I lack the specific experience on this subject in the field. The hydraulic radius is going to decrease in a braided or alluvial fan, because the wetted perimeter increases due to the multiple small shallow channels. The cross sectional areas of the individual channels might be fairly similar to the single thread or meandering channel, or even somewhat reduced as the channel capacity reduces with excess sediment, but the real reason of R reduction is the additive widths, even though shallow, increase the wetted perimeter. In an actively changing braided channel or delta system, the data collected may also be somewhat unstable. There may be instances or circumstances where sediment loading declines and the braided system begins to rechannelize and entrench, causing the hydraulic radius to increase As some of the braided segments loose connectivity. I would assume HEC RAS or some of the other modeling tools might help. I cannot remember if the Rivermorph software would evaluate this if you entered the braided channel cross section in question, but it might be worth exploring if this cross sectional detail of unstable channels through time can be measured and inputted into their software to develop a continuing data base.

I assumed your cross sections use a total station or laser level, so you can get all the channel detail. With a delta, I don’t know if one would use a straight cross section, or a topographic cross section, as you mentioned the convex nature of the sediment buildup in the center of the delta and tendency for slope drop off along the edges as less sediment is delivered and aggradation. Usually a stream cross section is perpendicular to the channel, and best to be perpendicular to valley as part of the consideration, and measure the channel to include its floodplain. But I can visualize in braided, meandering systems, there could be some braid channels oriented to the valley form direction, and others could be angled or even perpendicular to the valley direction. If one runs a linear braided channel cross section across a valley, may need to adjust braid channel measurements to be perpendicular to each braid channel. Otherwise, the cross section and wetted perimeter for some of the braid channels angled to the valley could be larger than appropriate. Sometimes, a degree of logic may be needed when channel form is atypical.

Hi Mr Niraj bal Tamang, can you send me your case? I mean share with me view of convex upwards cross section.

Davronjon Allayorov Thank you for your reply. Here is one of the cross section. The blue line represents original channel. The green line represents the new bed level after sediment deposition. I want to calculate the hydraulic radius for the green line.

William F. Hansen Thank you for your answer. I am still a bit confused on this. I have attached a sample cross section with similar case. I hope it will be easier to understand now.

Where is the line of water surface? You know Hydraulic radius is equal to cross section area divide watted perimeter, you can use lenght of the green line plus lenght of both side as a watted perimeter. But if in your case I think there is another option depens on releative width.

In your question, you mentioned a braided multiple channel. The drawing shows one channel that has aggraded and been basically buried. A cross section should continue fully across the floodplain, so as one of the braided channel fills, other channels will become established. As mentioned by Dr. Allayorou, if all the braided channels fill under extreme sediment load, you might have a temporary condition where the full width of the floodplain would express the wetted perimeter including the wetted banks. If the convex nature becomes great enough in the center so it it exposed at bankfull, the active channel essentially splits, so there are two or more channels to assess for wetted perimeter. Deep fresh alluvium could be potentially hazardous to survey by wading, so have a tether rope just in case. The original blue line channel is gone, and that becomes the problem in trying to remeasure as the changes can occur in both flooding and periods of flow where the channel(s) erode and continue to adjust back into the unstable floodplain.

Calculating the hydraulic radius for a multithread braided channel scenario with a sediment-filled convex upwards cross section can be challenging, especially if the flow path keeps changing due to the braiding of the channel. In general, the hydraulic radius is defined as the ratio of the cross-sectional area of flow to the wetted perimeter.

However, in the case of a sediment-filled convex upwards cross section, the wetted perimeter is not well-defined, since the flow path can change as the channel braids. Additionally, the average depth may not accurately represent the cross-sectional area of flow, especially if the channel is highly variable in shape.

One approach to calculating the hydraulic radius in this scenario is to use numerical modeling techniques, such as computational fluid dynamics (CFD), to simulate the flow and determine the cross-sectional area of flow and the wetted perimeter at different points in the channel. This can provide a more accurate representation of the hydraulic radius at any given location along the channel.

Alternatively, you may be able to make some simplifying assumptions to estimate the hydraulic radius. For example, you could assume that the wetted perimeter is equal to the channel width, since the flow is constrained by the sediment and can only flow in a narrow channel. In this case, the hydraulic radius would be equal to half the channel width. However, this assumption may not be accurate in all cases, especially if the channel is highly braided and the width varies significantly along its length.

Overall, calculating the hydraulic radius for a multithread braided channel scenario with a sediment-filled convex upwards cross section can be challenging, and it may be necessary to use numerical modeling or make simplifying assumptions to estimate the hydraulic radius.

Excellent Documentary [1] about the Canal du Midi in France (In French). Connecting the Atlantic to the Mediterranean by a large canal of more than 300 km is an idea that dates back to Antiquity. It was not until the 17th century and the reign of Louis XIV that this project came to fruition. It will be the Sun King's biggest construction site after Versailles and its digging will require all kinds of technological feats to span hills and rivers. The Canal du Midi was completed in 1681 after 12 years of work. Today listed as a UNESCO World Heritage Site, it is one of the oldest canals in Europe still in operation. (Own translation)

[1] The incredible story of the Canal du Midi: The project of Louis XIV - Complete documentary - AMP. “Canal du Midi, a revealed heritage” Director: Emmanuel Amara. https://www.youtube.com/watch?v=x4vmKsnxccA

See Also:

https://www.researchgate.net/post/Forum_for_Enthusiasts_of_Ancient_Hydrology_and_Old_Hydraulics