Chapter 7 Circuits with Hydraulic Machines: Pumps and Turbines In some hydraulic circuits, power is exchanged between the current and the machines. Pumps supply energy to the current and are called energy absorption devices, and are inserted in order to increase the head; turbines subtract energy from the current, usually transferring it to an electric generator, and are called energy production devices. The energy grade line has a jump across the machine. The characteristics of the machine are suggested by the general characteristics of the plant and the design is optimal, with the aim of minimizing costs and maximizing efficiency. In the energy balance, the pump increases the head according to a performance curve (or characteristic curve), a function that relates head, flow rate, speed of rota- tion, with an efficiency closely linked to the mechanical design of the components. The operating point is obtained as the intersection between the system curve and the performance curve: the system curve is representative of the head required to modify the static pressure, the dynamic pressure, the elevation of the fluid and to overcome the losses. However, for simplicity it is often assumed, in the exercises, that the pump is ideal, with a constant efficiency. The turbines reduce the head and generate energy according to an efficiency curve, where the rotation rate is set according to the characteristics of the electric generator and the frequency of generated alternating current (50 Hz in Europe, 60 Hz in the USA). A distinction is made between the gross head, which is the difference in level between the free surface level of the upstream tank and the free surface level of the downstream channel (or lake, or tank); and the net head, which is the difference between the immediately upstream section energy grade line and the outlet section of the draught pipe (or, in some cases, the immediately downstream section energy grade line). The draft pipe is designed as a diffuser to reduce energy losses. The difference between the gross head and the neat head is due to energy losses in the external hydraulic circuit. This difference is a function of the characteristics of the C u and C pu , that are two integer numbers between 0 and 9, for example, the last and second-last digit of the registration number. © Springer Nature Switzerland AG 2021 S. Longo et al., Problems in Hydraulics and Fluid Mechanics, Springer Tracts in Civil Engineering, https://doi.org/10.1007/978-3-030-51387-0_7 245