Open-Channel Specific Energy and Alternate Depth

E = y + q^2/(2 g y^2) is the flow energy measured from the bed, and for one discharge the same E passes at two alternate depths - a deep tranquil one and a shallow shooting one - that meet at the critical depth where the energy bottoms out at Ec = 1.5 yc. A 10 ft channel at 100 cfs and a 3 ft depth carries 3.17 ft of energy (Fr 0.34, subcritical); that same energy also passes at 0.81 ft (supercritical), and the minimum is 2.19 ft at the 1.46 ft critical depth. The two depths share their energy with no loss, unlike the hydraulic jump's sequent depth, which dissipates it. Rectangular, prismatic channel. A design aid; the engineer of record governs.

q = Q/b; V = q/y; E = y + q^2/(2 g y^2); yc = (q^2/g)^(1/3); Ec = 1.5 yc; Fr = V/sqrt(g y); y_alt = ((E - y) + sqrt((E - y)^2 + 2 q^2/(g y)))/2.

The open-channel specific-energy relation E = y + q^2/(2 g y^2), the rectangular critical depth yc = (q^2/g)^(1/3) with minimum specific energy Ec = 1.5 yc, and the alternate depth sharing the same E, as compiled in Chow's Open-Channel Hydraulics, by name.

The specific-energy relation, the critical-depth and minimum-energy results, and the alternate-depth (energy conjugate) are public results in the standard open-channel-hydraulics references.

Estimate. AHJ and licensed professional govern.

Field names used by the API: b_ft, q_cfs, y_ft, e_ft, yc_ft, ec_ft, y_alt_ft

• Specific energy E = y + q^2/(2 g y^2) is the flow energy above the channel bed for the unit discharge q = Q/bChow open-channel hydraulics
• Alternate depth the second positive root of y^3 - E y^2 + q^2/(2g) = 0 is the energy conjugate, sharing E with no loss (not the momentum sequent depth of a jump)Chow open-channel hydraulics
• Critical depth yc = (q^2/g)^(1/3) is where E is minimum at Ec = 1.5 yc; subcritical above yc, supercritical belowChow open-channel hydraulics