How can you model transient events in a sewer force main discharging to a manhole (gravity system)?
The main difference in modeling a sewer force main and a potable water system is how to approximate the downstream connection point to the gravity system. The wet well element in the sewer system would be modeled as a tank or reservoir. Everything else is essentially the same as a normal potable water pump model.If the sewer force main is discharging to a manhole that is submerged/surcharged, you may be able to approximate the downstream end of the system using a reservoir, with elevation set to the hydraulic grade in the submerged manhole.If the sewer force main is discharging to a manhole that is not submerged, you should use the Discharge to Atmosphere element. You would need to decide how to compute the headloss through the pipe outlet. This is done with the "Pressure Drop (Typical)" field. You can estimate this headloss with the following equation:
headloss = k*v^2/2g,
where k is set to 1, v is the flow velocity and g is the acceleration due to gravity.
Alternatively, if the outlet orifice is smaller than the pipe diameter you might want to use the orifice equation:
V = C.(2g.headloss)^0.5.
However in most cases, the outlet orifice would be the same as the pipe diameter.
These equations are very similar to each other. You can still expect to see some reflection of waves from an discharge/orifice to atmosphere element, because it still takes some time for flows through this orifice to reach a steady state. The reflection is similar to that which occurs in a pipe contraction.If you have high points between the pump station and the downstream gravity main, you may need to utilize the air valve element in order for the pump to 'see' the high point and add enough head to overcome it. See the following TechNote for more details on this: Modeling Force Mains with Air Valves in SewerCAD (GVF-Convex solver)
If you have an obstruction blocking the end of the force main that discharges into the gravity main (figure "A" below) you can use the discharge-to-atmosphere element, with its "Flow (Typical)" and "Pressure Drop (Typical)" values adjusted accordingly to account for the restriction. You could use the orifice equation to determine the head necessary to "push" a given flow through the blocked opening. This would still assume that the outflow discharges to atmospheric conditions (i.e., free discharge).
If the blockage is at the start or upstream end of the gravity pipe that leaves the manhole, determine if the water level would rise in the manhole to the point where it acts as a tailwater on the force main discharge (figure "B" below) or if it would result in the water level rising to the point where it only blocks part of the force main discharge (figure "C" below)
If the force main outflow is submerged (figure B), you could use the reservoir element with elevation set to the water surface elevation to represent the boundary condition. Any transient waves would reflect accordingly since this would act similar to a pond. You would need to consider if this boundary HGL would remain constant for the duration of the transient simulation, or if it might rise or fall. You might make a conservative assumption there for the purposes of simplicity.
In the case of Figure C where the downstream obstruction causes a partial submerging of the force main discharge, you may need to consider if a transient wave would reflect like an open discharge (use a Discharge to Atmosphere) or as a water source HGL that can accept and provide mass, such as a reservoir). Consider trying it both ways to test the sensitivity of the transient response.
Figure "D" below represents the obstruction on the inside the pressure pipe, with the discharge into the manhole still open. In this case, you could model the obstruction as a headloss using a valve such as a TCV, or with the Orifice Between Pipes element. A Discharge to Atmosphere would then be used immediately downstream of it to model the free discharge.
Modeling Reference - Discharge to Atmosphere
Can the storm-sewer products perform a transient analysis in the sewer force mains?