Regime Method

The regime method for stable channel design originated from irrigation design studies in Pakistan and India, and is based on a set of empirically derived equations, which typically solve for depth, width, and slope as a function of discharge and grain size.

1)	$\begin{array}{l}\displaystyle D,B,S=f(Q,d_{50})\end{array}$

Symbol	Description	Units
$\begin{array}{l}D\end{array}$	Depth
$\begin{array}{l}B\end{array}$	Channel width
$\begin{array}{l}S\end{array}$	Slope
$\begin{array}{l}Q\end{array}$	Discharge
$\begin{array}{l}D_{50}\end{array}$	median grain size

To be considered in regime, or equilibrium, transport of sediments is allowed as long as there is no net annual scour or deposition in the channel. The regime method is applicable to large-scale irrigation systems with a wide range of discharges of silts and find sands. Because regime equations are purely empirical and based on field observations, the regime method can only be used within its validity range (Van Rijn, 1993).

The Blench Regime Method (Blench, 1970) is used in HEC-RAS. These equations are intended to be used with channels that have sand beds. In addition to the typical independent variables of discharge and grain size, the Blench method requires an inflowing sediment concentration and some information about the bank composition. The three regime equations are:

2)	$\begin{array}{l}\displaystyle \displaystyle B= \left( \frac{F_B Q}{F_S} \right) ^{0.5}\end{array}$

3)	$\begin{array}{l}\displaystyle \displaystyle D= \left( \frac{F_SQ}{F^2_B} \right) ^{\frac{1}{3}}\end{array}$

4)	$\begin{array}{l}\displaystyle \displaystyle S= \frac{F^{0.875}_B}{\frac{3.63g}{\nu ^{0.25}} B^{0.25} D^{0.125} \left( 1+ \frac{C}{2330} \right)}\end{array}$

Symbol	Description	Units
$\begin{array}{l}D\end{array}$	Channel depth
$\begin{array}{l}B\end{array}$	Channel width
$\begin{array}{l}S\end{array}$	Channel slope
$\begin{array}{l}Q\end{array}$	Channel forming discharge
$\begin{array}{l}d_{50}\end{array}$	Median grain size of bed material
$\begin{array}{l}C\end{array}$	Bed material sediment concentration
$\begin{array}{l}\nu\end{array}$	Kinematic viscosity
$\begin{array}{l}F_B\end{array}$	Bed factor
$\begin{array}{l}F_S\end{array}$	Side factor

The bed factor can be determined by the following equation:

5)	$\begin{array}{l}\displaystyle F_B =1.9 \sqrt{d_{50}}\end{array}$

Blench suggests the following values be used for the side factor:

_{$\begin{array}{l}F_S\end{array}$} = 0.1, for friable banks
_{$\begin{array}{l}F_S\end{array}$} = 0.2, for silty, clayey, loamey banks
_{$\begin{array}{l}F_S\end{array}$} = 0.3, for tough clayey banks

The Blench regime method is applicable only to straight reaches with beds of silt to fine sand. In addition, Blench suggests that the regime equations be applied only under the following circumstances:

Sides behave as if hydraulically smooth (i.e. friction due only to viscous forces).
Bed width exceeds three times the depth.
Side slopes are consistent with those of a cohesive nature.
Discharges are steady.
Sediment load is steady.
Bed load is non-cohesive, and moves in dune formation.
Subcritical flow.
Sediment size is small compared with the depth of water.
Regime has been achieved by the channel.

These circumstances seem very confining, and in reality, no one channel or canal can claim to behave strictly in this manner. However, if the channel can be adequately approximated by these conditions, without deviating significantly from its true nature, the regime equations may be applicable. At a minimum, the Blench Regime method is a quick way of obtaining "ball-park" figures for results.