The treatment of minor losses in RAS pipe systems generally follows the guidance given in the Federal Highway Administration Urban Drainage Design Manual (FHWA, 2013). Losses through smooth pipe transitions (those without junction boxes) 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 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 (\frac{V^2}{2g}). 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.
Losses Through Pipe Bends
Minor losses at bends located within a section of pipe are computed automatically as a function of the local velocity head
|
H_L = 0.0033 \, \alpha \, \frac{V^2}{2g} |
where \alpha is the bend angle in degrees (FHWA, 2013).
Expansion and Contraction Losses
Expansion and contraction losses are applied at smooth pipe transitions 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.
|
H_L=K_{\textrm{ec}}\left|\frac{V_1^2}{2g}-\frac{V_2^2}{2g}\right| |
where K_{\textrm{ec}} is the expansion or contraction coefficient, depending on the orientation of the pipes and the direction of flow.
Angled Inflow Losses at Pipe Junctions
Additional energy losses are present at pipe junctions where inflows come together at an angle.

In these cases, the losses are calculated directly from the advection term in the momentum equation, and no minor loss terms are prescribed. 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.
Entrance and Exit Losses at Junction Boxes
Entrance and exit loss coefficients are specified by the user in the pipe conduit input shapefiles. Both entrance and exit loss coefficients are specified at each end of each pipe section. The choice between applying the entrance or the exit loss coefficient at each pipe end is made after determining the flow direction. In most situations, minor losses are applied as a function of the local velocity head:
|
H_L = K_L \, \frac{V^2}{2g} |
where K_L is either the entrance or exit loss coefficient and V is the velocity at that point within the pipe.
For losses at the terminal downstream ends of the pipe system, however, minor losses are specified as a function of the difference in local velocity heads:
|
H_L = K_L \, \left| \frac{V^2}{2g} - \frac{V_{\textrm{tw}}^2}{2g} \right| |
where V_{\textrm{tw}} is the tailwater velocity.