Hydraulic Jump

Downstream conditions for a rectangular concrete channel (b = 10 ft) are forcing a hydraulic jump. If Q = 100 cfs and the upstream Froude number is 2.5, find the horsepower lost in the jump. Assume steady flow.

The Froude number is defined as

where V = Q/A = Q/yb

Rearranging the equation to yield

The upstream water depth and velocity are determined as follows:

Using the following equation derived from the conservation of momentum, the depth after the jump can be calculated (for rectangular channel only):

V₁y₁ = V₂y₂ for steady flow, thus

The dissipation head loss across the jump is given by (assuming flat bottom channel, i.e., Δz = 0)

Using the sequent depth relationship for rectangular channel

     
then
     

  Power dissipated = ρgQh_f
                            = (62.4 lb/ft³)(100 cfs)(0.57265 ft)
                            = 3,573 lb-ft/s

Since 1 hp = 550 ft-lb/s,

  Power dissipated = 3,573/550 = 6.5 hp