Similitude and Dimensional Analysis

1
Similitude and Dimensional Analysis
2
Definition and uses of Similitude

• Usually we find it impossible to determine all
  essential facts for a given fluid flow by pure
  theory alone, and so we must often depend on
  experimental investigations. However, we can
  greatly reduce the number of tests needed by
  systematically using dimensional analysis and the
  laws of similitude or similarity.
• For these enable us to apply test data to
  other cases than those observed.

3
Definition and uses of Similitude

• The similarity laws enable us to experiment
  with a convenient fluid such as water or air, for
  example, and then apply the results to a fluid
  that is less convenient to work with, such as
  hydrogen, stream, or oil. Also in both hydraulics
  and aeronautics , we can obtain valuable results
  at a minimum cost from tests made with
  small-scale models of the full size apparatus.
  The laws of similitude enable us to predict the
  performance of the prototype, which means the
  full-size device, from tests made with the model.

4
Definition and uses of Similitude

• A few examples of where we have used models
  are ships in towing basins, airplanes in wind
  tunnels, hydraulic turbines, spillways of dams,
  river channels, and the study of such phenomena
  as the action of waves on beaches, soil erosion
  and the transport of sediment.

5
Definition and uses of Similitude

6
Three Basic Laws of Similitude

7
Three Basic Laws of Similitude