Introduction¶
This document describes the 1D computational engine for modelling unsteady flows in pipe networks, river networks and estuaries.
The modelling of unsteady flow is based on an implicit, finite difference numerical solution of the one-dimensional shallow water equations (Saint Venant equations). The numerical algorithms provide efficient and accurate solutions in branched and looped pipe and river networks.
The computational scheme is applicable to vertically homogeneous flow conditions. These conditions are found in pipes ranging from small profile collectors for detailed urban drainage and pressurised sewer mains affected by the varying water level at the outlet, to open rivers, channels and flood plains extending from steep rivers to tidal-influenced estuaries.
Both subcritical and supercritical flows are treated by means of the same numerical scheme that adapts to local flow conditions. Flow features such as backwater effects and surcharges are simulated precisely.
Pressurised flow computations are modelled using a narrow vertical extension of closed pipes. Free surface and pressurised flows are thus described with the same numerical scheme, which ensures a smooth and stable transition between the two flow types.
Advanced models describing flow over hydraulic structures including structure control are also included.
The features implemented in the conceptualisation of physical systems enable realistic and reliable simulations of the performance of both existing sewage and river network and those under design.
How To Use this Manual¶
This manual describes the 1D computational engine.
Setting up a model for the 1D engine can be done in MIKE+ or in the MIKE HYDRO River / MIKE 11 setup editor. This is not a manual for either MIKE+ or MIKE HYDRO River / MIKE 11. However, at times it is appropriate to refer to one of these, or to describe how certain things are handled in MIKE+ or MIKE HYDRO River / MIKE 11.
NOTE: As a rule of thump, comments made for MIKE 11 in this manual also apply to MIKE HYDRO River.
Throughout the manual, text that applies to only one product is placed in a product tab. Select the tab for the product you are using:
Text in this tab is relevant only when setting up a model with river components, in MIKE HYDRO River or MIKE 11. If river components are not relevant for you, this text can be omitted.
Text in this tab is relevant only when setting up a model with urban components, in MIKE+ (Collection System). If urban components are not relevant for you, this text can be omitted.
Your choice of product tab applies to every tab on every page of the manual, so you only need to select it once.
Symbols¶
- \(A\) — Without any subscript, it will refer to a flow area \(A_{fl}\)
- \(A_{fl}\) — Flow area, also called cross section area
- \(A_{s}\) — Surface area
- \(b_{s}\) — Storage width, the width of the surface in a cross section
- \(D\) — Water depth at node
- \(d\) — Water depth at grid point
- \(F\) or \(F_{r}\) — Froude number
- \(f\) — Friction factor (in HD context), right hand side (in solver context)
- \(g\) — Gravity
- \(H\) — Water level at a node
- \(h\) — Water level at a grid point
- \(H_{b}\) — Bottom level, lowest point of node. Also called invert level
- \(h_{b}\) — Bottom level, lowest point of cross section
- \(I\) or \(I_{b}\) — Bottom slope
- \(I_f\) — Friction slope
- \(I_h\) — Water level slope
- \(K\) — Conveyance
- \(q\) or \(Q\) — Flux through a grid point
- \(R\) — Hydraulic radius
- \(v\) — Flow velocity at grid point, \(v = \frac{Q}{A}\)
Common terms and definitions that will be used throughout the document¶
The friction slope If is equal to the slope of the energy grade line and is defined as:
Equation: Friction slope computed from shear stress, fluid density, gravitational acceleration, and hydraulic radius.
where:
- t — tangential stress caused by the wall friction, [Nm-2]
- r — density of water, [kgm-3]
- R — hydraulic radius, [m], (= A/P, where P is the wetted parameter).