Why we need Dimensional Analysis, Part 1, Design optimisations in fluid dynamics

This talk is on why we need dimensional analysis in fluid dynamics. In fluid dynamics, we see the force/moment and pressure are mostly given in forms of force/moment coefficient, pressure coefficient and many other non-dimensional parameters/groups, other than the force/moment, pressure... directly. Why we are doing this? the answer for this is a result of the dimensional analysis, a powerful tool in fluid dynamics.
As we all know it well in fluid dynamics, the main attention is on the solution of the fluid dynamics equations, such as N-S equation, potential flow equation..., in reality this is only a very important tool (also the experimental fluid dynamics). however, when comes to a practical problem of fluid dynamics, we wish to examine the dependencies of the forces/moments on the environmental parameters, such as, on the incoming flow velocity, the size of the structure, the fluid viscosity and density etc. If we employ the direct method to examine the changes of the individual parameter, we would have the problems of too many scenarios from which we obtain the required data (numerically or experimentally) and too much data for which how we can find the dependencies of the force on these parameters. Dimensional analysis is a powerful tool for simplifying the fluid dynamic problems.
In this talk, following contents will be discussed
- Basic solution approaches in fluid dynamics
- Introduction of the intermediate physical parameters in theoretical and experimental fluid dynamics
- Calculation of force/moment acting on the body
- The force dependence on the environmental parameters
- Difficulties in the direct method for optimisations