Pipe Minor Losses

The treatment of minor losses in HEC-RAS pipe networks generally follows the guidance given in the Federal Highway Administration Urban Drainage Design Manual (FHWA, 2013). In HEC-RAS pipe networks, the user can select between the SWE-ELM and Diffusion Wave solvers, and minor losses are handled slightly differently between the tow. The SWE-ELM solver is more robust in accounting for minor losses in the network implicitly due to the inclusion of of the acceleration terms. Losses through smooth pipe transitions (those without junction boxes; Base Area = 0) due to pipe diameter changes and losses resulting from changes in planform pipe network direction are calculated automatically and require no user input. Minor losses at the connection of pipes to junction boxes or access holes (Base Area >0) are specified by the user as entrance and exit loss coefficients at the end of each pipe. Entrance losses and exit losses within the pipe network interior are applied as a fraction of the local pipe velocity head ( $\begin{array}{l}\frac{V^2}{2g}\end{array}$ ). Exit losses at the terminal downstream ends of the pipe network are applied as a fraction of the difference between the velocity head at the end of the pipe and the velocity head in the receiving waters. More information on each type of loss is given below.

The diffusion wave approximation removes the acceleration terms so no losses due to the change in momentum and flow direction will be accounted for automatically. However, the diffusion wave solver does account for losses at bends within a conduit and minor losses at the connection of pipes to junction boxes can specified as entrance and exit loss coefficients.

Entrance and Exit Losses at Junction Boxes or Access Holes

Entrance and exit loss coefficients are specified by the user in the conduit attribute tables and are used in both the diffusion wave approximation and the shallow water equations when the Base Area of the junction is greater than 0. Both entrance and exit loss coefficients are specified at each end of each conduit such that coefficients for reverse flow can be specified differently. The choice between applying the entrance or the exit loss coefficient at each pipe end is made after determining the flow direction. At junctions between conduits, minor losses are applied as a function of the local velocity head:

$\begin{array}{l}\displaystyle H_L = K_L \, \frac{V^2}{2g}\end{array}$

where $\begin{array}{l}K_L\end{array}$ is either the entrance or exit loss coefficient and $\begin{array}{l}V\end{array}$ is the velocity at that point within the pipe.

Angled Inflow Losses at Pipe Junctions

Additional energy losses are present at junctions where inflows come together at an angle. Losses due to the angle of flows at junction are only accounted for in the SWE-ELM solver.

Loss due to angled flows are calculated directly from the advection term in the momentum equation. Depending on the flow direction, velocity is backtracked through the junction for use in the Eulerian-Lagrangian Method of advection discretization. Losses resulting from angled inflows are implicitly taken into account within this method.

Expansion and Contraction Losses

Expansion and contraction losses are applied at smooth pipe transitions (junction Base Area = 0) where the pipe diameter changes. These losses are prescribed as a function of the difference in velocity head at computational faces bracketing the pipe transition.

$\begin{array}{l}\displaystyle H_L=K_{\textrm{ec}}\left|\frac{V_1^2}{2g}-\frac{V_2^2}{2g}\right|\end{array}$

where $\begin{array}{l}K_{\textrm{ec}}\end{array}$ is the expansion or contraction coefficient, depending on the orientation of the pipes and the direction of flow.

Bends within a Conduit

Minor losses at bends located within a section of conduit are computed automatically in diffusion wave and shallow water equations as a function of the local velocity head. The energy loss is applied locally across the mesh cell that contains the bend.

$\begin{array}{l}\displaystyle H_L = 0.0033 \, \alpha \, \frac{V^2}{2g}\end{array}$

where $\begin{array}{l}\alpha\end{array}$ is the bend angle in degrees (FHWA, 2013).

Exit Losses at Outfalls

For losses at the terminal downstream ends of the pipe network, however, minor losses are specified as a function of the difference in local velocity heads:

$\begin{array}{l}\displaystyle H_L = K_L \, \left| \frac{V^2}{2g} - \frac{V_{\textrm{tw}}^2}{2g} \right|\end{array}$

where $\begin{array}{l}V_{\textrm{tw}}\end{array}$ is the tailwater velocity.

Plunging Flow Losses at Junctions

Losses due to plunging flow at junctions are accounted for automatically when using the shallow water equations. When a plunge is occurring at a junction (as shown below) the velocity backtracking is turned off so that momentum from the plunging conduit is not carried into the junction. For more information on plunging flow see Plunging Flow In Pipe Networks.