Specific Energy Calculator

E = y + V²/(2g) — energy per unit weight measured from the channel bed. Computes specific energy, Froude number, critical depth, minimum energy, and the alternate depth on the other branch of the E-y diagram.

Open Channel Flow · Hydraulics

Inputs

Specify flow by:

Flow depth y (m)

Flow velocity V (m/s)

Theory

Specific energy definition:

E = y + V²/(2g) = y + q²/(2g × y²) [m]

V = q / y q = unit discharge [m²/s]

Fr = V / √(g × y) [dimensionless]

Critical conditions (rectangular channel):

y_c = (q²/g)^1/3 critical depth

E_c = (3/2) × y_c minimum specific energy

Fr_c = 1 critical Froude number

Alternate depth:

For a given specific energy E > E_c and flow rate q, two depths satisfy E = y + q²/(2gy²) — one subcritical (y > y_c) and one supercritical (y < y_c). These are called alternate depths. A hydraulic jump connects the supercritical depth to its sequent (conjugate) depth, not its alternate depth.

E-y diagram key points:

Branch	Depth	Flow type
Upper branch	y > y_c	Subcritical (Fr < 1) — controlled from downstream
Vertex	y = y_c	Critical (Fr = 1) — minimum energy
Lower branch	y < y_c	Supercritical (Fr > 1) — controlled from upstream