General Flow Conditions

This page is a placeholder for information about general flow conditions and boundary conditions in MIKE 1D structures.

In this section, we discuss general aspects that apply to all structures.

Zero flow

In general, if the water level on both sides of a structure are below the invert level of the structure, or the water levels upstream and downstream of the structure are equal, then the flow over the structure will be zero. Many of the 1D structures can have an associated valve. If the valve is closed, then the flow over the structure will also be zero.

Drowned flow

If the flow on either side of the structure is in the same state as over the structure itself, i.e. both subcritical or both supercritical, then the flow across the structure will be drowned flow. For example, the discharge over a simple broad crested weir with constant width b, the drowned flow is generally given by:

\[ Q = \mu b (h_1 - Z_c)(h_1 - h_2)^{1/2} \]

Equation: Drowned flow discharge over broad-crested weir as function of upstream and downstream heads.

where m is the weir discharge coefficient, h₁ and h₂ the upstream and downstream water levels respective, and Z_c the weir crest elevation.

Free overflow

Free overflow occurs when the water levels at both sides of a structure are such that the system seeks to deliver the maximum discharge for a given energy head at the upstream side of the structure. This leads to critical flow at (or very near to) the most narrow section (called the control section).

In the case of free overflow, the discharge is independent of the downstream water level, i.e. upstream controlled. In principle the discharge can be computed from the condition that the flow is critical at the control section for the given upstream energy head.

Several factors influence the actual free overflow discharge through a structure:

• the section where critical flow occurs is often located downstream of the most narrow section, especially for well designed spillways
• the velocity is not distributed uniformly over the cross section, thus the critical discharge is reduced
• the water level is not constant over the cross section, especially in the case of an irregular section

River (MIKE 11 / MIKE HYDRO)

In MIKE 11, the critical discharge is corrected with a coefficient, a_c, (in the Headloss Factors box) in an attempt to account for the three factors above. This gives the real discharge:

\[ Q = \alpha_c Q_c \]

Equation: Critical discharge corrected by calibration factor to account for energy losses and scale effects.

where Q_c is the critical discharge. Free overflow is modelled on the basis of a relationship between the discharge and the upstream water level. This relationship is generated automatically by MIKE 11 for Broad Crested Weirs and Culverts QH Relations Calculated. In the case of user-defined structures (i.e. Special Weirs and Culverts) the specified QH relation is applied. For the remaining structure types, the critical discharge is computed during the simulation.

Contraction and expansion losses

Broad Crested Weir, Special Weir and Culverts use an energy headloss formulation. These headlosses are functions of the coefficients z_in and z_out and the ratios of the structure area and the cross section areas in the immediately adjacent reach.

IMPORTANT! During pre-processing of QH-relation in Broad Crested Weirs, the ratio of structure area and river cross section area is used to compute the QH-relation. This requires that the cross section area of the reach is always greater than that at the structure. An error message will appear in case the weir area is larger than the up- or downstream cross section area, as it is not possible to establish the QH-relation for free overflow. To correct this, check cross sections and weir geometry. The values of  z_in and z_out are typically 0.5 and 1.0, respectively.

River (MIKE 11 / MIKE HYDRO)

In MIKE 11, the coefficients z_in and z_out are specified in the Headloss Factors box.

See Appendix A.2.4 for details of how energy headlosses are calculated for Broad Crested Weir, Special Weir and Culverts.

Composite structures

Several structures can be defined on the same q-grid point. The total discharge across the combined structures (also called a composite structure) is calculated by iteration until a stable flow is achieved.

During the iteration, the energy headloss of the structures is modified; thus, only structures that apply an energy description are modified in the iteration process. These include Special Weirs, Culverts and Broad Crested Weirs. If none of these structures are present in a composite structure, then no iterations are performed.

External structures with reservoir

River (MIKE 11 / MIKE HYDRO)Urban (MIKE+)

MIKE 11 has the option of specifying a structure as external, meaning that downstream, the structure is not connected to the network. If water flows across the structure, then it runs out of the network.

If a reservoir is attached to the external structure, then water is collected in a reservoir downstream of the structure. The downstream water level is given by the water level in the reservoir which is determined by the reservoir geometry. Based on the upstream and downstream water levels the structure can allow the water to run out of the reservoir and back into the network.

The reservoir geometry is specified by a table which can either contain the reservoir surface area as a function of water level or the reservoir volume as a function of water level.

External structures with a reservoir are equivalent to a structure with a downstream basin which is only connected to the structure, where the basin has the exact same geometry as the reservoir.