This post comes from teaching on the new Integrated Engineering Programme at University College London.

First year undergraduate students from computer science, civil & environmental, mechanical and biomedical engineering had to work together to solve a problem and design a prototype - in this case a hydro-electric power plant. Each design was different which meant there was no "right answer" and teaching staff could not say at a glance whether a number was "right".

## Checking your own work

Here are some of the checks you can do for yourself:

**Units:**"my formulae are right but my numbers seem wrong"…have you used the correct units?**Benchmarking:**"I have some numbers but are they realistic?" Can you compare your scheme to real schemes? What sort of heights, diameters, power outputs sound realistic?**What if…:**"other groups have different numbers/my Matlab model is different from my hydraulics calcs?!"…. Can you see why the numbers are different? What if you changed each parameter - what changes?**Real life:**"I have fallen off the Moody diagram, what’s gone wrong?!" In reality, if you have a very long pipe (200m), a smallish pipe diameter (1.5m) and a very smooth pipe (steel), a) the flow will be so fast and turbulent that you will lose a lot of energy and b) it will be REALLY expensive. What materials would you use for a massive diameter long pipe in real life and how would this affect your theoretical calculations?

## Making a scale model of a hydro-electric power plant

**Scaling:** "our scale model is 10 times smaller so we divided everything by 10, is that ok?" This is ok for an architectural model - you just make every piece 10 times smaller to get a complete building that is 10 times smaller. This isn't ok for a model that involves fluids because the things that are important in the way fluids behave become more or less important at different scales. You can understand this intuitively by looking at old-school special effects like this clip from Jason and the Argonauts (1963). Why does this look weird?

**Scaling up instead of down:** "we scaled up from the experiment to the full scale: is this ok?"... Some groups did not have the numbers they wanted from other engineering groups so they scaled up from their experimental model to a full scale version. Mathematically, your equations may be correct but in engineering terms this is not quite right because:

- Designing an efficient and cost effective hydroelectric power plant boils down to specification of an optimal turbine.
- Turbine performance is very sensitive to many factors like Q (flow rate), N (rotational speed), D (rotor diameter), intake dimensions and other important variables.
- Design has to start from a full scale system with optimal turbine performance. If you start from the small scale system, you are not designing to optimize anything: you took what you had and built something that would fit. You can work out flow parameters and scale them up and you will end up with a Q, N and D for a full scale version.
- If you hand these over to a turbine manufacturer, you are forcing the manufacturer to design a “random” turbine that has not been designed for the best performance of the full scale. You may even ask for a turbine that is impossible to manufacture or very inefficient because to make one with your N and D that works with your flow rates might be 10% efficient or too big to install….