The simple model of the pipe gives possibilities for easy modelling of different conduit: intake race, penstock, tail race, etc.
This model is described by the momentum differential equation, which depends
on pressure drop through the pipe together with friction and gravity forces.
The main defined variable is volumetric flow rate Vdot.
In this pipe model, the flow rate changes simultaneously in the whole pipe (an information about the speed of wave propagation is not included here). Water pressures can be shown just in the boundaries of pipe (inlet and outlet pressure from connectors).
It should be noted that this pipe model provides possibilities for modelling of pipes with both a positive and a negative slopes (positive or negative height difference).
If the pipe is slightly tapered then this can be taken into account by adjusting
K_c based on your taper geometry: 0.05–0.15 for gentle cones,
up to 0.6 for sharp contractions.
More info about the pipe model can be found in [Vytvytskyi2017] and [Splavska2017a].
Updated formulation for non-equal inlet- and outlet diameter.