4.15. Infinite Pipe¶

4.15.1. INFPIP (class)¶

../_images/image511.png — Fig. 4.15.1 Infinite pipe¶

Supplier type

type label	description	active
Infinit Pipe (H-bound)	Infinite pipe with initial pressure head	No
Infinit Pipe (Q-bound)	Infinite pipe with initial discharge	No

4.15.1.1. Mathematical model¶

The infinite pipe model is used in case of detailed analyses of e.g. pumping stations. In such cases the internal piping and check valves are modelled in detail leading to a small time step. As a consequence the long transportation line departing from the station would get far too many elements for the computation to be feasible anymore. As long as the simulation time is shorter than 2L/c no reflection other than line packing will be present. With the infinite pipe component the user can apply a reflection-free pipe boundary condition. The initial hydraulic gradient in the infinite pipe is determined by:

(4.15.1)¶\[\frac{\Delta H}{\Delta x}=\frac{\lambda}{D} \frac{v^{2}}{2 g}\]

where:

Variable	Description	Units
\(\Delta H\)	Head difference	m
\(\lambda\)	Darcy-Weisbach friction factor	-
\(D\)	Internal pipe diameter	m
\(v\)	Flow velocity	m/s
\(g\)	Gravitational acceleration	m/s²

The length is determined by the water hammer wave velocity c and the computational time step with . For further explanation of the input parameters see “Definitions” on page 147. The initial flow or head results from the steady state balance.

Each time step the equation specified by the infinite pipe is the standard C^- water hammer equation (see Conceptual Model:

(4.15.2)¶\[\left(H-H_{i}\right)-R\left(Q-Q_{i}\right)+S Q_{i}\left|Q_{i}\right|=0\]

in which:

Variable	Description	Units
H	unknown head at node	m
Q	unknown discharge into pipe	m³/s
H_i	head in pipe at previous time step	m
Q_i	discharge in pipe at previous time step	m³/s
R	Inertance	s/m²
S	Resistance	s²/m⁵

The values of Hi and Qi are computed together with two extra internal points in the pipe. At each internal point the C⁺ and C^- water hammer equations are solved, except the last point, where only the C^- equation is available and the second equation is constituted by time extrapolation.

Tip:

INFPIP may be used for flows from the system into the infinite pipe (Q > 0) or for flows from the infinite pipe into the system (Q < 0).

4.15.2. Infinit Pipe (H-bound)¶

4.15.2.1. Hydraulic specifications¶

Description	input	unit	range	remarks
inner diameter	real	[m]	(0-5)
friction factor	real	[-]	(0-1)
wall thickness	real	[m]	(0-0.50)	only in transient mode
Young’s modulus	real	[N/m²]	(0-10¹⁴)	only in transient mode
initial head	real	[m]

See also “Mathematical model” (Section 4.15.1.1) and “PIPE” (Section 4.18).

4.15.2.2. Component specific output¶

Delivery rate [m³/s]

4.15.2.3. H-actions¶

None

4.15.2.4. Component messages¶

None

4.15.3. Infinit Pipe (Q-bound)¶

4.15.3.1. Hydraulic specifications¶

Description	input	unit	range	remarks
inner diameter	real	[m]	(0-5)
friction factor	real	[-]	(0-1)
wall thickness	real	[m]	(0-0.50)	only in transient mode
Young’s modulus	real	[N/m²]	(0-10¹⁴)	only in transient mode
initial discharge	real	[m³/s]

See also “Mathematical model” (Section 4.15.1.1).

4.15.3.2. Component specific output¶

Delivery rate [m³/s]

4.15.3.3. H-actions¶

None

4.15.3.4. Component messages¶

None