River Ford: Stepping Stones & Flow · 2D

-Depth

-Speed

-d·V

-Stones dry

-Verdict

Plan view and cross-section at the stone row

Long profile: water surface along the river

Hazard plane: depth vs speed

Flow and stones

Discharge Q

Slope S

Roughness n

Stone spacing s

Readouts

The science

Manning, continuity, Froude

V = (1/n) R^(2/3) S^(1/2),  R = w d / (w + 2 d)
Q = V w d      Fr = V / sqrt(g d)      d_c = (q^2/g)^(1/3)

Stone row choke

A_b(d) = sum a min(h_i, d)     A_c = w d - A_b
E = d + Q^2/(2 g A_c^2)        E_min = min E(d)
E0 < E_min: level upstream rises to E_min (afflux)

Wading hazard and the test post

H = d V (guide 0.6 m^2/s)
F = 1/2 rho Cd wf min(d,Hf) V^2
SF_slide = mu W_eff / F     SF_topple = W_eff c_heel / (F min(d,Hf)/2)

Same physics module as the 3D lab, so both pages print identical numbers. Simplifications: steady uniform flow in a 6 m rectangle plus a loss-free energy balance at the stones; no turbulence, wakes or stone movement; thresholds are rules of thumb (verify). The test subject is an inanimate post.

Educational model with simplifications. Never use it to decide whether to cross real water. Fast shallow water can sweep an adult off their feet.

Independent checks