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Water flow in open channels is often measured using hydraulic structures such as weirs, which allow precise calculation of discharge. In a rectangular channel, flow rates are measured using three types of weirs: rectangular sharp-crested, triangular sharp-crested, and broad-crested. The weir head is set at a fixed height above the channel bottom, simplifying calculations and enabling the relationship between depth and flow rate to be analyzed.For the rectangular sharp-crested weir, the flow...
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Related Experiment Video

Updated: May 2, 2026

Visualizing Hyporheic Flow Through Bedforms Using Dye Experiments and Simulation
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Apparent Hack's law in river deltas.

Tian Y Dong1, Lawrence Vulis2, Hongbo Ma3

  • 1School of Earth, Environmental, and Marine Sciences, University of Texas Rio Grande Valley, Edinburg, TX, USA.

Science (New York, N.Y.)
|April 30, 2026
PubMed
Summary
This summary is machine-generated.

River deltas build land through distributary channel networks. A global analysis reveals a universal scaling law for channel length and land area, but local patterns vary, showing both simple and complex delta growth.

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Area of Science:

  • Geomorphology
  • Hydrology
  • Earth System Science

Background:

  • River deltas are critical ecosystems and densely populated regions facing threats from rising sea levels.
  • The relationship between the complex organization of distributary channel networks and the land-building processes they drive is not well understood.

Purpose of the Study:

  • To investigate the scaling relationship between distributary channel networks and land-building processes in river deltas.
  • To identify distinct patterns of deltaic land growth and network organization globally.

Main Methods:

  • Analysis of a global dataset of river delta distributary networks.
  • Application of scaling laws, inspired by Hack's law from tributary networks, to distributary networks and their associated nourishment areas.

Main Results:

  • A consistent scaling relationship was found between distributary channel length and nourishment area across global deltas, mirroring Hack's law.
  • Two distinct local land-building patterns were identified: uniform delta networks adhere to Hack's law, while composite delta networks exhibit a scale break, transitioning growth patterns.

Conclusions:

  • River delta growth exhibits both global simplicity, through a universal scaling law, and local variability in network organization and land-building patterns.
  • Understanding these patterns is crucial for predicting deltaic responses to environmental changes like sea-level rise.