First Derivation

This first derivation carried a water flow rate of 25 kg/s towards a cistern that took approximately one hour to be filled with 66 m3 of water.

Regarding the transport of water, each part of the derivation has good characteristics.

The shape given to the mortar, ensuring the fitting of the basic pipes of the canalization into each other, prevents the appearance of vortices (see Figs. 8.21 And 8.22), and hence decreases the energy loss in the canalizations. The glazing of the pipes ensures the walls to be hydrodynamically smooth walls (at least in the absence of calcareous deposit). The energy drop coefficient CC1 (Equation (8.10)) is equal to 0.26 m-1 when there is no calcareous deposit.

It can be pointed out once again that the energy loss associated with the 90° bend is negligible in comparison with energy losses in other parts of the derivation. Thus, it has almost no influence on the flow rate in the derivation. The engineering technique of this kind of bends had not to be improved.

No vortex is generated in the room of visit. The flow is conducted from the entrance to the exit by the room walls. However, a stagnant zone is observed in the room (see Fig. 8.18). Such a stagnant zone consumes a lot of energy and indeed, the major part of the energy loss in the derivation is located in this room.

Finally, the connection between the aqueduct and the room of visit has a large cross-section. Hence, the energy loss associated with this entrance is negligible (see Equation (8.3)), compared to energy losses in other parts of the derivation.

Q/Qmax is close to 0.3. Therefore, in the total absence of energy loss in the entire derivation (physically impossible as energy is needed to sustain the turbulent flow of the water) the cistern would take approximately 20 minutes to be filled instead of 1 hour.

It can be computed that a similar derivation built with modern techniques and materials would have an efficiency of 0.72. To calculate this value, several assumptions have been made. 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 16 cm. It is also assumed that no energy loss occurs at the connection between the pipes. Finally it is assumed that the 90° bend is constructed following actual rules. The data and correlations needed to compute the efficiency of this modern derivation have been found in (Lencastre 1995).

In this modern derivation, the energy drop coefficient CC1 of the flow in 1 m of the canalization is equal to 0.07 m-1. It has been calculated using the Colebrook-White formula (Lencastre, 1995). At a same flow rate, the energy loss in the modern derivation would be three times smaller than this energy loss in the roman derivation.

It can finally be pointed out that the position of the cistern entrance allows a natural regulation of the incoming flow rate. As long as the level of water in the cistern is below the end of the canalization, the incoming flow rate is constant in time. When the level of water in the cistern is above the end of the canalization, the incoming flow rate is continuously decreased in time until a zero flow rate is reached.

This analysis clearly demonstrates that the first derivation, built in the 6th century, is a very good work, reflecting an excellent technical knowledge of water supply, until the end of antiquity. The Byzantine city was not only using the Roman aqueduct but was also able to rebuild a new efficient water supply system. Therefore, the analysis of the efficiency of this first derivation provides a new interesting element regarding the answer to the second open historical question about Apamea tackled in this chapter.