Answer:
It seems like you want to determine the channel type, flow surface profile, and perform a numerical calculation for a triangular channel based on the provided data. However, you mentioned parameters like Q (discharge), J₀ (base slope), n (Manning's roughness coefficient), and m (slope slope), but it looks like some values are missing. I'll provide you with a general approach, but please provide the missing parameters so I can offer more accurate assistance.
1. Determine Channel Type and Flow Surface Profile:
- To determine the channel type (subcritical or supercritical), compare the Froude number (Fr) to 1. Fr = V / √(g * R), where V is velocity, g is acceleration due to gravity, and R is the hydraulic radius.
- If Fr < 1, the flow is subcritical (controlled by friction), and if Fr > 1, the flow is supercritical (controlled by slope).
- Based on the channel type, you can estimate the flow surface profile (normal depth or critical depth) using appropriate equations.
2. Calculate Flow Surface Profile Numerically:
- Use the Manning's equation for open channel flow: Q = (1/n) * A * R^(2/3) * S^(1/2), where A is cross-sectional area, R is hydraulic radius, and S is slope.
- Calculate velocity (V) using Q and A.
- Calculate the flow area (A) and hydraulic radius (R) for the given depth values (starting from the channel end and moving upstream).
- Determine the Froude number (Fr) using V, A, R, and g.
- Based on Fr, estimate the flow type (subcritical or supercritical) and calculate the corresponding flow surface profile.
To proceed, please provide the missing values for Q, J₀, n, and m. With those values, I can help you perform the calculations and provide a more accurate response.