Why Slope in HEC-14 Riprap Calculator?

06 April 2018


I was wondering how the riprap apron design values are calculated since they seem to include the slope value which does not appear in the HEC-14 equation from Fletcher and Grace (1972).



Plainwater response:

The culvert slope is accounted for implicitly through the normal depth, when flow is supercritical. The culvert diameter is adjusted (as shown below), which results in the median rock diameter being adjusted for slope.

The following equation (Fletcher and Grace, 1972) is recommended for circular culverts:

D50 = 0.2⋅D(Q/(√g⋅D2.5))4/3(D/TW) (10.4)


  • D50 = riprap size, m (ft)
  • Q = design discharge, m3/s (ft3/s)
  • D = culvert diameter (circular), m (ft)
  • TW = tailwater depth, m (ft)
  • g = acceleration due to gravity, 9.81 m/s2 (32.2 ft/s2)

Tailwater depth for Equation 10.4 should be limited to between 0.4D and 1.0D. If tailwater is unknown, use 0.4D.

Whenever the flow is supercritical in the culvert, the culvert diameter is adjusted as follows:

D’ = (D + yn)/2 (10.5)


  • D’ = adjusted culvert rise, m (ft)
  • yn = normal (supercritical) depth in the culvert, m (ft)



Great Site!

02 April 2018

I just happened across your site while designing some rock slope protection for a stream restoration project in the Bay Area. I work for a consulting firm called FlowWest (www.flowwest.com). You should update the about site with your info and get some credit!



Plainwater response:


Thanks for the compliments!

I started this site about a year ago, for my own personal benefit, as I was tired of trying to remember where to find relevant online information quickly. I am a practicing Civil Engineer in the San Francisco Bay Area, California, specializing in water resources, with some work in general site development, grading and structural design. I also have some experience in the Caribbean and Russia.

I see your company is also in the San Francisco Bay Area. Your website looks great and your staff look like they are in tune with company objectives. The projects you work in are quite challenging, but important, in the Bay Area. I hope the entire world will one day undertake such projects.

Please let me know if there is anything specific you would like me to address on this website,