Second Derivation

The relation between the flow rate Q and the final height of a hypothetic second derivation, ending close to the Cardo Maximus, has been established (see Fig. 8.28). It is shown that if the derivation ends on the first floor of a building close to the Cardo Maximus, the flow rate in the derivation would be approximately 24 kg/s.

Therefore, the analysis of the second derivation demonstrates that, during the 6th century, it was technically possible to provide large amount of water to the part of the city located beyond the Cardo Maximus. This gives a new interesting element for the answer to the third historical questions about Apamea tackled in this chapter.

Regarding the transport of water, the technical design of this derivation is clearly not as good as the one of the first derivation. This observation is valid for each part of the derivation.

The energy loss in the room of visit in the second derivation is, at a same flow rate, more than twice the energy loss in the room of visit in the first derivation (Fig. 8.19). There is no shaping of the room walls, leading to the formation of a large vortex that consumes a lot of energy (Fig. 8.20).

At a same flow rate, the energy loss per unit length of the canalization in the second derivation is almost twice the energy loss per unit length of the canalization in the first derivation (Fig. 8.24). The vortex generated at the connection between basic pipes is mainly responsible for this difference (Fig. 8.22). In the first derivation, it is the shape given to the mortar that prevents the appearance of this vortex (Fig. 8.21).

At a same flow rate, the energy lost at the entrance of the second derivation is 15 times larger than the energy lost at the entrance of the first derivation. In the second derivation, the area of the section of the connection between the room of visit and the aqueduct is equal to 0.0048 m2, while in the first derivation it is equal to 0.019 m2. As it can be seen in Equation (8.3), the energy lost at the entrance of a derivation increases with an increasing velocity in the connection between the room of visit and the aqueduct, and therefore with a decreasing area of the section of this connection. The energy loss associated to the entrance in the second derivation is more than 10 percent of the total energy loss in the derivation.

Some words can be said about the decanter. The first question arising concerns the utility of this decanter. A possible answer is that it could have been placed there to eliminate solid particles produced by the erosion of the walls in the room of visit. Indeed, no water repellent coating has been found in this room. It could have been omitted in the reconstruction of this room later, after its destruction by an earthquake.

The second question arising concerns the efficiency of this decanter. As it can be seen in Fig. 8.27, the main part of the flow shortcuts the decanter, with a residence time of approximately 0.6 s. Hence, the decantation of solid particles in suspension is unlikely to take place in the decanter, only larger particles, sedimented in the bottom of the canalization and drifted by the flow, can be collected in the decanter.

When D2 = 4 m, Q/Qmax is equal to 0.16. Therefore, in the total absence of energy loss in the entire derivation the flow rate would be approximately six times larger than the real flow rate.

It can be computed that a similar derivation built with modern techniques and materials would have an efficiency of 0.45. To calculate this value, several assumptions are realized. It is first assumed that the modern derivation does not include a room of visit, the canalization is directly connected to the aqueduct. It is further assumed that the canalization is made of plastic pipes having a diameter of 14 centimetres. It is finally assumed that no energy loss occurs at the connection between the pipes. The data and correlations needed to compute the efficiency of this modern derivation have been found in (Lencastre, 1995).