Piping

The connection between difference of pressure Δp und mass flow m· can be described by the Darcy-Weisbach flow law (see [6]):

The pipe constant r is given by

The entire decrease of pressure between pipe entry and pipe exits is made up of the decrease of pressure of a straight pipe, which is described with the help of the friction in pipe number ξR and the decrease of pressure by additional resistances such as elbows, narrowings and branches. These additional resistances are described by the coefficients of drag ξ. These are empirically determined values which can be inferred from appropriate tables (e.g. [2]) The friction in pipe number ξR depends on the flow form present in the pipe and is calculated with laminar current (the flow characterizing Reynolds number Re is smaller than 2300) according to Gl. 20.3 (Hagen-Poiseuille):

in transition and turbulent flow range according to the formula of Prandtl-Colebrook:

The unsteadiness of the flow equation with Re =^ 2300 (the transition between laminar and turbulent or between Gl. 20.3 and Gl. 20.4) is eliminated by linear interpolation within the range Re = 2000 to Re = 3000 in accordance with:

The miscalculation arising with it is negligible for total hydraulics.

Pumps

Since in remote heating and water nets speed adjusted centrifugal pumps are predominantly used as pressure increase or circulation pumps, the modelling is limited to this pump type.

The pressure increase of a centrifugal pump is a function of the pumped mass flow m· and the number of revolutions n. The following picture shows the set of characteristics of a speed adjusted centrifugal pump.

Operational ranges and efficiencies of a centrifugal pump at different numbers of revolutions

It is appropriate to represent the characteristic of a centrifugal pump at a given number of revolutions n as a polynomial of 2nd order:

The polynomial coefficients ai depend on the speed of revolution. Using the affinity law, according to [4], the dependence of the polynomial coefficients on the number of revolutions can be described by Gl. 20.7:

Here n0 is a given number of revolutions for which the polynomial coefficients must be known (usually the rated speed of the pump).

Valves

The following designs are modelled as control valves in remote heating networks:

• Valves
• Flaps

The pressure loss of a valve or a flap can be determined according to the following calculation equation:

The flow coefficient kV can be calculated for valves with the same percent characteristic according to Gl. 20.9, with linear characteristic according to Gl. 20.10 as a function of the valve hub:

Here kVS is the intended flow coefficient of a series with nominal hub, kV0 the intersection of the characteristic with the Y-axis (only with linear characteristic) and hub the relationship from the adjusted hub to the nominal hub [14].

For flaps the change of the flow coefficient kv must be given as a function of the flap position by a number of flow coefficients for different flap positions, since so far no description of the dependence of the flow coefficient on the flap position exists.