# Pipe¶

## Create Function¶

create_pipe(net, from_junction, to_junction, std_type, length_km, k_mm=1, loss_coefficient=0, sections=1, alpha_w_per_m2k=0.0, text_k=293, qext_w=0.0, name=None, index=None, geodata=None, in_service=True, type='pipe', **kwargs)

Creates a pipe element in net[“pipe”] from pipe parameters.

Parameters
• net (pandapipesNet) – The net for which this pipe should be created

• from_junction (int) – ID of the junction on one side which the pipe will be connected to

• to_junction (int) – ID of the junction on the other side which the pipe will be connected to

• std_type (str) – Name of standard type

• length_km (float) – Length of the pipe in [km]

• k_mm (float, default 1) – Pipe roughness in [mm]

• loss_coefficient (float, default 0) – An additional pressure loss coefficient, introduced by e.g. bends

• sections (int, default 1) – The number of internal pipe sections. Important for gas and temperature calculations, where variables are dependent on pipe length.

• alpha_w_per_m2k (float, default 0) – Heat transfer coefficient in [W/(m^2*K)]

• name (str, default None) – A name tag for this pipe

• index (int, default None) – Force a specified ID if it is available. If None, the index one higher than the highest already existing index is selected.

• geodata (array, shape = (,2L), default None) – The coordinates of the pipe. The first row should be the coordinates of junction a and the last should be the coordinates of junction b. The points in the middle represent the bending points of the pipe.

• in_service (bool, default True) – True for in service, False for out of service

• type (str, default "pipe") – An identifier for special types of pipes (e.g. below or above ground)

• qext_w (float, default 0) – External heat feed-in to the pipe in [W]

• text_k (float, default 293) – Ambient temperature of pipe in [K]

• kwargs – Additional keyword arguments will be added as further columns to the net[“pipe”] table

Returns

index - The unique ID of the created element

Return type

int

Example
>>> create_pipe(net,from_junction=0,to_junction=1,std_type='315_PE_80_SDR_17',length_km=1)


## Component Table Data¶

net.pipe

 Parameter Datatype Value Range Explanation name string Name of the pipe from_junction integer $$>$$ 0 Index of junction at which the pipe starts to_junction integer $$>$$ 0 Index of junction at which the pipe ends std_type string A selected std type for the pipe length_km float $$>$$ 0 Length of the pipe [km] diameter_m float $$\gt$$ 0 Inner diameter of the pipe [m] k_mm float $$\gt$$ 0 Pipe roughness [mm] loss_coefficient float $$\geq$$ 0 An additional loss coefficient which might account for e.g. bends alpha_w_per_m2k float $$\geq$$ 0 Heat transfer coefficient [W/(m^2K)] qext_w float $$>$$ 0 An additional heat flow entering or leaving the pipe [W] text_k float $$>$$ 0 The ambient temperature used for calculating heat losses [K] sections integer $$\geq$$ 1 The number of internal pipe sections in_service boolean True / False Specifies if the line is in service. type string Type variable to classify junctions

net.pipe_geodata

 Parameter Datatype Explanation coords list List of (x,y) tuples that mark the inflexion points of the pipe

## Physical Model¶

For both the hydraulic and temperature calculation mode, the main function of the pipe element is to calculate pressure and heat losses, respectively.

### Hydraulic mode¶

The following image shows the implemented pipe model with relevant quantities of the hydraulic calculations:

Losses are calculated in different ways for incompressible and compressible media. Please also note that for an incompressible fluid, the velocity along the pipe is constant. This is not the case for compressible fluids.

#### Incompressible media¶

The pressure loss for incompressible media is calculated according to the following formula:

\begin{align*} p_\text{loss} &= \rho \cdot g \cdot \Delta h - \frac{\rho \cdot \lambda(v) \cdot l \cdot v^2}{ 2 \cdot d} - \zeta \cdot \frac{\rho \cdot v^2}{2} \\ \end{align*}

#### Compressible media¶

For compressible media, the density is expressed with respect to a reference state using the law of ideal gases:

\begin{align*} \rho &= \frac{\rho_N \cdot p \cdot T_N}{T \cdot p_N} \\ \end{align*}

As reference state variables, the normal temperature and pressure are used by pandapipes. With this relation, also the pipe velocity can be expressed using reference values:

\begin{align*} v &= \frac{T \cdot p_N}{p \cdot T_N} \cdot v_N \\ \end{align*}

Inserting the equations from above in the differential equation for describing the pressure drop along a pipe results in the following formula, which is used by pandapipes to calculate the pressure drop for compressible media:

\begin{align*} \text{d}p_\text{loss} &= -\lambda(v) \cdot \frac{\rho_N \cdot v_N^2}{2 \cdot d}\cdot \frac{p_N}{p} \cdot \frac{T}{T_N} \cdot K \cdot \text{d}l \\ \end{align*}

The equation for pressure drop also introduces a variable K. This is the compressibility factor, which is used to account for real gas behaviour.

After calculating the gas network, the pressure losses and velocities for the reference state are known. During post processing, the reference velocities are recalculated according to

\begin{align*} v &= \frac{T \cdot p_N}{p \cdot T_N} \cdot v_N \\ \end{align*}

The equations from above were implemented following [Eberhard1990].

Because the velocity of a compressible fluid changes along the pipe axis, it is possible to split a pipe into several sections, increasing the internal resolution. The parameter sections is used to increase the amount of internal pipe sections.

#### Friction models¶

Two friction models are used to calculate the velocity dependent friction factor:

• Prandtl-Colebrook

Nikuradse is chosen by default. In this case, the friction factor is calculated by:

\begin{align*} \lambda &= \frac{64}{Re} + \frac{1}{(-2 \cdot \log (\frac{k}{3.71 \cdot d}))^2}\\ \end{align*}

Note that in literature, Nikuradse is known as a model for turbulent flows. In pandapipes, the formula for the Nikuradse model is also applied for laminar flow.

If Prandtl-Colebrook is selected, the friction factor is calculated iteratively according to

\begin{align*} \frac{1}{\sqrt{\lambda}} &= -2 \cdot \log (\frac{2.51}{Re \cdot \sqrt{\lambda}} + \frac{k}{3.71 \cdot d})\\ \end{align*}

Equations for pressure losses due to friction were taken from [Eberhard1990] and [Cerbe.2008].

### Heat transfer mode¶

The following image shows the implemented pipe model with relevant quantities of the heat transfer calculations:

For heat transfer, two effects are considered by the pipe element:

• The heat loss due to a temperature difference between the pipe medium and the surrounding temperature is calculated

• An additional heat in- or outflow can be specified by the user

The heat losses are described by

\begin{align*} Q_\text{loss} &= \alpha \cdot (T - T_\text{ext})\\ \end{align*}

according to [Baehr2010]. If the default value of the sections parameter is changed, the resolution of temperature values can be increased.

## Result Table Data¶

For incompressible media:

net.res_pipe

 Parameter Datatype Explanation v_mean_m_per_s float The mean pipe velocity [m/s] p_from_bar float Pressure at “from”-junction [bar] p_to_bar float Pressure at “to”-junction [bar] t_from_k float Temperature at “from”-junction [K] t_to_k float Temperature at “to”-junction [K] mdot_from_kg_per_s float Mass flow into pipe [kg/s] mdot_to_kg_per_s float Mass flow out of pipe [kg/s] vdot_norm_m3_per_s float Norm volume flow [m^3/s] reynolds float Average Reynolds number lambda float Average pipe friction factor

For compressible media:

net.res_pipe

 Parameter Datatype Explanation v_from_m_per_s float The velocity at the pipe entry [m/s] v_to_m_per_s float The velocity at the pipe exit [m/s] v_mean_m_per_s float The mean pipe velocity [m/s] p_from_bar float Pressure at “from”-junction [bar] p_to_bar float Pressure at “to”-junction [bar] t_from_k float Temperature at “from”-junction [K] t_to_k float Temperature at “to”-junction [K] mdot_from_kg_per_s float Mass flow into pipe [kg/s] mdot_to_kg_per_s float Mass flow out of pipe [kg/s] vdot_norm_m3_per_s float Norm volume flow [m^3/s] reynolds float Average Reynolds number lambda float Average pipe friction factor normfactor_from float Normfactor to calculate real gas velocity at “from”-junction (only for gas flows) normfactor_to float Normfactor to calculate real gas velocity at “to”-junction (only for gas flows)