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Bradshaw Model (Hydraulic Geometry) — Velocity Calculator

Hydraulic geometry relationship between river velocity and discharge.

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Velocity

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Overview

The Bradshaw Model for velocity describes the downstream relationship between river discharge and the speed of flow as a power function. It demonstrates that as a river moves towards its mouth and discharge increases, the mean velocity typically increases due to higher hydraulic efficiency and reduced relative bed roughness.

Symbols

Variables

v = Velocity, k = Coefficient, Q = Discharge, m = Exponent

Velocity
m/s
Coefficient
Variable
Discharge
Exponent
Variable

Apply it well

When To Use

When to use: Apply this equation when modeling the longitudinal profile of a river system to understand how flow speed evolves from source to mouth. It is essential for comparative hydrology and when predicting changes in flow dynamics as discharge accumulates in a drainage basin.

Why it matters: This model is crucial for managing flood risks and predicting sediment transport capacity along a river's course. It corrects the common misconception that mountain streams are faster than lowland rivers, showing that increased water volume and channel efficiency usually lead to higher velocities downstream.

Avoid these traps

Common Mistakes

  • Assuming velocity must increase at the same rate as width.
  • Using point velocity rather than mean velocity.

One free problem

Practice Problem

A river has a discharge of 50 m³/s. If the coefficient k is 0.4 and the exponent m is 0.15, calculate the average stream velocity.

Discharge50 m^3/s
Coefficient0.4
Exponent0.15

Solve for:

Hint: Raise the discharge to the power of m before multiplying by k.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Leopold, L. B., & Maddock, T. (1953). The Hydraulic Geometry of Stream Channels and Some Physiographic Implications. U.S.
  2. Wikipedia: Hydraulic geometry
  3. Britannica: River
  4. Leopold, L. B., Wolman, M. G., & Miller, J. P. (1964). Fluvial Processes in Geomorphology. W. H. Freeman.
  5. Knighton, D. (1998). Fluvial Forms and Processes: A New Perspective. Arnold.
  6. Goudie, A. (2013). Encyclopedia of Global Change: Environmental Change and Human Society. Oxford University Press.
  7. David Knighton, "Fluvial Forms and Processes" (2nd ed., 2014)
  8. A-Level Geography - Hydrology