Critical Depth Calculator

Depth at which the Froude number equals 1 — minimum specific energy for a given discharge. Supports rectangular (closed form), trapezoidal, and circular channels (bisection method).

Open Channel Flow · Hydraulics

Inputs

Channel cross-section:

Flow rate Q (m³/s)

Bottom width b (m)

Also compute critical slope S_c — enter Manning's n

Theory

Critical depth condition (all shapes):

Fr = 1 → V_c = √(g × D_h)

Q²/g = A_c³ / T_c [general critical condition]

D_h = A_c / T_c [hydraulic depth]

T_c = dA/dy|_y=yc [top width at critical depth]

Closed-form solutions:

Rectangular: y_c = (q²/g)^1/3 q = Q/b

Rectangular: E_c = (3/2) × y_c

Trapezoidal / Circular: bisection on Q²T/g = A³

Critical slope:

S_c = (n × V_c / R_c^2/3)²

If actual slope S > S_c → steep (supercritical normal flow) S < S_c → mild (subcritical normal flow)

Specific energy diagram:

Specific energy E = y + V²/(2g) = y + Q²/(2gA²). For a given Q, the E-y diagram has two branches meeting at y_c (minimum energy). Depths greater than y_c are subcritical; depths less than y_care supercritical. Hydraulic jumps transition from supercritical to subcritical with energy loss.