GVF Profile Lab
Arrange slope, critical depth, normal depth and the two end depths to reproduce the classical gradually varied flow profiles.
—Current profile
About this model
Scientific basis
For steady one-dimensional flow in a prismatic channel, with hydrostatic pressure and a velocity-distribution coefficient close to one, the gradually varied flow equation is
\[
\frac{dy}{dx}=\frac{S_0-S_f}{1-\mathrm{Fr}^2}
\]
Here S₀ is the bed slope, S_f is the friction slope and Fr is the Froude number. For the rectangular Manning channel used here,
\[
\mathrm{Fr}^2=\frac{Q^2T}{gA^3},
\qquad
S_f=\left(\frac{nQ}{A R^{2/3}}\right)^2.
\]
The sign combinations on either side of normal and critical depth generate the classical profile families. The numerical model solves the equivalent steady energy balance stepwise between sections.
References
- Chow, V. T. (1959). Open-Channel Hydraulics. McGraw-Hill. Classical derivation and M/S/C/H/A profile classification.
- Henderson, F. M. (1966). Open Channel Flow. Macmillan. Classical treatment of gradually varied flow, controls and water-surface computation.
- USACE Hydrologic Engineering Center. HEC-RAS Hydraulic Reference Manual. Modern reference for steady one-dimensional water-surface profiles using the energy equation and Manning friction.