Hydraulic Machines


This course introduces the working principles of fluid machines such as pumps and turbines. It’s aimed at developing an understanding, from a fluid-mechanics and thermodynamics point of view, how these devices work, performs and can be regulated.


By the end of the course students should have knowledge and understanding of:

- The mechanics of turbomachines: Euler equation,  velocity triangles and ideal efficiency.

- The concept of dynamic similarity and the use of dimensional analysis in the context of hydraulics machines.

- The physics of cavitation and its importance in the design and operation of systems involving pumps and turbines.

 - Selection of the type and estimation of main dimensions of a hydraulic machine.



By the end of the course students should be able to:

- Apply similarity concepts and dimensional analysis to hydraulics machines characteristics curves.

- Analyse problems involving the selection and performance of hydraulics machines.

- Apply the equations of motion and velocity triangles to the generality of turbomachines.

-  Integrate the above skills and solve practical engineering problems such as: pumping systems and power plants.



By the end of the course students should have gained intellectual, practical and transferable skills so that they are able to:

- Use the Buckingham-PI method of dimensional analysis.

- Conduct laboratory experiments and log data in organised way.

- Analyse laboratory data and report results in organised way.

- Use library and www as sources of useful information.

- Work effectively in a group.


General characterization





Responsible teacher

José Fernando de Almeida Dias, Luís Miguel Chagas da Costa Gil


Weekly - 4

Total - 62

Teaching language



Dinâmica dos fluidos I


Gil. L., Araújo, S. B. (1997-2013), Apontamentos de Máquinas Hidráulicas, F.C.T.-U.N.L.
Falcão, A. F. O. (1998), Mecânica dos Fluidos II (Turbomáquinas), AEIST, Lisboa.
Henshaw, T. L. (1987), Reciprocating Pumps, Van Nostrand Reinhold Company New York.
White, F. M. (1988), Fluid Mechanics (Turbomachinery), McGraw-Hill
Macintyre, A. J. (1997), Bombas e Instalações de Bombeamento , L.T.C
Gil, L (2013), Laboratório Virtual de Máquinas Hidráulicas

Teaching method

  • Lectures and problem-solving sessions.
  • Laboratory sessions.

Evaluation method

Método de Avaliação Contínua (Genérico)

2 mini testes + 1 trabalho laboratorial

Nota final - 0.4x(1ºT)+0.4x(2ºT)+0.2x(TL)

Nota minima na componente teórico prática (testes) de 9.0 valores

Frequência - Aprovação no trabalho laboratorial

Subject matter

Hydraulical Machines

1-Introduction to the hydraulical machines.

2-Hydraulical machines types: Turbines and pumps.

3-Fundamentals of turbomachine theory: momentum principle applied to flow through a rotor; thrust on the rotor; torque exerted on the rotor; Euler equation for turbomachines; velocity triangles. Axial reaction turbines. Radial reaction turbines (Francis). Pelton turbines. Kaplan and propeller turbines. Centrifugal pumps: impeller vanes design; diffuser design.

4-Dimensionless parameters and similarity laws applied to the design and selection of turbomachines.

5-Volumetric pumps: selection and dynamic characteristics.



Programs where the course is taught: