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Bradshaw Model (Hydraulic Geometry) — Width Calculator

Hydraulic geometry relationship between river width and discharge.

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Width

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Overview

The Bradshaw Model for width characterizes the relationship between a river's discharge and its surface width as it progresses downstream. This power law relationship demonstrates how channel geometry adjusts to accommodate increasing volumes of water, typically showing that width increases as a function of discharge raised to a specific hydraulic exponent.

Symbols

Variables

w = Width, a = Coefficient, Q = Discharge, b = Exponent

Width
Coefficient
Variable
Discharge
Exponent
Variable

Apply it well

When To Use

When to use: Apply this equation when analyzing the downstream hydraulic geometry of a river system in equilibrium. It is specifically used to predict how channel width changes in response to discharge variations across different geographical locations along the same river course.

Why it matters: Understanding this relationship allows geomorphologists and civil engineers to predict flood behavior and design stable river crossings. It provides critical data for environmental management, helping to estimate habitat availability and potential erosion zones as discharge fluctuates.

Avoid these traps

Common Mistakes

  • Using a negative exponent for b.
  • Mixing discharge units between sites.

One free problem

Practice Problem

A river has discharge Q = 50 m³/s. Using w = aQ^b with a = 2.0 and b = 0.5, calculate the channel width w.

Coefficient2
Discharge50 m^3/s
Exponent0.5

Solve for:

Hint: Compute first, then multiply by a.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Leopold, L.B. and Maddock, T. (1953) The Hydraulic Geometry of Stream Channels and Some Physiographic Implications
  2. Waugh, D. (2000) Geography: An Integrated Approach
  3. Wikipedia: Hydraulic geometry
  4. Fluvial Processes in Geomorphology by Luna B. Leopold, M. Gordon Wolman, and John P. Miller, W. H. Freeman, 1964
  5. Geomorphology: A Global Synthesis by Andrew Goudie, Palgrave Macmillan, 2013
  6. Leopold, L. B., & Maddock, T. (1953). The Hydraulic Geometry of Stream Channels and Some Physiographic Implications. U.S.
  7. Wikipedia article 'Hydraulic geometry'
  8. A-Level Geography - Hydrology