Currents in pipelines

Liquid flow in pipelines or closed channels is one of the three flow models of hydrodynamics (in addition to flows in open channels and seepage flows ) and is also referred to as pipe hydraulics .

Basics

The term encompasses the aspects of the flow processes in fully filled pipelines , i.e. systems in which the liquid completely fills the pipe (in technical applications) or channel bed (in hydrology). Currents in partially filled pipelines, canals, rivers etc. are currents in open channels .

Essential properties for describing a pipe flow are the volume flow or the velocity profile and the pipe friction coefficient for calculating the pressure drop. In the case of a laminar flow in a circular pipe, the volume flow and the velocity profile as a function of the radius of the pipe can be described with the Hagen-Poiseuille law . The dependence of the flow velocity with a changing pipe cross-section is known as the Venturi effect .

Examples of such flow forms in pipeline construction are :

• Water distribution systems
• Sewer systems
• irrigation
• Plant construction
• Pressure tunnel

In hydrology ( limnology ):

• Phreatic caves
• larger aquifers (fissures)
• Artesian water situations

Stationary and unsteady currents

One speaks of stationary conditions when the flow conditions (e.g. flow pressure) at one point in the pipeline do not change over time. Such a simplifying assumption is sufficient for many hydraulic tasks in pipelines. Such systems are calculated by applying Bernoulli's energy equation and knowing z. B. the behavior of pumps (see z. B. centrifugal pump ) and containers.

Unsteady conditions always occur when changes over time play a role. A practical example is the pressure surge when a valve suddenly opens or closes . Significant dynamic forces (impacts) occur. This can be observed, for example, with water hoses or sometimes heard in domestic water pipes. This can damage lines and pipe supports. This is of particular importance in the operation of hydropower plants, especially with great heads. The pressure fluctuations that occur when turbines are switched on and off or gate valves are opened and closed are alleviated by so-called water locks (equalization basins) or by slow movement (opening or closing) of the shut-off devices.

Bernoulli's equation for unsteady flows of incompressible frictionless fluids reads:

${\displaystyle {\frac {c_{1}^{2}}{2}}+{\frac {p_{1}}{\rho }}+gz_{1}={\frac {c_{2}^{2}}{2}}+{\frac {p_{2}}{\rho }}+gz_{2}+\int _{1}^{2}{\frac {dc}{dt}}\,ds}$

Especially for steady-state flows (e.g. through a rigid pipe) and taking flow losses into account, the following results:

${\displaystyle {\frac {c_{1}^{2}}{2}}+{\frac {p_{1}}{\rho }}+gz_{1}={\frac {c_{2}^{2}}{2}}+{\frac {p_{2}}{\rho }}+gz_{2}+{\frac {dc_{n}}{dt}}\int _{1}^{2}{\frac {A_{n}}{A(s)}}\,\mathrm {(} ds)+{\frac {\Delta p_{V1-2}}{\rho }}}$

Is in here

${\displaystyle c}$ the speed of the fluid,

${\displaystyle g}$the acceleration due to gravity ,

${\displaystyle p}$the pressure (absolute),

${\displaystyle \rho }$(rho) the density of the medium,

${\displaystyle z}$ the height above / below a reference plane with the same geodetic height

${\displaystyle A}$ the cross-sectional area of ​​the stream filament,

${\displaystyle s}$ the path coordinate,

${\displaystyle \Delta p_{V1-2}}$the pressure loss between points 1 and 2

Index 1 = one point of the stream filament upstream

Index 2 = a point of the stream filament downstream

Index n = any point on the stream between 1 and 2

For the practical calculation of pipe flows and the associated pressure losses, pressure loss coefficients and pipe friction coefficients are used.

Network forms

The simplest network form is the connection from a feed point (e.g. pump or tank) to a consumer. When such a system branches out to several consumers, a tree-shaped network is created. Such networks can be calculated comparatively easily, but have no security in the event of failure of partial strings and under certain circumstances lead to unequal pressure distributions.

So-called ring-shaped or meshed networks connect the feed point (s) and the consumer (s) through several lines. As a result, a more even pressure distribution and a higher security of supply can be achieved. The meshing of originally tree-shaped networks may reduce supply bottlenecks. It is possible to feed into the network at several points. However, such systems are more complicated to calculate (e.g. using the finite element method or the Cross method , which can also be used in structural engineering to calculate frames).

Design and dimensioning

The calculation of the pressure losses in pipelines due to pipe friction and due to individual resistances must be carried out as incompressible or compressible flow, depending on the medium. Very detailed algorithms exist, for example, for sections and small networks for self-programming.

Individual evidence

1. ↑ Equation (4.3-1) In: H. Schade, E. Kunz: Fluid Mechanism . 3. Edition. Walter de Gruyter, Berlin 2007, ISBN 978-3-11-018972-8 .
2. ↑ Bernd Glück: Hydrodynamic and gas-dynamic pipe flow, pressure losses. Pressure drop algorithms for programming