Spillway model height, head and flow

Spillway flow is gravity-dominated, so the Froude law is used. Length scale $L_r = L_m/L_p = 1/16$.

(i) Model dimensions

$$\begin{aligned} H_m &= \frac{12.5}{16} = 0.78125\ \text{m} \approx 0.78\ \text{m} \\ h_m &= \frac{2}{16} = 0.125\ \text{m} = 12.5\ \text{cm} \end{aligned}$$

(ii) Flow per metre length of the prototype

Model flume width $= 0.60$ m, $Q_m = 20$ L/s.

$$q_m = \frac{20}{0.6} = 33.33\ \text{L/s per m}$$

For Froude similarity, the discharge scale is $Q_r = L_r^{5/2}$, and the discharge per unit length scale is $q_r = L_r^{3/2}$:

$$q_p = \frac{q_m}{L_r^{3/2}} = 33.33\times16^{3/2} = 33.33\times64 = 2133\ \text{L/s per m}$$

Answer: (i) model spillway height $= 0.781$ m and head $= 0.125$ m; (ii) prototype discharge $\approx 2133$ L/s per metre length $= 2.13\ \text{m}^3/\text{s}$ per m.