterion

From: Plugging efficiency of pouring aggregates through multiple boreholes into an inundated tunnel to prevent groundwater inrush disasters

Scale for

\({\text{F}}_{{\text{r}}}\)

Inertial force/gravity

\({\text{v}}^{{2}} /{\text{Lg}}\)

Length \({\uplambda }_{{\text{L}}}\)

\({\uplambda }_{{\text{L}}} { = 20}\)

Time \({\uplambda }_{{\text{t}}}\)

\({\uplambda }_{{\text{L}}}^{{\frac{{1}}{{2}}}} { = 4}{\text{.47}}\)

Flow velocity \({\uplambda }_{{\text{v}}}\)

\({\uplambda }_{{\text{L}}}^{{\frac{{1}}{{2}}}} { = 4}{\text{.47}}\)

Flow quantity \({\uplambda }_{{\text{Q}}}\)

\({\uplambda }_{{\text{L}}}^{{\frac{{5}}{{2}}}} { = 1788}{\text{.85}}\)

Pressure \({\uplambda }_{{\text{p}}}\)

\({\uplambda }_{{\text{L}}} { = 20}\)

Force \({\uplambda }_{{\text{F}}}\)

\({\uplambda }_{{\uprho }} {\uplambda }_{{\text{L}}}^{{3}} { = 8000}\)

Power \({\uplambda }_{{\text{P}}}\)

\({\uplambda }_{{\uprho }} {\uplambda }_{{\text{L}}}^{{\frac{{7}}{{2}}}} { = 35777}\)

Roughness \({\uplambda }_{n}\)

\({\uplambda }_{{\text{L}}}^{{\frac{{1}}{{6}}}} { = 1}{\text{.65}}\)