A 60 cm valve is designed for control of flow in a petroleum pipeline. A one-third-scale model of the full-size valve is to be tested with water in the laboratory. If the prototype flow rate is to be 0.5 m³/s, what flow rate should be established in the laboratory test for dynamic similitude to be established? Also, if the pressure coefficient C_p in the model is found to be 1.07, what will be the corresponding C_p in the full-scale valve? The relevant fluid properties for the petroleum are S_G = 0.82 and μ = 3 × 10^–3 N^∙s/m². The viscosity of water is 10^–3 N^∙s/m².