The secondary headlosses due to friction through fittings are included in analysis. Fittings most commonly included in pipelines are bends and tees. IRRICAD calculates an approximate equivalent length of pipe to represent the headloss through these fittings. The friction loss through a fitting is a function of diameter, i.e.,
hf = fn(d)
In theory, the form of this equation in terms of an equivalent length of pipe will be:-
L=Kdx where K is a constant and x an index.
The value for x can be derived from any pipe friction loss formula and can range from 0.75 to 1.1, depending on which formula is used.
In practice, we have found experimentally that x is close to 1.0. Bearing in mind that the Hazen-Williams pipe friction loss formula is used for pipe friction loss calculations in analysis (which would result in x – 0.87) and the fact that in practice x is close to 1.0, an index of 0.94 has been chosen as a suitable index.
i.e. L = Kd0.94
L – the extra pipe length in metres
D – pipe diameter in metres.
The value of K depends on:
- the direction of flow through the fitting
- the geometry of the fitting
In IRRICAD, in order for secondary losses to be included in analysis, the calculated equivalent lengths are added in to the system before analysis proceeds. No allowance is made for flow direction through a junction as direction of flow is unknown at the stage equivalent lengths are calculated. However, by adding an equivalent length of pipe to the pipe segment the effect of flow is inherently taken into account. Although it is possible to include the effects of actual fitting geometry and flow direction a pre-analysis which included determination of flow without secondary losses, a full fitting selection, and the K values entered in the database for each fitting would be necessary.
Therefore, the conservative values IRRICAD uses for K based on the number of pipes at a junction are:-
1) 35.55 for a 2 pipe junction (bend or change in diameter).
2) 45.46 for a 3 pipe junction (Tee).
3) 45.46*2 for a 4 pipe junction (2 Tees).
The equivalent length calculated is then proportioned according to the number of pipe segments meeting at the junction. For example, if 3 pipes meet at a particular junction, one third of the equivalent length is added to each pipe segment, i.e., for a 50mm three pipe junction each pipe would have 45.46/3 * 0.050.94 = 0.907 metres of equivalent length added.