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Backwater Direct Step

Compute gradually-varied flow profile in a trapezoidal channel using the direct-step method — identifies M/S profile type.

Inputs

Q (m³/s)

Bottom width b (m)

Side slope z (H:1V)

Slope S₀

Manning's n

Δx step (m)

y₁ start depth (m)

n_steps

Method — Direct step

Compute V, R, E = y + V²/(2g) at y₁; specific energy.
Δx = (E2 − E1) / (S0 − Sf,avg); Sf = (Q·n / (A·R^(2/3)))².
March downstream/upstream by stepping y; produces water surface profile.

Step	x (m)	y (m)	V (m/s)	E (m)

Results

Normal depth y_n—

Critical depth y_c—

Profile type—

Final y—

Total Δx—