Hydraulics · sample calcsheet · 6 pages
Water spilling over a dam races down the chute and enters the stilling basin shallow and fast; a hydraulic jump turns it back into deep, slow flow and destroys most of its energy on the way. This sheet finds the discharge over the ogee crest, steps the flow down the spillway in three reaches to estimate the friction loss along it (local losses at the crest and the toe are neglected), solving each reach's depth with root(), then sizes the jump: the sequent depth, the energy head destroyed and the power the basin must absorb. Crest, chute and basin are rectangular and of one width.
The ogee crest acts as a weir: the discharge grows with the head over the crest to the power 3/2. The flow passes through the critical depth close to the crest, which is the depth and velocity the first reach starts from.
The chute is split into three reaches of equal length. In each, the energy equation is written between its two ends — bed level, plus the depth measured normal to the bed (y·cos θ), plus the velocity head — with the Darcy–Weisbach friction loss taken at the mean of the friction slopes at the two ends: the standard-step method. That loss depends on the unknown downstream depth, so each reach's balance is solved implicitly with root().
Collected as vectors: the depth and velocity at the end of each reach, and the loss in each. The flow keeps accelerating down the chute, so most of the loss falls in the last reach — judging the whole chute by its toe velocity alone would roughly double the total.
The toe depth and velocity are the jump's upstream conditions. For a rectangular channel the momentum equation gives the depth after the jump from the upstream Froude number (the Bélanger equation); a jump forms only if the entering flow is supercritical.
