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Depth variable resistance number

Depth-variable resistance number

The engine accepts a specification of a non-linear variation of the resistance number, based on a relative water depth. Three parameters define the resistance number variation: a bottom value, a full flow value and a non-linear exponent. Intermediate values are calculated by the expression, here for Manning’s M:

\[ M_{a c t}=M_{b o t}+(M_{t o p}-M_{b o t})\cdot\left(\frac{y}{D}\right)^{e x p} \]

Equation: Depth-dependent Manning resistance number interpolated between bottom and full-flow values using a nonlinear exponent.

where:

Mact            =   calculated resistance number, Mbot, Mtop            =   resistance numbers at bottom/top of cross section, exp      =   variation exponent, y      =   the current water depth in the cross section D      =   Height of cross section.

The formula is used for relative depths h/D in the interval 0.0 - 1.0. For relative depth > 1.0 the actual value is set to the Mtop value.

Relative variation of the Manning number with relative depth

Figure: Relative variation of the Manning number with relative depth.

The variation between Mbot and Mtop is controlled by the “variation Exponent”. The variation of the resistance number in relative terms is illustrated in the relative variation of the Manning number with relative depth.

In MIKE+ (Collection System), the Manning number variation is specified through the ASCII file *.ADP. The specified Manning numbers in the *.ADP file must follow the selected option for the Manning number convention. Syntax of the format of the *.ADP files must be as shown in the 'DHIAPP.INI and *.ADP Reference Manual'.

The lines of the *.ADP file related to the Manning number variation may be easily compiled by copy-and-paste operations from the MOUSE650.OUT file. This ASCII file is generated by every computation with the MOUSE Pipe Flow Model.

Before using the *.ADP file, the Manning number parameters for the selected lines must be modified, i.e. values for bottom and top of pipe Manning numbers and possibly the variation exponent must be adjusted for the pipes or canals where varying Manning numbers are to be used.