The shear rate is an important variable which is utilized in the rheological models. Vertically averaged models - such as those in HEC-RAS – make assumptions on the vertical profile of the current velocity in order to estimate a vertically-averaged shear rate. Common profiles found in literature include:

  1. Linear (e.g. Bird et al., 1960)
  2. Parabolic (e.g. Julien 1995; Iverson and Denlinger, 2001)

The general formula for the vertically-averaged shear rate is given by:

\dot { \gamma } = \frac{B |V| }{h \cos \varphi \cos\psi }

where |V| is the current velocity magnitude, h is the flow depth, \varphi is the water surface slope, and \psi is the inclination angle of the current velocity direction. The shear rate coefficient B is equal to 2 and 3 for the linear and parabolic profiles, respectively. The parabolic velocity profile was original used in the Quadratic model (O'Brien and Julien 1988), and is the profile currently used in HEC-RAS. The Voellmy (1955) model does not require a shear rate and only utilizes the average velocity for the turbulent-dispersive stress.