Headloss calculation for inflowing water¶

Water looses energy as it flows into a node. Depending on conditions, this energy loss can be negligibly small, or significant.

Therefore, the 1D engine has an option to fully ignore this energy loss and to set the energy of the water in a node equal to that of the incoming reach (or the weighted average if there are several inlets). Without doubt, this approach proves valuable for some specific situations, particularly for the flow-through manholes with ‘normal’ flow conditions. However, due attention must be paid to cases with high inlet energy levels, e.g. a small pipe with high-velocity flow entering a large basin. In such cases, the energy level of otherwise still water in the basin would be calculated as equal to the energy level of the approaching flow, i.e. much higher than in reality, with erroneous results as a consequence.

If inlet headloss is included in the simulation, then it is calculated in the following way: it is assumed that the water level in the node is equal to the water level in the incoming reaches. The change in energy (head) is then given by the change in water velocity:

\[ \Delta E_{i}~=~\frac{{v_{i}}^{2}-{v_{m}}^{2}}{2g} \]

Equation: Energy head loss at inlet from velocity change between incoming reach and manhole node.

for inlet reach i and the node m.

The velocity in the inlet is known, while the velocity in the node must be calculated:

\[ v = \frac{Q}{A_{fl}} = \frac{Q}{(H - H_b) \cdot D} \]

Equation: Velocity in a manhole node computed from discharge divided by flow area.

where Q is the discharge through the node and \(A_{fl}\) is the flow area in the node. On the right-hand side of equation the velocity in a manhole node computed from discharge divided by flow area, the flow area is calculated as the area of a circular manhole, where H is the water level in the node, \(H_{b}\) is the node bottom level, and D is the node diameter. Note that a uniform horizontal velocity distribution is assumed.