Summary

The treatment of minor losses in HEC-RAS pipe networks generally follows the guidance given in the Federal Highway Administration Hydraulic Engineering Circular No 22 (HEC-22) (FHWA, 2024). The primary minor losses computed in HEC-RAS are summarized below:

Entrance / Exit at junctions and outfalls - losses associated with flows entering and exiting a conduit. Computed based on user defined loss coefficients and local conduit velocity head.
Angled flows at junctions - losses associated with the change in flow direction between inflows and outflows at a junction. Computed as a function of angles of inflow pipes relative to the outflow pipes and the entrance losses.
Plunging flows at junctions - losses associated with flows plunging into a junction. Computed as a function of relative plunge height, outflow pipe area and entrance losses.
Bends within conduits - losses at bends within a conduit. Computed as a function of velocity head and the angle of the bend.

The minor losses at junctions or access holes are often the most impactful energy losses in a system. In HEC-RAS, losses due to angled flows and plunging flows are accounted for automatically at junctions that have entrance loss coefficients defined on the outflow conduits. This is because the computation of angled losses and plunging losses are a function of the entrance losses at a junction, as described in HEC-22. If no entrance loss is defined on the outflow conduit, angled/plunging losses are zero (not applied).

Minor Loss Changes

In previous beta versions, entrance and exit losses were only applied at junctions that had Base Areas > 0. In HEC-RAS version 7.0 entrance and exit losses are applied regardless of junction Base Area.

The minor loss components described here are applied in both the shallow water equations and the diffusion wave equations. However, the shallow water equations calculate more accurate minor losses due to the inclusion of the acceleration terms and the accuracy of resulting velocities.

Minor Loss Components

The section below describes in detail how each of the minor loss components are computed in Pipe Networks.

Entrance and Exit Losses at Junctions

At junctions between conduits, minor losses are applied as a function of the local velocity head in the conduit. Entrance and exit loss coefficients are specified by the user in the conduit attribute tables and describe losses associated with flow entering a conduit from a junction or exiting a conduit into a junction. 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 conduit end is made after determining the flow direction.

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

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.

Exit Losses at Outfalls

For losses at the terminal downstream ends of the pipe network, exit 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.

Angled Flow Losses at Junctions

Losses are computed automatically at junctions where inflows come together at an angle. Following the HEC-22 (FHWA, 2024) approach, a weighted flow is computed from the product of each conduit's angle and flow:

$\begin{array}{l}\displaystyle \theta_w = \frac{\sum\left(Q_j\,\theta_j\right)}{\sum Q_j}\end{array}$

Where:
$\begin{array}{l}Q_j\end{array}$ = Contributing inflow from conduit
$\begin{array}{l}\theta_j\end{array}$ = Angle measured from the outlet conduit (180 degrees is straight)

Flow Angle Measurement At Access Holes (FHWA, 2024)

Then an angled inflow coefficient is calculated:

$\begin{array}{l}\displaystyle C_{\theta} = 4.5\,\frac{\sum Q_j}{Q_o}\,\cos\left(\frac{\theta_w}{2}\right)\end{array}$

Where:
$\begin{array}{l}Q_o\end{array}$ = Flow in the outflow conduit

Finally the angled loss coefficient is multiplied by the entrance loss to determine the angled flow loss which is applied at the first face in the outflow conduit.

$\begin{array}{l}\displaystyle H_{\theta}=C_{\theta}\left(H_{Ent})\end{array}$

Plunging Flow Losses at Junctions

Plunging losses are computed automatically where conduit flows are plunging into a junction. Plunging losses are computed using the Federal Highway Administration's method in HEC-22 (FHWA, 2024). First, a relative plunge height is computed:

$\begin{array}{l}\displaystyle h_{k}=\frac{z_{k}-H_{i}}{D_{o}}\end{array}$

Where:
$\begin{array}{l}z_k\end{array}$ = invert of the inflow pipe
$\begin{array}{l}H_{i}\end{array}$ = junction hydraulic grade at the start of the timestep
$\begin{array}{l}D_o\end{array}$ = outflow pipe rise

Per HEC-22, the relative plunge height $\begin{array}{l}\mathrm{h_k}\end{array}$ is capped at 10 to prevent the plunge loss from growing unbounded. Then a plunging coefficient $\begin{array}{l}\mathrm{C_p}\end{array}$ is computed for the junction and multiplied by the entrance loss to determine the plunge loss.

$\begin{array}{l}\displaystyle C_P = \frac{\sum \left(Q_k\,h_k\right)}{Q_o}\end{array}$

Where:
$\begin{array}{l}Q_o\end{array}$ = Flow in the outflow conduit

$\begin{array}{l}\displaystyle H_{p}=C_{p}\left(H_{Ent})\right.\end{array}$

The plunge loss is applied at the first face of the outflow conduit. For details on how the plunge itself is handled in the hydraulic computations see the Plunging Flow in Pipe Systems.

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 pipe 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 and is always less than 180 degrees (FHWA, 2024).

References:

Federal Highway Administration, (FHWA). 2024. Urban Drainage Design Manual. Hydraulic Engineering Circular No. 22, 4th edition. Publication FHWA-HIF-24-006.

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Pipe Minor Losses