Final answer:
To determine the normal depth of flow in a rectangular channel, we can use Manning's equation. First, we calculate the cross-sectional area using the discharge and channel width. Then, we calculate the hydraulic radius using the cross-sectional area and wetted perimeter. Using Manning's equation, we solve for the normal depth of flow. The critical depth of flow can be calculated using specific energy, and the state of flow can be determined by comparing the normal depth with the critical depth.
Step-by-step explanation:
To determine the normal depth of flow in a rectangular channel, we can use Manning's equation: n = roughness coefficient, R = hydraulic radius = A/P where A is the cross-sectional area and P is the wetted perimeter, S = bed slope = tan(theta) where theta is the angle of the bed slope, Q = discharge = A * V where V is the average velocity. Given: Discharge (Q) = 5.2 m3/s,Channel width (B) = 2 m, Bed slope (S) = 1:625 = 0.0016,Roughness coefficient (n) = 0.013. First, we can calculate the cross-sectional area (A) using the discharge and channel width: A = Q / V = (5.2) / (2) = 2.6 m2. The wetted perimeter (P) can be calculated using the channel width and normal depth (y): P = B + 2y = 2 + 2y. Next, we can calculate the hydraulic radius (R): R = A / P = 2.6 / (2 + 2y). Using Manning's equation: n = (1.49 / R) * S^0.5. Plug in the values and solve for y: 0.013 = (1.49 / (2.6 / (2 + 2y))) * 0.0016^0.5. Simplify the equation: 0.013 = 1.49 * (2 + 2y) / (2.6 * 0.0016)^0.5, 0.013 * (2.6 * 0.0016)^0.5 = 1.49 * (2 + 2y), 0.013 * (2.6 * 0.0016)^0.5 = 1.49 * 2 + 1.49 * 2y. Solve the equation to find y, which represents the normal depth of flow. The critical depth of flow can be calculated using specific energy: Specific energy (E) = y + (V^2 / 2g) where g is the acceleration due to gravity. The critical depth (yc) occurs when the specific energy is at a minimum. The state of flow can be determined by comparing the normal depth with the critical depth. If the normal depth is greater than the critical depth, the flow is subcritical. If the normal depth is equal to the critical depth, the flow is critical. If the normal depth is less than the critical depth, the flow is supercritical.