modelPipe

Information

Simple Pipe Model

The simple model of the pipe gives possibilities for easy modelling of different conduit: intake race, penstock, tail race, etc. The model assumes incompressible water and inelastic walls since there are only small pressure variations.

Figure: Model for flow through a pipe.

Mass and Momentum Balance

Mass Balance: For incompressible water, the mass in the filled pipe is constant:

$$ \frac{\mathrm{d}m_\mathrm{c}}{\mathrm{d}t} = \dot{m}_\mathrm{c,in} - \dot{m}_\mathrm{c,out} = 0 $$

Momentum Balance: The momentum balance is expressed as:

$$ \frac{\mathrm{d}M_\mathrm{c}}{\mathrm{d}t} = \dot{M}_\mathrm{c,in} - \dot{M}_\mathrm{c,out} + F_\mathrm{p,c} + F_\mathrm{g,c} + F_\mathrm{f,c} $$

where:

• M_c = m_c v_c is the momentum
• F_p,c is the pressure force due to inlet/outlet pressure difference
• F_g,c = m_c g cos θ_c is the gravity force
• F_f,c is the friction force calculated using the Darcy friction factor

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 (information about the speed of wave propagation is not included). Water pressures are shown at the pipe boundaries (inlet and outlet pressure from connectors).

Features

It should be noted that this pipe model provides possibilities for modelling of pipes with both positive and 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.

Friction Specification

Friction is specified via the inherited FrictionSpec base class, which supports pipe roughness, Moody friction factor, and Manning coefficient methods.

Initialization

By default, the pipe provides an initial equation for the flow rate: either der(mdot) = 0 (steady state) or Vdot = Vdot_0. When the pipe is connected to a component that already imposes the flow (e.g., VolumeFlowSource), these initial equations become redundant and may cause an over-determined initialization problem in some tools (e.g., Dymola). Set useInitialFlow = false to disable the initial equation in such cases.

More Information

More info about the pipe model can be found in [Vytvytskyi2017] and [Splavska2017a].

Parameters

Connectors

Components