# Are my numbers right?!

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".

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….

# Getting help with your PhD from other people

It can be useful to share work and ask for feedback from researchers in your field who are not part of your supervision team. But it can also be unhelpful if the advice or format of advice is different from the stuff your official supervisor normally provides.

These 'ground rules' are developed from my experience of PhD supervision, as a student and as an occasional supervisor, and are designed to make the process of occasional supervision as positive and helpful as possible.

What you can expect from me

• I will read 10-20,000 words of an upgrade report, draft paper or substantially developed thesis chapter
• I will provide a 1 hour face to face supervision
• I will provide one page of written feedback including practical tips or references, if needed
• I will provide, on request, a marked up copy of your written work but this is optional depending on how you like to receive feedback
• I will offer a further 1 hour supervision to follow up on questions, if needed
• I will thank you for inviting me to review your work.

What I expect from you

• You will book a time and place to meet via Outlook
• You will send your written work 7 days before the meeting
• You will prepare for the supervision by considering a number of questions in advance (see below)
• You will give me feedback at the end of the supervision on what was useful or not useful and how this supervision fits in (or not) with other reviews you have had on this work
• You will have the option to meet again especially if you feel, during or after the supervision, that something was not clear, not complete or not reasonable

Format of the supervision

The aim of this supervision is for you, as a PhD student, to develop your ideas with an independent researcher and have a chance to 'think out loud' about your work in a non-judgemental setting. My role is to set out a series of questions based on my reading of your work that help me to talk to you about your research. To do this, I would like to start the supervision with the following questions which I'd like you to think about in advance.

• Where I am: my background, how I approached your work, what I am interested in and how I like to learn/teach and give/get feedback
• Where you are: your background, how far along you feel you are in your PhD and how you like to learn/teach and give/get feedback
• What you would like from the supervision i.e. to talk about a specific problem or struggle with your research, to chat generally about producing the PhD, to respond to my questions, to hear my feedback and discuss it, to go through the document page by page ...