Discussion
In a laboratory experiment using a scaled down model to measure scour at a bridge pier, the Froude number is important. The ratio of the prototype length to the model length is 100. If the velocity of the model is 1 m \(\text{s}^{-1}\), the velocity (in m \(\text{s}^{-1}\)) of the prototype is
Answer: C
The prototype velocity is 10 m \(\text{s}^{-1}\).
Froude similarity requires equal \(V/\sqrt{gL}\) in model and prototype. With the same \(g\):
\[ \begin{aligned} V_{p} &= V_{m}\sqrt{L_{p}/L_{m}} \\ &= 1\times\sqrt{100} = 10\ \text{m/s} \end{aligned} \]
100 scales velocity with length directly, as Reynolds or geometric reasoning might suggest, and 0.1 inverts the ratio. 1 would hold only for a full-scale model.
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