Water at 70^{\circ } F flows in a prototype rectangular open channel with a width of 10 ft, and a sluice gate with a free outflow is inserted in the channel, as illustrated in Figure EP 11.16, in order to measure the flowrate. The opening of the gate is set at 3.28 ft, the depth of flow upstream of the sluice gate is 6.56 ft, and the depth of flow downstream of the sluice gate is 3.11 ft. A smaller model of the larger prototype is designed in order to study the flow characteristics of open channel flow in the flow-measuring device. The model fluid is also water at 70^{\circ } F F, the ideal downstream velocity (see Equation 9.285 v_{2i} = \frac{\sqrt{2g(y_{1}- y_{2})} }{\sqrt{1- \left(\frac{A_{2}}{A_{1}} \right)^{2} } } = \frac{\sqrt{2g(y_{1}- y_{2})} }{\sqrt{1- \left(\frac{by_{2}}{by_{1}} \right)^{2} } } = \frac{\sqrt{2g(y_{1}- y_{2})} }{\sqrt{1- \left(\frac{y_{2}}{y_{1}} \right)^{2} } } ) of flow of the water, v_{2i} in the smaller model open channel fitted with a sluice gate is 8.46 ft/sec, and the model scale, λ is 0.25. (a) Determine the actual discharge in the model sluice gate. (b) Determine the ideal downstream velocity of flow of the water in the prototype sluice gate in order to achieve dynamic similarity between the model and the prototype. (c) Determine the actual discharge in the prototype sluice gate in order to achieve dynamic similarity between the model and the prototype.