IncompressiblePipeAPI

CentrifugalPump(; name, D, ω, c_0, c_1, ρ)

Component: CentrifugalPump

Ideal H-Q Characteristic curves of Centrifugal Pumps:

\[H_t=\frac{(r\omega)^2}{g}-\frac{\omega \cot\beta }{2\pi bg}Q=c_0\omega^2-c_1\omega Q=a_0-a_1Q\]

Parameters:

• D: [m] Diameter of pipe
• ω: [r/min] rotary speed
• c_0: parameter in H-Q Characteristic curves
• c_1: parameter in H-Q Characteristic curves

Connectors:

• in: Inlet of pump
• out: Outlet of pump

ElbowPipe(; name, D, K, ρ, zin, zout)

Component: ElbowPipe(pipe with fixed local resistance loss coefficient f)

Energy conservation equation in the form of Bernoulli Equation between two ports:

\[\frac{p_{in}}{\rho g} +\frac{8q_{in}^{2}}{\pi^2D^4g} + z_{in}= \frac{p_{out}}{\rho g} +\frac{8q_{out}^{2}}{\pi^2D^4g} + z_{out}+h_f+h_m\]

Parameters:

• D: [m] Diameter of pipe
• K: Local resistance loss coefficient

Connectors:

• in: Inlet of pipe
• out: Outlet of pipe

Arguments:

• zin: [m] The height of inlet port
• zout: [m] The height of outlet port
• ρ: [`m³/kg] The density of fluid passing the port

PipeNode(; name, z)

A pipe port(inlet or outlet) in an pipe network.

States:

• p(t): [Pa] The pressure at this port
• q(t): [m³/s] The volume flow passing through this port

Parameters:

• z: [m] The hight of port, expressing potential energy

SimplePipe(; name, L, D, f, ρ, zin, zout, K_inside)

Component: SimplePipe(pipe with fixed friction factor f)

Energy conservation equation in the form of Bernoulli Equation between two ports:

\[\frac{p_{in}}{\rho g} +\frac{8q_{in}^{2}}{\pi^2D^4g} + z_{in}= \frac{p_{out}}{\rho g} +\frac{8q_{out}^{2}}{\pi^2D^4g} + z_{out}+h_f+h_m\]

Parameters:

• D: [m] Diameter of pipe
• L: [m] Length of pipe
• f: Friction factor
• K_inside: Coefficient of local resistance loss inside the pipe

Connectors:

• in: Inlet of pipe
• out: Outlet of pipe

Arguments:

• zin: [m] The height of inlet port
• zout: [m] The height of outlet port
• ρ: [`m³/kg] The density of fluid passing the port

Sink_P(; name, p)

Component: Sink_P

Sink_P can be defined as a source(where fluids are from) or sink(where fluid are going to).

Connectors:

• port: port of sink

Arguments:

• p: [Pa] The pressure of sink, default: 101325 (standard atmospheric pressure)

Source_P(; name, D, z, ρ, p, K_inlet)

Component: Source_P(source with inlet pressure losses)

Parameters:

• D: [m] Diameter of pipe
• K_inlet: Local resistance loss coefficient of Inlet port, default: 0.5

Connectors:

• port: port of source

Arguments:

• z: [m] The height of source
• ρ: [m³/kg] The density of fluid
• p: [Pa] The pressure of source, default: 101325 (standard atmospheric pressure)

_NodeEnergy(node, D, ρ) -> Any

To get the energy at the port.

The governing equation of incompressible pipe network is Bernoulli Equation:

\[\frac{p}{\rho g} +\frac{v^{2}}{2g} + z=\mathrm{constant}\]

In volume flow form:

\[\frac{p}{\rho g} +\frac{8q^{2}}{\pi^2D^4g} + z=\mathrm{constant}\]

• D: [m] Diameter of pipe
• ρ: [`m³/kg] The density of fluid passing the port

_h_f(node, f, L, D) -> Any

To get the loss of resistance along the pipe(between two ports).

In volume flow form:

\[h_f = f\frac{L}{D} \frac{8q^{2}}{\pi^2D^4g}\]

_h_m(node, K, D) -> Any

To get the local resistance loss the components.

In volume flow form:

\[h_m = K \frac{8q^{2}}{\pi^2D^4g}\]