Bradshaw Model (Hydraulic Geometry) — Depth Calculator

Formula first

Overview

The Bradshaw Model for depth is a power function used in fluvial geomorphology to relate water depth to the volume of discharge moving through a channel. It forms part of the hydraulic geometry framework, illustrating how river channels typically become deeper as they progress downstream and accumulate more water.

Symbols

Variables

d = Depth, c = Coefficient, Q = Discharge, f = Exponent

Apply it well

When To Use

When to use: Apply this equation when predicting how channel depth adjusts to downstream increases in discharge or during temporal variations at a single cross-section. It is specifically useful for modeling alluvial rivers where the channel boundary is adjustable by the flow.

Why it matters: Accurately predicting depth is vital for engineering infrastructure like bridges and flood defenses to ensure they withstand high-flow events. It also helps environmental scientists assess the suitability of a river reach for various fish species and aquatic vegetation.

Avoid these traps

Common Mistakes

• Confusing coefficient c with exponent f.
• Using discharge from different measurement methods.

One free problem

Practice Problem

A river has discharge Q = 50 m³/s. Using d = cQ^f with c = 0.3 and f = 0.4, calculate the depth d (m).

Solve for: $d$

Hint: Compute $Q^f$ then multiply by c.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. Leopold, L. B., Wolman, M. G., & Miller, J. P. (1964). Fluvial Processes in Geomorphology. W. H. Freeman and Company.
2. Wikipedia: Hydraulic geometry
3. Wikipedia: Hydraulic geometry (geomorphology)
4. Leopold, Luna B., M. Gordon Wolman, and John P. Miller. "Fluvial Processes in Geomorphology." W. H. Freeman, 1964.
5. Ritter, Dale F., R. Craig Kochel, and Jerry R. Miller. "Process Geomorphology." Waveland Press, 2011.
6. A-Level Geography - Hydrology