Pipe flow
Liquid flow in pipes or closed clotting is called (besides flows in open channels and seepage ) and is also known as hydraulic pipe one of the three flow models of hydrodynamics.
Basics
The term includes the aspects of flow phenomena in full pipes, ie systems in which the liquid pipe ( for industrial applications ) or river bed fills ( in Hydrology ) in its entirety. Flows in partially filled pipelines, canals, rivers etc. are flows in open channels.
Essential characteristics for the description of a pipe flow are the volume flow and the velocity profile and the pipe friction factor for the calculation of the pressure drop. In the case of laminar flow in a circular pipe can be the volume flow and the velocity profile as a function of the radius of the tube described by the Hagen- Poiseuille. The dependence of the flow rate with variable pipe cross-section is known as the Venturi effect.
Examples of such flow patterns are in the pipeline:
- Water distribution systems
- Sewers
- Irrigation
- Plant
- Pressure tunnel
In hydrology ( Limnology ):
- Phreatic caves
- Major aquifers ( fissures )
- Artesian water situations
Steady and unsteady flows
From stationary conditions is when the flow conditions ( eg flow pressure ) at a point of the pipeline in time do not change. Such a simplifying assumption is sufficient for many tasks in the hydraulic piping. The calculation of such systems is performed by application of Bernoulli's equation and energy knowledge of the behavior of the pump, for example ( see, e.g., centrifugal pump ), and a container.
Unsteady conditions occur whenever temporal changes play a role. A practical example is the sudden increase in pressure when opening or closing a valve. In this case, considerable dynamic forces (beats ). You can see this for example in water hoses or hear in house water pipes sometimes. This damage to pipes and pipe fittings may arise. Has special significance this in the operation of hydroelectric power plants, particularly with large heads. The pressure fluctuations occurring during the switching on and off of turbines or opening and closing of valves are doing by so-called water towers (which are compensating basin ) or mitigated by slow processes ( opening or closing) of the shut-off devices.
The Bernoulli equation is for unsteady flows of incompressible inviscid fluids:
Especially for directional steady flows (eg by a rigid line ) and taking into account flow losses is the result:
Herein is
For the practical calculation of pipe flows and the associated pressure drop pressure loss coefficients and pipe friction coefficients are used.
Web forms
The simplest form is the network connection from a feed point (e.g., a pump or tank) to a consumer. In branching of such a system to several consumers creates a tree -like network. Such networks can be relatively easily calculated, but have no collateral in case of failure of partial strands and potentially result in unequal pressure distributions.
So-called ring or meshed networks connect the feed point ( s) and / consumers through multiple lines. This allows a more even distribution of pressure and a higher degree of security can be achieved. By meshing originally a tree-like networks on supply may be reduced under certain circumstances. It is possible, that is injected at multiple points in the network. Such systems, however, are more complicated to calculate (eg, using the finite element method or the method according to Cross, which can also be used in the structural analysis for the calculation of frame).
Design and dimensioning
The calculation of pressure losses in pipes due to pipe friction, and by individual resistors must be made depending on the medium as incompressible or compressible flow as. Very detailed algorithms exist for example .. for parts and for small networks for programming by